Aerosol Science for Industrial Hygienists

Aerosol Science for Industrial Hygienists

Related Titles

Books

B R A D E N and KOLSTAD Measuring the Demand for Environmental Quality M A S U A D A and T A K A H A S H I Aerosols, Proceedings of the Third International Aerosol Conference WILLIAMS and L O Y A L K A Aerosol Science: Theory and Practice Z A N N E T T I et al. Air Pollution

Journals

Journal of Aerosol Science Aerosol Science and Technology Annals of Occupational Hygiene Applied Occupational and Environmental Hygiene Atmospheric Environment Environmental Health and Pollution Control Occupational Health and Industrial Medicine Full details of all Elsevier Science publications and free specimen copies of any Elsevier Science journals are available on request from your nearest Elsevier office.

Aerosol Science f o r I n d u s t r i a9l H y "g l e n l "s t s JAMES H. VINCENT

Professor, Division of Environmental and Occupational Health, School of Public Health, University of Minnesota, Minneapolis, U.S.A

@ Pergamon

U.K.

Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, U.K.

U.S.A.

Elsevier Science Inc., 660 White Plains Road, Tarrytown, New York 10591-5153, U.S.A.

JAPAN

Elsevier Science Japan, Tsunashima Building Annex, 3-20-12 Yushima, Bunkyo-ku, Tokyo 113, Japan Copyright 9 1995 Elsevier Science Limited

All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical photocopying, recording or otherwise, without permission in writing from the publisher First edition 1995

Library of Congress Cataloging in Publication Data Aerosol science for industrial hygienists/James H. Vincent. p. cm. Includes index. 1. Aerosols-Toxicology. 2. Indoor air pollution. 3. Industrial hygiene. I. Title. RA577.5.V56 1995 615.9' 02-dc20 95--4232

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library

ISBN 008 042029X

Printed and bound in Great Britain by Bookcraft, Bath

This book is dedicated, with love, to my mother Elvina Vincent

who celebrated her 87th birthday as I was putting the finishing touches to the work

This Page Intentionally Left Blank

Contents xiii

PREFACE Chapter 1.1 1.2 1.3 1.4

1. I N T R O D U C T I O N TO A E R O S O L S What is an aerosol? 'Good' versus 'bad' aerosols Workplace aerosols and occupational health Aerosols and gases

Chapter 2. T H E P R O P E R T I E S OF AIR AND GASES Introduction 2.1 Basic nature of gases 2.2 Pressure, volume and temperature Mean free path Diffusion Viscosity Gas mixtures Phase transitions: solids, liquids and gases Elementary fluid mechanics 2.3 Basic physics Streamlines Boundary layers Similarity Potential flow Stagnation Separation Turbulence

11 11 11 11 15 16 18 20 21 24 24 25 27 28 31 32 32 34

Chapter 3. P R O P E R T I E S OF A E R O S O L S 3.1 Aerosol generation in workplaces Mechanical generation of dry aerosols Mechanical generation of liquid droplet aerosols Formation by molecular processes

37 37 37 40 41

vii

Contents

3.2

3.3

3.4 3.5 3.6 3.7 3.8 3.9

The evolution of aerosols Coagulation, agglomeration and coalescence Condensation and evaporation Particle morphology Particle shape classification Fibres Aerosol concentration Particle size Elementary particle size statistics Electrical properties Mineralogical and chemical properties Biological properties

42 43 43 46 46 51 51 52 56 62 66 67

Chapter 4. THE M O T I O N OF A I R B O R N E PARTICLES 4.1 Introduction 4.2 Drag force on a particle Drag 4.3 Particle motion Equations of motion Motion under the influence of gravity Motion under electrical forces Motion in thermal gradients Motion without external forces 4.4 Similarity in particle motion 4.5 Particle aerodynamic diameter 4.6 Impaction 4.7 Elutriation Aspiration 4.8 4.9 Diffusion Molecular diffusion Coagulation Turbulent diffusion

72 72 72 72 77 77 77 83 85 88 89 91 95 99 103 107 107 111 113

Chapter 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10

116 116 116 118 122 125 127 129 131 132 134

5. THE OPTICAL P R O P E R T I E S OF A E R O S O L S Introduction Physical basis Concept of extinction or transmittance Particle extinction coefficient Experimental measurements of extinction Light scattering Particle scattering coefficient Mass concentration aerosol photometry The visual appearance of aerosols Optical microscopy

viii

Contents

Chapter 6.1 6.2 6.3

6. THE I N H A L A T I O N OF A E R O S O L S Introduction The human respiratory tract Aerosol inhalation Basic definitions and terminology Concept of inhalability Experimental measurements of inhalability Physical basis of inhalability 6.4 Experiments to investigate aerosol deposition in the respiratory tract 6.5 Extrathoracic deposition Physical basis Experimental results 6.6 Thoracic deposition Physical basis Tracheobronchial deposition Alveolar deposition Thoracic deposition and penetration Total respiratory tract deposition 6.7 6.8 Deposition of fibrous aerosols Electrostatic respiratory tract deposition 6.9 6.10 Mathematical modelling of lung deposition

Chapter 7.1 7.2 7.3

7.4 7.5 7.6 7.7 7.8

7. THE FATE OF I N H A L E D PARTICLES Introduction Biological mechanisms of clearance and re-distribution Experimental methods The use of animals in inhalation research Experimental approaches Studies of clearance and build-up Experimental studies of dust accumulation in lung-associated lymph nodes The significance of 'overload' Kinetics of clearance Dosimetry

147 149 149 150 151 151 152 153 155 156 158 159 162

166 166 166 170 170 171 174 182 185 187 197

Chapter 8. 8.1 8.2

S T A N D A R D S FOR H E A L T H - R E L A T E D A E R O S O L M E A S U R E M E N T AND C O N T R O L Introduction Progress towards criteria for measurement of coarse aerosols

136 136 136 140 140 143 143 146

ix

204 204 207

Contents

8.3

8.4 8.5

Progress towards criteria for the measurement of finer aerosol fractions Thoracic aerosol Tracheobronchial and alveolar aerosol Harmonisation of criteria for aerosol standards Fibrous aerosols Standards The 'traditional' approach The new criteria and health effects Strategies for exposure assessment Limit values

Chapter 9. A E R O S O L SAMPLING IN W O R K P L A C E S Introduction 9.1 9.2 Sampling by aspiration Background Identification of aerosol sampler performance indices 9.3 Aspiration efficiency of thin-walled sampling probes in moving air Qualitative physical picture for a thin-walled probe facing the wind Simple impaction model Effects of orientation 9.4 Aspiration efficiency of blunt samplers Sampling from calm air 9.5 9.6 Physical factors which can complicate sampler performance Effects of freestream turbulence on aspiration efficiency Effects of external wall interactions on aspiration efficiency Effects of electrostatic interference on aspiration efficiency Transport losses of particles after aspiration Overall sampler performance 9.7 Sampling in stacks and ducts 9.8 Sampling for coarse aerosols in workplaces Static (or area) samplers for 'total' or inhalable aerosol Static (or area) samplers intended primarily for finer aerosol fractions Personal samplers for 'total' or inhalable aerosol Personal samplers intended primarily for finer aerosol fractions

211 211 212 214 223 225 225 226 227 230 238 238 238 238 239 241 241 243 247 251 256 261 261 262 263 264 267 268 269 269 274 275 280

Contents

9.9

9.10 9.11 9.12 9.13

9.14

9.15

Sampling for respirable aerosol in workplaces Static samplers for the respirable fraction Personal samplers for the respirable fraction Sampling for 'respirable' fibres Practical sampling for thoracic aerosol Sampling for more than one fraction simultaneously Aerosol spectrometers Sampling of bioaerosols Criteria for bioaerosol sampling Sampling Sampling system components Pumps Filters Quantitation of collected samples

282 282 284 287 289 289 291 295 296 296 297 297 298 299

Chapter 10. 10.1 10.2

10.3 10.4 10.5 10.6 10.7 10.8 10.9 Chapter 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10

D I R E C T - R E A D I N G M O N I T O R I N G OF WORKPLACE AEROSOLS Introduction General characteristics of optical monitoring Extinction monitoring Light scattering photometry Light scattering photometers Optical particle counters Electrical particle measurement Condensation nuclei particle counters (CNC or CPC) Mechanical aerosol mass monitors Nuclear mass detectors Overview

304 304 305 306 307 307 313 320 323 325 327 328

11. C O N T R O L OF W O R K P L A C E A E R O S O L S Introduction Adjustments to industrial processes Behaviour of aerosols in the workplace atmosphere Extraction of workplace aerosols by exhaust systems Transport of aerosols in ventilation ducts Particle removal systems Gravitational separation Inertial separation Cyclone separation Wet scrubbers Spray towers Venturi scrubbers Energy considerations in wet scrubbers

332 332 333 334 336 339 346 347 350 353 356 356 359 361

xi

Contents

11.11 Filtration

11.12

11.13 11.14 11.15 Chapter 12.1 12.2 12.3 12.4 12.5 12.6 12.7

361 362 365 368 371 373 374 376

Macroscopic picture of a filter Single fibre collection efficiency Practical filters Electrostatic precipitation Corona discharge Particle charging Particle electrical migration velocity Simple model of precipitator collection efficiency Practical precipitator systems Comparison between air cleaning systems Containment of aerosols Personal respiratory protection

377 379 381 383 386

12. AEROSOLS AND VAPOURS Introduction The transport of gases Inhalation of gases The sampling of gases Direct-reading instruments for gases Air cleaning for the control of gases Industrial hygiene importance of aerosols and vapours

389 389 389 392 392 397 398 398

POSTSCRIPT

401

INDEX

403

, o

Xll

Preface The idea for this book began in December 1989 when I visited the Republic of China, Taiwan at the invitation of the Council of Labor Affairs to give a series of lectures on aerosol science to occupational health professionals in that country. That experience provided the stimulus for thinking about how the subject of aerosol science in its widest sense could be presented as a coherent and relevant body of knowledge. Further stimulus was added soon afterwards when I joined the School of Public Health at the University of Minnesota. It has been said so many times as to be almost r e d u n d a n t - but it is worth repeating anyway ~ that there is nothing so powerful as teaching itself in helping the teacher better understand his or her own subject. Airborne contaminants in workplaces are the sources of a high proportion of occupational illness. Such airborne contaminants may appear either as gases or aerosols. Aerosols in workplace atmospheres have been ~ and continue to be ~ a major focus of industrial hygiene. So aerosol science remains an important component in the graduate-level education of industrial hygienists and other occupational health professionals. Several excellent texts already exist which lay out the elements of aerosol science in a way which is accessible to such students. I especially admire the work of Professor William C. Hinds, 'Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles' published by John Wiley and Sons in 1982, and continue to recommend it as a reference text to my own students. My new book sets out to be complementary to this and other such texts. In particular, worker exposure is taken as the central concept, around which most of the subject matter revolves. This has resulted in a structured approach which draws together wide-ranging aspects of aerosol science within the occupational health framework. This text deals specifically with aerosols, and provides a broad introductory overview of modern aerosol science as it relates to industrial hygiene and to occupational health in general. It is intended to provide the basis of graduate-level coursework which deals with the properties, behaviour and effects of airborne contaminants. The introductory chapters are concerned with the nature and properties of aerosols, and how they are generated in the occupational environment. The book then goes on to provide a description

xiii

Preface of the fundamental mechanical properties of aerosols, in particular those mechanical properties associated with the motion of airborne particles (since it is these properties which govern how particles are transported in the workplace air, are inhaled and are deposited in the respiratory tract, in addition to how exposure to them might be effectively measured and controlled). The next chapter is devoted to the optical properties of workplace aerosols since these are important in the visual appearance of aerosols and in many aspects of measurement. This leads to the core of the book which deals with the processes which govern the nature of exposure to and the subsequent fate and effects of airborne particles, building up to a rational framework for standards, measurement and control. In this core are chapters describing: (a) the inhalation of airborne particles and how they can reach the interface between the workplace environment and the biological system of interest (i.e., the worker); (b) the clearance, re-distribution and storage of particulate material in the respiratory tract and elsewhere in the body; (c) the development of scientifically-based standards; (d) the development of health-related sampling and measurement; and (e) the technical means by which workplace aerosols (and particularly worker exposures) are controlled to within demonstrably safe levels. Included here also is a chapter which deals with the direct-reading instrumentation for aerosols which provides an increasingly important tool in the technical armory of the modern industrial hygienist. Finally, a chapter is added which relates what has been said about aerosols to gaseous and vapour contaminants. Here, there are of course important differences. However, there are also some similarities, and I have felt that a discussion of these is useful in helping to dispel the notion that aerosols (and so aerosol scientists) and contaminant gases (and so chemists) are totally disparate and 'never the twain shall meet'. The overriding goal is to provide a means for u n i f y i n g - not d i v i d i n g - the science of industrial hygiene. As already stated, the book is targetted at graduate students in industrial hygiene and other occupational (and environmental) health disciplines. As such it differs from and is broader than ~ my previous book, 'Aerosol Sampling: Science and Practice' published by John Wiley and Sons in 1989, which was aimed primarily at researchers. This new text recognises that graduates entering any of these fields come from a very wide range of starting disciplines, but acknowledges that all such graduates should satisfy the prerequisites of a broad undergraduate education in the physical and life sciences and mathematics (including calculus). The approach is therefore intentionally somewhat rudimentary. However, it is hoped that sufficient pointers are g i v e n - and references c i t e d - to enable more advanced students (and, indeed, experienced practitioners and researchers) to move into more challenging realms. As such, therefore, it is my intention that the book should also be seen as a framework for more advanced study and reflection. The book derives from research, experience and time spent thinking about

xiv

Preface the subject over many years. It therefore goes without saying that I owe a debt of gratitude to a very large number of people. So, firstly, thanks go to all my colleagues past and present. For the most part, they are too large in number to list individually. However I do wish to mention specifically the contributions of David Mark for the countless hours of discussion which provided the early stimulus for much of what is in this book, and of Sidney Soderholm for his careful reading and critique of the chapter on aerosol standards. I also wish to thank my many students who, inevitably, have acted as 'guinea pigs' for the ideas and approach which are contained in these pages. I especially wish to thank Perng-Jy Tsai for taking the time to check the worked examples. Finally, my everloving thanks go to my wife, Christine, for her patience and support during the period of writing, not least for her cheerful acceptance of the fact that I failed to keep my promise that my previous book was to have been "my last" . . . J A M E S H. V I N C E N T Minnetonka, Minnesota December 1994

XV

A NOTE ON UNITS AND DIMENSIONS Industrial hygiene is a field which, by virtue of the wide range of disciplines from which it draws, is plagued by confusing combinations of units. For example, it is the most c o m m o n convention to talk of concentration of an airborne contaminant in terms of [mg m-3], whilst at the same time be thinking of linear dimensions in terms of [feet], of air velocities in terms of [feet per minute, or fpm], or air flowrates in terms of [cubic feet per minute, or cfm]. Meanwhile, in aerosol science in general, the old ~ and somewhat unwieldy ~ 'centimetre-gram-second' (or 'cgs') system of units is still commonly used, especially in the United States. In an attempt to simplify the system of units used in the physical sciences and engineering, the 9th General Conference of the Weights and Measures in 1948 proposed the new 'Syst6me Internationale d'Unit6s' (or 'SI') system. This is the chosen approach in this book. In the SI system, the following so-called 'base' units are relevant here. These are :the metre [m] for length the kilogram [kg] for mass the second [s] for time the ampere [A] for electric current the degree Kelvin [~

for t e m p e r a t u r e

the mole for amount of a given substance. In addition, there is a range of primary units which are derived from the base units. Relevant ones are:the litre [1] for volume [ - m 3 • 10 -3 ] the micrometer [l~m] for size [ -- m x 10 -6

]

the Pascal [Pa] for pressure [ - kg m -1 s -2 ] the Newton [N] for force [ - kg m s -2 ] the Joule [J] for energy [ - kg m 2 m s -2 ] the watt [W] for power [ - kg m 2 s -3 ] the Coulomb [C] for electrical charge [ - A s -1 ] the volt [V] for electrical potential difference [ - J C -1 ,

C-1 C1].

xvi

or kg m 2 s -2

A note on units a n d d i m e n s i o n s

Finally there are some physical quantities which appear frequently in the book and whose dimensions are as follows" viscosity [ N s m -2, or kg m -1 s -1 diffusivity [ m 2 s -1

]

]

density [ kg m -3 ]. Working within the SI system of units is usually very straightforward, and so its use is strongly recommended. While most of the equations given in this book apply directly in other systems of units, the reader who wishes to do so is advised always to check the dimensional consistency of the relationship used. This is particularly important when constants are involved which themselves have dimensions.

xvii

This Page Intentionally Left Blank

CHAPTER 1

Introduction to aerosols 1.1 W H A T IS AN A E R O S O L ? 'Aerosol' is a scientific term which applies to any disperse system of liquid or solid particles suspended in a gas usually air. It therefore is much wider than suggested by the narrow popular use of the term in relation to pressurised spray-can products. The term 'aerosol' applies to a very wide range of particulate systems encountered terrestially. First there are naturally-occurring aerosols. These include, for example, snowstorms, duststorms, sandstorms, volcanic ashes, smokes (from fires), mists, clouds, and so on. They also include biologicallyactive systems such as airborne pollens, fungi, viruses and bacteria. In terms of overall global amount (e.g., mass or particle number), such naturallyoccurring particulate clouds are thought to represent the majority of overall terrestial aerosol. However, we also have man-made aerosols, resulting from a wide range of anthropogenic ~ including industrial activity. Such aerosols may be found either outdoors or indoors, and become important in relation to the natural aerosol background because they are usually quite inhomogeneous (with relatively high local concentrations). Many aerosols, either natural or man-made, may contain toxic substances which can lead to adverse effects when they come into contact with plant and animal life. Such aerosols are regarded as pollutants, hence the need is clearly identified to: understand their physical, chemical and biological nature and behaviour; understand their interactions with ecological and biological systems; and develop means for monitoring and controlling their presence. It is clear from these introductory remarks that aerosols feature very widely in nature and in human experience. So it comes as no surprise to find that the study of aerosols ~ their characteristics, effects and applications ~ has grown into a major field of scientific enquiry, touching on many individual disciplines, including physics, chemistry, mathematics, engineering, biology and medicine.

Aerosol science for industrial hygienists Many, indeed most, industrial processes produce aerosols, releasing airborne particles into the air so that, in the absence of control measures, they may be discharged either into the outdoor environment or into the workplace atmosphere. The former contributes to the pollution of the ambient atmosphere and so impacts on populations and the environment at large. This is 'air pollution' in its widest sense. In the primary context of this book, contamination of a workplace atmosphere impacts primarily on the working population in question. Here the local concentrations of airborne particles tend to be higher than in the ambient atmosphere, leading in some cases to high prevalences of aerosol-implicated health effects. Because specific aerosol types and properties tend to be associated with specific industries, then so too do those occupational health effects. For example, it is well-known that pneumoconiosis, a disease of the alveolar region of the lung, has been associated with the mining and extraction industries in which workers are exposed to relatively insoluble mineral dusts; asbestosis, lung cancer and mesothelioma have been associated with exposure to asbestos fibres in industries where asbestos is mined or processed; nasal cancer has been associated with some hard wood dusts found in the furniture industries; and so on. It is fair to surmise that a significant proportion of the working population is exposed occupationally to aerosols of one sort or another. Workplace aerosols therefore require the attention of all those concerned with quality of the workplace environment, none more so than the industrial hygienist. Indeed, over the years, aerosols of widely-varying types in a highly diverse range of industrial settings have been the focus of a major part of industrial hygiene research and practice. Most such interest in aerosols stems from the ability of particles to be inhaled into the respiratory tract. To a lesser extent, there is interest in toxic particles which can be deposited onto and absorbed through the skin (e.g., from pesticide sprays). There is also some interest in very large, gritty dust particles from certain industrial processes which are not actually suspended but, rather, are projected into the air and can cause discomfort or damage upon impaction onto the skin or (particularly) the eyes. A summary classification of a range of typical aerosols is given in Figure 1.1. It contains not only examples of the workplace aerosols with which this book is primarily concerned but also, for the sake of comparison, some naturally-occurring and man-made aerosols found in the outdoor atmospheric environment. At the top of this figure, a number of types of aerosol are shown which relate primarily to the material from which the aerosol is formed and manner of its formation. These are:

Dust, an aerosol consisting of solid particles made airborne by the mechanical disintegration of bulk solid material (e.g., during cutting, crushing, grinding, abrasion, transportation, etc.), with sizes ranging

Introduction to aerosols from as low as sub-micrometer (~m) to over 100 ~xm. In principle, there is no upper limit in this category. But whether or not 'particles' of 'rock-like' dimensions (which are certainly produced during many of the industrial processes mentioned) can be considered to be part of an aerosol depends on the extent to which they are truly 'airborne'.

Spray, an aerosol of relatively large liquid droplets produced by the mechanical disruption of bulk liquid material, with sizes upwards of a few micrometres. Here the upper limit is more clearly defined than for dusts because, above a certain size, droplets become unstable (due to the relationship between surface tension and gravitational and shearing forces) and so break up. Thus, for example, an 'aerosol' consisting of large, centimetre-sized, water droplets is unheard of. Mist, an aerosol of finer liquid droplets produced during condensation or atomisation, with sizes up to a few micrometres. Fume, an aerosol consisting of small solid particles produced by the condensation of vapours or gaseous combustion products. Usually, such particles are aggregates made up from large numbers of very small primary particles, with the individual units having dimensions of the order of a few nanometres (nm) and upwards. These primary particles are difficult to discern under the optical microscope. Aggregate sizes are usually less than 1 p~m. Smoke, an aerosol of solid or liquid particles usually resulting from incomplete combustion, again usually in the form of aggregated very small primary particles. The aggregates themselves have extremely complex shapes, frequently in the forms of networks or chains, having overall dimensions that are usually less than 1 p~m. Bioaerosol, an aerosol of solid or liquid particles consisting of, or containing, biologically-viable organisms (viruses, bacteria, allergens, fungi, etc.), with sizes ranging from sub-micrometre to greater than 100 ~m. In the main body of Figure 1.1, the examples of aerosols given are classified according to their ranges of particle size, a property which is highly influential in nearly all aspects of aerosol behaviour. The bottom part of the figure includes an indication of the particle size ranges of some health-relevant fractions ~ inhalable, thoracic, tracheobronchial and alveolar. These refer to particles which, by virtue of their size, can be inhaled through the nose and/or mouth of an exposed subject during breathing and can subsequently penetrate to and be deposited in progressively deeper parts of the human respiratory tract. A more detailed account of these fractions will be given in Chapters 6 and 8.

Aerosol science for industrial hygienists 0.01

Liquid

Physical definitions

0.1

1.0

10

'

I

I ~---. I Dust I Fly ash

~ M i s t

I I Fume ~ ~ I I -q---Oil smokes--~ ~1

Solid

Tobacco

~ I smoke _. -.. I I I

I00

~-- Cement dust--~ n dust I Coal a I

]

, -----~

Atmospheric dust I

Typical

aerosols and aerosol particles

Viruses

I l

-~ I Airborne asbestos ~ (diameter) I I

~ _/ I .4--Bacteria-~ | -I ~

Pollens I I

I Airborne' asbestos --~ (length)

I Respirable _ I particles Tracheobronchial I I I particles U ~ q:horacic particles i ~ I , I I inhalable particles I I I I I I I I j I I

Health-related deft n it ion s/fraction s

0.01

O. I

I000

' Spray i 1 I I

! .0

I0

I I I I I I I ~ I I I I O0

1000

of aerosols (from Vincent, J.H., 1989, a d a p t e d b y p e r m i s s i o n Wiley and Sons Limited).

Aerosol

Particle d i a m e t e r (l~m) Figure

1.1.

Summary

classification

Sampling." Science and Practice, C o p y r i g h t

of John

1.2 ' G O O D ' VERSUS 'BAD' A E R O S O L S 'Aerosol science' in general covers all aspects of airborne particulate matter. Many aerosols are considered to be 'good' insofar as they make positive contributions to the earth and to man. For example, a balanced climate requires cloud and droplet formation in the atmosphere. Many industrial processes require aerosols as components vital to their effectiveness (e.g., photo-reproduction, chemical reactors, materials synthesis, etc.). Many therapeutic substances need to be aerosolised before they may be delivered to the site in the body where they can be effective (e.g., as in inhalers for the treatment of respiratory complaints such as asthma, etc.). Elsewhere, industry usefully employs sprays for the efficient delivery of pesticides and paints, etc. to their desired sites. There is clearly plenty of scope for aerosol science to continue to make direct 'positive' contributions to the earth's environment and ecology and to man's health and industrial activities. Modern aerosol research is therefore increasingly motivated in these directions.

Introduction to aerosols However, there is just as wide a range of aerosols which are clearly perceived as 'bad'. An unwanted aerosol is, by definition, a 'pollutant' and particles once they are airborne are capable of rapid dispersal and may be difficult to recapture. One aspect which is growing in importance in terms of its potential cost to industry is the problem of the contamination of products (e.g., electronics components, pharmaceuticals, food, etc.) by unwanted particle deposition. A whole branch of aerosol science has grown out of this need for 'clean technology'. However, the area where interest has consistently remained high since the birth of aerosol science is that concerned with the ill-health that can arise from human exposure to aerosols by inhalation, whether it be in the home, in the outdoor environment, in public buildings, or in the workplace. Such exposure needs to be eliminated or, at least, kept to within limits considered to be 'safe'. Historically, workplace aerosols have long been a major source of concern. It therefore comes as no surprise to find that much of the pioneering work carried out in aerosol science during the latter half of the twentieth century has been driven by the needs of industrial hygiene.

1.3 W O R K P L A C E A E R O S O L S A N D O C C U P A T I O N A L H E A L T H Depending on the nature of a particular industry and its working materials, workplace aerosols can occur in almost any of the categories listed in Figure 1.1, sometimes of one type only but often in the form of complex aerosol combinations. It is therefore part of an industrial hygienist's job to: recognise the nature and magnitudes of the hazards associated with particular types of workplace aerosol; assess the levels of worker exposure to aerosols of the types suspected of being associated with ill-health; and observe standards and, where appropriate, to initiate appropriate control measures. Therefore, for an enquiring industrial hygienist, a grasp of the relevant fundamentals of aerosol science is essential. This book sets out to provide an appropriate framework. The scope of that framework, and hence of this book, is summarised in Figure 1.2. Here the primary component is identified as worker exposure to aerosols (E) and the way in which this can lead to ill-health. The central 'tree' of Figure 1.2 therefore links the processes of exposure, dose, response and effect. In the first instance, exposure leads to the arrival and accumulation of particulate material in the body, leading to a cumulative 'dose' at vulnerable

Aerosol science for industrial hygienists

Figure 1.2. Framework for an integrated approach to the study of aerosols in the industrial hygiene context.

sites of some quantity representing 'harmfulness'. This leads in turn to a biological response which, depending on the body's recovery-and-repair defence mechanisms, might ultimately be the precursor to substance-related ill-health in a form that can be identified clinically or pathologically. Statistical analyses of the relationship between exposure and the incidence of ill-health have sometimes been used as the basis for the setting of health-based exposure limit values ~ that is, quantitative guidelines for controlling the quality of the workplace environment. This is largely a 'black box' approach and, in principle, the process may be improved by incorporating into the modelling process the kinetics and dynamics of the various components of the disease processes describing the fate and biological effects of the inhaled particulate material. With the improved knowledge that we now have from inhalation toxicological and other research, this may now be feasible for some hazardous substances. In addition, however, working exposure limit values need to incorporate pragmatic considerations of what is achievable under practical

Introduction to aerosols industrial conditions. Inevitably, health-based limit values are usually more stringent than actual, pragmatic ones. It is, of course, an ultimate goal to close the gap between them. The right 'arm' of Figure 1.2 concerns the measurement of aerosol exposure. Here, ideally, a criterion for measurement needs to be established so that the index of exposure which is provided is valid in relation to the disease or ill-health in question. Only then can appropriate instruments be designed, built and made available to industrial hygienists. In turn, these instruments may be used in measurement strategies designed to provide reliable exposure histories of exposed workers. Such data can then be used as the basis of epidemiological research to determine the true relationship between aerosol exposure and ill-health (where that relationship is not yet known or known sufficiently well), or for evaluating risk. More immediately, however, the results can be matched against existing exposure standards so that an assessment can be made of the control measures that need to be carried out in order to achieve compliance. The left 'arm' of Figure 1.2 closes the loop by introducing the engineering control of the workplace environment that is carried out to ensure that worker exposure is kept to within safe limits. Appreciation of the nature and behaviour of aerosols is involved at all stages of the integrated industrial hygiene philosophy embodied in Figure 1.2. These aspects are summarised in Figures 1 . 3 - 1.6, underlining the fact that, in industrial hygiene, the term 'aerosol science' refers not just to aerosol physics but also to engineering, chemistry and biology and beyond. In turn we see that industrial hygiene is not only highly multi- and inter-disciplinary but also ~ arguably ~ central to the study and practice of occupational health.

Figure 1.3. Summaryof the aerosol science considerations that occur in relation to aerosol generation and exposure in the workplace.

Aerosol science for industrial hygienists

Figure 1.4. Summary of the aerosol science considerations that occur in relation to linking exposure, dose and response - - leading to the setting of health-based standards for workplaces.

Figure 1.5.

Summary of the aerosol science considerations that occur in relation to the measurement of workplace aerosol exposures.

Introduction to aerosols

Figure 1.6.

Summary of the aerosol science considerations that occur in relation to controlling workplace aerosol exposures.

Later chapters in this book will address many of the scientific areas touched on in these figures. Finally, returning to Figure 1.2, it is relevant to note that the scope of this description can be widened to cover almost every aspect of occupational and environmental health, not just in relation to aerosols but also to gaseous contaminants and other agents or factors which may cause illness or injury.

1.4 A E R O S O L S A N D GASES In considering airborne contaminants in workplaces, the industrial hygienist is concerned not only with aerosols but also with gases and vapours. Although the latter lie outside the primary scope of this book, it is however important to recognise the similarities and differences between them. Gaseous and vapour contaminants are similar to aerosols in the sense that they too consist of disperse systems of unconnected entities. That is, both classes of contaminant are contained in and transported by the air and are therefore

Aerosol science f o r industrial hygienists

readily available for worker exposure by inhalation. The behaviour of gas molecules is governed by the gas and fluid laws, so they can exhibit motions in the form of convection and diffusion. In turn they may be inhaled and deposited selectively in the respiratory tract. In addition, depending on the environmental (physical and chemical) conditions, they may undergo chemical changes, or become excited, ionised or dissociated. However, unlike relatively macroscopic aerosol particles, they do not experience gravitational, inertial or electrical forces (unless ionised), nor do they undergo other mechanical processes of coagulation, agglomeration, break-up, etc. In general, relative to aerosol particles, individual molecules are better-defined by virtue of their unique molecular structures. So, from the industrial hygiene perspective, they are usually simpler to recognise and evaluate (but not necessarily control).

REFERENCES The reporting of the science and applications of aerosols is widely distributed throughout the peer-reviewed literature. In the first instance, there are the premier aerosol science journals such as: Journal of Aerosol Science m

Aerosol Science and Technology Journal of Aerosols in Medicine.

Other journals containing significant amounts of aerosol-related material directly relevant to occupational health include:m

Annals of Occupational Hygiene The American Industrial Hygiene Association Journal Applied Occupational and Environmental Hygiene Scandinavian Journal of Work Environment and Health Journal of Occupational Hygiene Atmospheric Environment

as well as a wide range of medical, environmental and engineering journals.

10

CHAPTER 2

The properties of air and gases 2.1 I N T R O D U C T I O N This book is concerned, as its title suggests, with aerosols. However the discussion of particulate material ~ liquid or solid ~ suspended in air cannot take place without understanding the nature of the air itself. It is therefore appropriate to provide a rudimentary outline of the main physical properties of air as they relate to aerosol science and industrial hygiene. The discussion is widened further to include brief description of the properties of airborne contaminant gases and vapours as a basis for recognising the similarities and differences between aerosol and gasesous contaminants (see also Chapter 12).

2.2 BASIC N A T U R E OF GASES Much of industrial hygiene is concerned with the transport of pollutants of various kinds in the vicinity of human subjects, both through and by the workplace atmospheric air. Air is a mixture of gases, the main constituents being nitrogen (about 78% by volume) and oxygen (21%), with a variety of other trace gases including argon, carbon dioxide, water vapour, etc. (amounting to about 1% in total). It is a colourless, odourless gas of density 1.29 kg m -3 at a standard temperature and pressure (STP) of 20~ (293~ and pressure of 1.01 • 105 Pa, respectively. The basic physics of matter, in particular of gases and about the phase changes that can take place between gases and liquids (and vice-versa), are covered very widely in the many excellent physics texts that are available.

Pressure, volume and temperature The dynamical behaviour of a gas may be based on what we refer to as the 'kinetic theory of gases'. This treats a gas as a 'billiard ball' system; that is, one

11

Aerosol science for industrial hygienists

Figure 2.1.

Schematic diagram to indicate the basis for developing the kinetic theory of gases.

where the molecules are small rigid spheres which undergo perfect collisions with one another in which no energy is lost. Starting from the molecular concentration n, mass rn, effective diameter d m and random velocity u between collisions, kinetic theory provides a basis for relating the properties of temperature, pressure and mean free path (the mean distance between inter-molecular collisions), and the phenomena of diffusivity, viscosity and thermal conductivity. Consider a box of volume V containing N molecules, so that the number concentration, n = N / V (see Figure 2.1). As molecules near the walls collide with the walls, they exchange momentum and hence a force is experienced. For an analogy, consider a room full of people throwing tennis balls at one of the walls. The impact of a single ball is experienced by the wall as a single impulse, and is associated with the momentum which is exchanged during impact. A succession of such impulses becomes equivalent to a series of such individual forces. When the number of impulses becomes very large, then the series of impulsive forces becomes indistinguishable from a continuous steady force acting on the wall. Likewise for the molecules in the box, the net effect of many molecular collisions with the wall, averaged over time, appears as a steady force which in turn may be represented as the pressure P (i.e., force per unit area). From the mechanics of the 'billiard ball' collisions and the

12

The properties of air and gases

application of some statistics, it may be shown that the pressure on the walls of the box may be expressed as mNums (2.1)

Force/Area - P = 3V

leading to mNums

P V =

(2.2)

In this expression, Urns is the mean-square (ms) random velocity of the gas molecules ~ in other words, the arithmetic mean of the squares of the randomlydirected molecular velocities. This comes from the Maxwell-Boltzmann statistical distribution of the magnitudes of the molecular velocities (u) arising from the inter-molecular collisions. This distribution is given by

f ( u ) -- 4rru 2

exp

(2.3)

2zrR T

2R T

where M is the molecular weight (29 g mole -1 for air). From Equation (2.3) we have oo Urms

"-- { fa bl2 f ( u )

1/2 du

}1/2 --

(2.4)

M

0

where Urms is the root-mean-square (rms) molecular velocity. A typical distribution, describing the probability of finding molecules moving at the velocities indicated in air at a temperature of 20~ is illustrated in Figure 2.2. It shows, as described by Equation (2.3), that molecules may experience a very wide range of random velocities, in principle from zero to greater than 1000 m s -1. Figure 2.2 shows not only Urms for the distribution in question but also the related ~ but mathematically different ~ mean random velocity (urn) given by oo blm --

fur(u)du

8R T ~ 1/2 =(

~rM )

(2.5)

0 By comparing Equations (2.4) and (2.5) we can see that Urms

13

>

Um.

Aerosol science for industrial hygienists Urns (at STP)

am

"X

f (u)

,,4 500

0

I000 u

I

1500

(m/s)

Figure 2.2. Statistical distribution of random velocities of air molecules under standard atmospheric conditions, indicating the mean and root-mean-square molecular velocity. For the gas contained inside the box shown in Figure 2.1, the ideal gas law relates P, V, N and the temperature T by means of the familiar expression

PV-

nmRT

(2.6)

where

mN nm =

(2.7) M

is the number of moles of air in the box. Here R is the universal gas constant, and is usually given in SI units as 8.314 J ~ mole -1 (although it is sometimes useful to give it as 82 atmosphere cm 3 oK-1 m o l e - l ) . Also in Equation (2.6) n m is the number of moles of gas present, and T is the absolute temperature expressed in degrees Kelvin (~176 where ~ refers to temperature in degrees Centigrade). When temperature is held constant, then this reduces to the simple form

PV= constant

(2.8)

known as Boyle's law. From Equations (2.4) and (2.5), it is clear that, for a given gas, t e m p e r a t u r e and rms molecular velocity are physically equivalent. Thus, for example, we have

umsM T =

(2.9) 3R 14

The properties of air and gases Example 2.1. W h a t are the r o o t - m e a n - s q u a r e and m e a n velocities, respectively, for air at 35~ at atmospheric pressure T (in ~

= 273 + 35 = 308~

Note that M = 29 g mole -1 = 0.029 kg mole -1 From Equation (2.4) 3 x 8.314[J ~ Um S

mole -1] x 308[~

-"

0.029[kg mole -1] so that Urns ~ 26.49 X 104 m 2 s-2 and hence *

Urms = 515 m s -1

Similarly, from Equation (2.5) we get *

Mean

u m = 474 m s -I

free path

T h e mean free path (mfp) is t h e m e a n d i s t a n c e t h a t a gas m o l e c u l e t r a v e l s b e t w e e n c o l l i s i o n s w i t h o t h e r gas m o l e c u l e s . A g a i n f r o m t h e ' m o l e c u l e s - i n the-box' m o d e l and the application of s o m e m o r e statistics, we get V

mfp

1

-

= ~/~N

1r d 2

(2.10) ~/~n

~r d2m

T h i s s h o w s t h a t , f o r a g i v e n gas, mfp d e p e n d s i n v e r s e l y o n gas d e n s i t y In t u r n , f r o m E q u a t i o n ( 2 . 1 ) , this m e a n s t h a t mfp is also i n v e r s e l y p r o p o r t i o n a l to gas p r e s s u r e . A d d i t i o n a l l y , f o r c o n s t a n t v o l u m e it is d i r e c t l y p r o p o r t i o n a l to t e m p e r a t u r e .

15

Aerosol science for industrial hygienists

Example 2.2. What is the mean free path for air molecules at STP? What does its value become at the top of Mount Everest (where the air pressure falls to about 50% of that at sea level)? Note that d m = 0.00037 Ixm = 37 X 10-11 m n = 25 x 1024 molecules m -3 at STP

From Equation (2.10) *

mfp = 0.066 ~m.

At the top of Mount Everest, Equation (2.1) gives n = 12.5 x 1024 molecules m -3 so that *

mfp = O.13 jxm

As we shall discuss in a later c h a p t e r , the m a g n i t u d e of m f p b e c o m e s very i m p o r t a n t in relation to the a e r o d y n a m i c b e h a v i o u r of particles in s o m e w o r k p l a c e aerosols w h e r e t h e r e are high p r o p o r t i o n s of particles w h o s e sizes are of the s a m e o r d e r of m a g n i t u d e as m f p (or less).

Diffusion D i f f u s i o n relates to the mass transfer associated with the r a n d o m m o l e c u l a r m o t i o n s . F o r a gas species which is u n i f o r m l y d i s p e r s e d in air (for e x a m p l e , a c o n t a m i n a n t trace gas well-mixed in w o r k p l a c e air), t h e r e is no net t r a n s f e r of gas due to these m o t i o n s , m e r e l y the m u t u a l e x c h a n g e of individual m o l e c u l e s each way across any defined b o u n d a r y . If, h o w e v e r , t h e r e is a g r e a t e r c o n c e n t r a t i o n of the trace m o l e c u l e s on o n e side, t h e n t h e r e is an i m b a l a n c e in the e x c h a n g e process, resulting in a net flux of m o l e c u l e s f r o m regions of high to low c o n c e n t r a t i o n . This scenario is illustrated in Figure 2.3. Kinetic t h e o r y p r o v i d e s the e x p r e s s i o n ( k n o w n as Fick's law) On

N e t flux = J = - D m

(2.11) Ox

16

The properties of air and gases

Figure 2.3.

Schematic diagram to illustrate the phenomenon of molecular diffusion.

w h e r e On/Ox is the local c o n c e n t r a t i o n g r a d i e n t which is driving the flux a n d w h e r e the m i n u s sign indicates that the net flux is t o w a r d s the r e g i o n of l o w e r c o n c e n t r a t i o n . D m is the m o l e c u l a r diffusion coefficient given by

mfp Dm

=

u m

(2.12)

which d e p e n d s on b o t h t e m p e r a t u r e a n d p r e s s u r e . In fact, we see f r o m the p r e c e d i n g section that D m increases as the gas t e m p e r a t u r e i n c r e a s e s b u t d e c r e a s e s as p r e s s u r e increases. Example 2.3. What is the diffusion coefficient for air molecules at STP? For STP, Equation (2.4) gives um

"

-

470 m s-1

Also, note that

mfp = 0.066 p~m = 6.6 • 10 -8 m Equation (2.12) gives *

D m ~- 1 0 - 5

m 2 s-1

17

Aerosol science for industrial hygienists As we shall see later, the diffusivity of gas molecules u n d e r n o r m a l atmospheric conditions is many orders of m a g n i t u d e greater than for even very small aerosol particles.

Viscosity Viscosity is associated with a moving gas, in particular with the forces acting between regions moving at different velocities. This physical scenario, k n o w n as 'shear', is illustrated in Figure 2.4 which shows a pair of plates of area A i m m e r s e d in the gas, separated by a distance y, and moving at velocity U relative to one another. The law of m o t i o n for a real fluid requires that the velocity of the gas at the surface of each plate must be zero, hence there is 'shear' associated with their relative motions. The internal m o t i o n of the molecules in the gas between the plates is such that there is a net force resisting this shear (and hence this relative motion). This is r e g a r d e d as a 'friction' force, and kinetic theory again comes into play to give ~A U Friction force, F v =

(2.13)

where the coefficient o f viscosity is given by

mfp Ix - n m u m

Figure 2.4.

(2.14)

Illustration of the phenomenon of viscosity and how it relates to the kinetic theory of gases.

18

The properties o f air and gases Here we see by application of Equations (2.5) and (2.10) that the coefficient o f v i s c o s i t y is i n d e p e n d e n t o f p r e s s u r e , a n d - - f o r a g i v e n g a s - - is d e p e n d e n t only on temperature.

Example 2.4.

W h a t is the viscosity of air at S T P ?

Note again that n = 25 x 1024 molecules m -3 at STP mfp = 6.6 x 10 -s m u m = 470 m s-1 Note also that the molecular mass is given by

m = M/Na where N a is the number of molecules per mole (referred to as Avagadro's number) and is 6 x 1023 molecules per mole. Thus 0.029 [kg mole -1] m

-

6 x

10 23

[molecules mole- l]

= 4.8 x 10-26kgmolecule -l Equation (2.14) now gives Ix = 25 x 1024[molecules m -3] x 4.8

x 10-26[kg

molecule -l]

x 470 [m s-'] x 6.6 x 10 -s [m]

*

Ix = 12.4 x 10 -6 kg m -1 s -1 (or N

s m -2)

N o t e , h o w e v e r , t h a t this r e s u l t h a s b e e n o b t a i n e d f r o m a c a l c u l a t i o n b a s e d on kinetic theory. In actual fact, thisas f o r t h e o t h e r q u a n t i t i e s c a l c u l a t e d above is o n l y a n e s t i m a t e s i n c e t h e i n i t i a l i d e a l i s i n g a s s u m p t i o n s d o n o t h o l d strictly. It is i m p o r t a n t t o n o t e t h a t , in c a l c u l a t i o n s w h i c h f o l l o w l a t e r in this b o o k , t h e t r u e v i s c o s i t y o f air at S T P is 1 8 . 3 2 6 x 10 - 6 N s m - 2 ( w h e r e 18 • 10 - 6 N s m - 2 is u s u a l l y a g o o d e n o u g h a p p r o x i m a t i o n ) .

19

Aerosol science for industrial hygienists Gas mixtures

The gas laws can be applied to systems of mixed gases. Extending Equation (2.6), Dalton's law gives

PV + P1V1 + P2V2 + P3V3 + ' ' " --(nml

+ nm2 + r i m 3 ' '

(2.15)

")RT

where the nm'S are the numbers of moles present for each gas component in the overall volume V, and P~, V2, etc. are their partial pressures and volumes, respectively. For fixed pressure (e.g., for contaminant gases in workplace air), this becomes V

--

Vl

-+- V 2

-.~- V 3

-Jr- 9 9 9

(2.16)

Here, therefore, the total volume is equal to the sum of the partial volumes of the individual gas components, where it is assumed that the molecules of each component have been brought together so that the pressure of that component is equal to the overall pressure P. For a single gaseous contaminant in air (where air for this purpose is treated as a single gas), this gives V-

Vai r -F Vcontaminan t

(2.17)

In turn this can be written as the concentration of the contaminant gas. Expressed in terms of relative volume, this is Vcontaminant c = (Vai r -+- Vcontaminant) Vcontaminant

(2.18) for Vcontaminan t 1 can be achieved by cooling a vapour that is already saturated. This is referred to as 'supersaturation'. Here, the reduction in temperature causes the saturation vapour pressure to be reduced while the partial pressure remains the same. Referring back to water, for a given mass concentration of vapour in the air, R H can therefore be raised by lowering the temperature (and hence raising SR). Conversely, raising the temperature lowers RH. For cooling, the temperature at which the water vapour becomes saturated is known as the dew point. Below this, condensation may take place, hence the appearance in the air of water droplets which are visible as mist or fog. The preceding discussion provides an i m p o r t a n t mechanism for the formation and evolution not only of water droplet aerosols but also aerosols of other substances where phase changes can take place (see Chapter 3).

23

Aerosol science for industrial hygienists 2.3 E L E M E N T A R Y F L U I D M E C H A N I C S Since, by definition, an aerosol consists of particles suspended in air, it is inevitable that the behaviour of an aerosol will be highly dependent on the properties and behaviour of the air itself ~ including the nature of its motion. This therefore requires a discussion of elementary fluid mechanics. Here the general term 'fluid' is used to refer to what in industrial hygiene is 'air'. But it also applies to gases other than air (and, to a considerable extent, liquids as well). There are two fluid mechanical aspects relevant to aerosol behaviour. At one end of the scale ~ the microscopic level ~ we are concerned with the flow of air over and around a small airborne particle of matter, and therefore to the fluid mechanical drag (and lift) forces acting on it. At the macroscopic level, interest is focused on the behaviour of larger-scale moving air systems (e.g., in workplace atmospheres at large, around samplers, in ducts, in filtration devices, etc.) within which aerosols are contained and dispersed.

Basic physics The starting point for describing the dynamical behaviour of a fluid is the familiar 'second law' of Sir Isaac Newton, the great English physicist from the 1600s. This states that the product of mass and acceleration of a 'body' is equal to the sum of all the forces acting. For a fluid, this law is applied to each small elemental packet and the forces include body forces (e.g., buoyancy, gravity), pressure forces (associated with local gradients in static pressure) and shearing forces (associated with viscosity and local gradients in velocity). Applying this to each of the three available spatial dimensions (x, y and z) provides three equations of motion. These, in themselves, are not sufficient to completely describe the motion of the fluid system because it is also necessary to ensure that the amount of fluid in the system is conserved. That is, no fluid is gained by ~ or lost from ~ the system. This is taken care of by the addition of a fourth equation which ensures that continuity is maintained. Altogether, therefore, we have a system of four equations, and this is the well-known set of Navier-Stokes equations from which all else in fluid dynamics is derived. In general, these equations include the possibility that the fluid density may vary (i.e., the flow may be compressible). However, as far as industrial hygiene is concerned, this feature may usually be neglected and flows may be treated as incompressible. The qualitative physical basis of the Navier-Stokes equations is deceptively simple. In practice, however, the resultant equations themselves are quite complex when it comes to applying them to realistic systems, and analytical solutions for the behaviour of flowing systems are available only for the very simplest cases. So it is not appropriate to go into further details in this book.

24

The properties of air and gases But there is ample literature available elsewhere for the interested reader. The ageless classic text of Schlichting (1968) is a good starting point for an in-depth reading of the subject. In terms of applications, the advent of m o d e r n c o m p u t e r s and appropriate software m e a n s that numerical solutions are now b e c o m i n g increasingly accessible.

Streamlines

O n e i m p o r t a n t set of solutions that can be provided by the N a v i e r - S t o k e s equations is the pattern of streamlines (or, perhaps m o r e a p p r o p r i a t e l y in three dimensions, streamsurfaces). It is this pattern which most graphically characterises the flow. Described most simply, it is equivalent to the flow visualisation that would be obtained by m a r k i n g the fluid with a suitable

Figure 2.5. Some streamline patterns typical of flows of interest to industrial hygienists: (a) flow about a particle falling under gravity; (b) flow into the hood of a local exhaust ventilation system and then through the ventilation ducting; and (c) flow about a worker (facing the wind) and into a small aspirating personal aerosol sampler attached to his body.

25

Aerosol science for industrial hygienists visible tracer. To illustrate this point, Figure 2.5 shows sketches of a number of flow systems relevant to aerosols in industrial hygiene situations. Figure 2.6 is another, describing the flow near an idealised single-orifice blunt aerosol sampler of axially-symmetric geometry, placed facing into the wind. Figure 2.6a is a sketch based on an actual photograph of an experimental flow pattern in a wind tunnel, where visualisation was achieved using fine balsa dust which was viewed in a two-dimensional slice through its axis under intense 'slit' illumination provided by an ordinary domestic slide projector. Figure 2.6b shows the approximately equivalent streamline pattern obtained by solution of the flow equations. From such comparisons, it is clear that experiment and theory are in good agreement. One feature in particular is worth noting in Figures 2.5 and 2.6. Based on the fact that there can be no transfer of fluid across streamlines, it follows directly that the convergence of the streamlines represents an increase in fluid velocity (as the fluid is being 'squeezed' into a smaller volume). The converse is true for diverging streamlines.

Figure 2.6. Streamline pattern for the flow near a simple idealised blunt aerosol sampler: (a) sketch based on a photograph from flow visualisation (from Vincent and Mark, 1982); and (b) corresponding streamline pattern obtained from potential flow theory.

26

The properties of air and gases In the preceding, the concept of laminar flow is invoked to convey how the fluid motion involves the smooth sliding over one a n o t h e r of layers of fluid contained within streamlines.

Boundary layers One physical constraint applicable to real fluids is that the velocity of the fluid must be zero everywhere at solid boundaries to the flow. This means that there must be a strong velocity gradient b e t w e e n the ftow very close to the wall and the faster-moving fluid further outside. The region over which the fluid is sheared in this way is referred to as the boundary layer. F r o m solutions of the N a v i e r - S t o k e s equations, we would find that this is where the effects of viscosity are most strongly felt. It is from the effects of such boundary layers that, for aerosol particles and for other bodies i m m e r s e d in fluids, the forces of drag and lift are derived.

Figure 2.7. Illustration of boundary layer flows: (a) for plane flow over a thin flat plate; and (b) for the flow into a channel between a pair of plates.

27

Aerosol science for industrial hygienists By way of illustration, Figure 2.7a illustrates the nature of a typical boundary layer for a thin plate immersed in and parallel to ~ a moving air stream. The approaching flow is uniformly distributed, but once it strikes the leading edge of the plate, the zero velocity boundary condition immediately comes into effect. As shown, the boundary layer close to the leading edge (see hatched area) is very thin; but it increases in thickness with distance downstream. Figure 2.7b shows the equivalent flow inside a channel made up of two such plates. Here the boundary layer on each plate grows until it merges with the other, at which point the flow is considered to be 'fully developed'. Now the velocity profile across the channel takes on a classic parabolic shape which is well-known for laminar channel flows.

Similarity One important consequence of boundary layers which is important in all applications of fluid mechanics is the concept of dynamic similarity. In general, the concept of similarity relates to the way in which the characteristics and behaviour of physical systems can be scaled as the variables (e.g., physical dimensions, velocities and other physical quantities) change. In fluid mechanics, in particular, similarity provides an important link between the behaviours of the microscopic and macroscopic systems described above. The scaling of the dynamical nature of geometrically-similar flows can be derived directly from solutions of the Navier-Stokes equations. This is achieved mathematically by non-dimensionalising the physical dimensions, velocities and pressures in the basic equations (e.g., by dividing local velocities by a characteristic main velocity U, and local dimensions by a characteristic main dimension D), and re-organising the terms in the basic equations. This is a standard approach applied widely throughout physics and engineering. To demonstrate this here would require us to set out the Navier-Stokes equations in greater detail than is desirable for present purposes. A simpler physically-based approach which ultimately comes down to the same thing requires consideration of the relative magnitudes of inertial forces (reflecting mass • acceleration of elements of the fluid) and viscous forces (reflecting the forces on fluid elements associated with shearing). For the inertial forces (IF), their magnitude for a flow represented by local velocities and scale of u and x, respectively, and characterised by the overall characteristic velocity and scale U and D respectively, may be written in the form

Ou I IFI~

Pair U

U2 ~

(2.23)

Pair

Ox

D

28

The properties of air and gases where Pair is the density of the air. Such forces are responsible for the main flow in the body of the fluid (i.e., away from the effect of solid surfaces). For viscous forces (VF), their magnitude may be written as

O2U

I VFI

[.I,U

(2.24)

---> OX2

D 2

where, as defined earlier, Ix is the viscosity of the air. Such forces occur close to flow boundaries where the fluid is undergoing 'shear', and are the forces responsible for what we refer to as 'friction' associated with energy loss. Such energy loss occurs in the form of heat. From Equations (2.23) and (2.24), the ratio of these forces is

IIFI

Pair

-

UD -= Re

(2.25)

IVf[ and this dimensionless quantity is known as the Reynolds' number (Re, after Sir Osborne Reynolds, a pioneering British fluid dynamicist of the late 1800s). For the microscopic flow of air about a small airborne particle, for example, D would be the particle diameter and U the relative velocity between the particle and the surrounding air. For the macroscopic flow of air in a pipe, D now becomes the internal diameter of the pipe and U the mean air velocity inside the pipe. The same result as Equation (2.25) can be achieved by purely dimensional arguments, and it is instructive to present this alternative approach. This follows the law of dimensional analysis which states that, for any physical system, any solution for its behaviour must be independent of the system of units using for describing it. Here we begin by making a list of all the possible basic independent physical variables that can influence the behaviour of the system in question, and noting their dimensions. For most fluid flow systems, the variables in question are the dimension D and characteristic velocity U as already defined. Now we assign the dimensions M - time, L -- length and T - time. To achieve similarity by the dimensional argument requires D a U b Pair c p.d =

dimensionless in M, L and T

For the variables indicated we have D in [LI U in [L T -1] [3air in [M L -3] I~ in [M L - 1 T - I ]

29

(2.26)

Aerosol science for industrial hygien&ts From the dimensional statement in Equation (2.26), we must now ensure that the dimensions of M, L and T are each zero. This results in the three equations ForM, c + d = 0 ForL, a+ b + 3c-d-0 For T , - b - d = O By setting a --1, we may solve these three equations simultaneously to determine b, c and d. It is a simple matter to obtain b = 1, c - 1 and d = - 1 . Thus, the dimensionless group which achieves the dynamic scaling required is again D U Pair =- Re

(2.27)

as in Equation (2.25). The Reynolds' number concept identified in this discussion embodies some of the most important ideas in the whole of fluid dynamics. Physically, its meaning is rooted in the boundary layer concept. As described in the first analysis, it is effectively the ratio of the magnitude of inertial forces in the main body of the flow (e.g., near the axis of the pipe) to the magnitude of viscous forces close to the flow boundaries (e.g., near the pipe wall). For large Re (i.e., large U and D), it means that the boundary layer part of the flow has relatively small effect on the overall character of the flow system as a whole. On the other hand, for small Re (i.e., small U and D), the boundary layer flow and associated viscous effects dominate. Many properties of the flow (e.g., streamline pattern, drag force, etc.) vary quite sharply with changes in Re at small values of Re, but become much less sensitive to changes at large values. In general, for dynamical similarity to occur in the shape and nature of fluid flows having geometrically similar boundaries, Re should be kept constant. Thus, for example, for a pair of such flows (say System 1 and System 2) where the dimensional scale of System 1 is 10 times greater than that for System 2, then the characteristic velocity in System 1 should be 10 times less.

Example 2.6. Consider the flow of air at atmospheric pressure moving through a pipe of diameter 10 cm at a mean velocity of 2 m s -1. What is Reynolds' number and what is the nature of the flow? Pair -- 1 . 2 9 3

kg m -3

Ix -- 1 8 . 3 x 1 0 - 6 N s m - 2

30

The properties of air and gases so that 0.1[m] x 2[m s-11 X 1.293[kg m -31 R E -18x10-6[N s m -2]

14,250 Here Re is large, so inertial forces dominate.

Example 2.7. Consider from the same point of view the flow of air around a small particle of diameter 10 txm where the relative velocity between the air and the particle is 1 mm s -1. 10-5 x 10-3 x 1.293 Re = 18 x 10 - 6

0.0007

*

Here Re is very small, so viscous forces dominate.

The following easy-to r e m e m b e r expression is useful and accurate enough for most workplace or laboratory estimates" Re-

7 x 104DU

(2.28)

where D is in [m] and U is in [m s - l ] .

Potential flow

For large enough Re, a given flow system may be treated for many purposes as if it were inviscid (i.e., having zero viscosity). Then the N a v i e r - S t o k e s equations become much simpler and amenable to mathematical treatment. In fact, they become equivalent to equations familiar to physicists and engineers working in other fields ~ for example, the flow of heat in a t e m p e r a t u r e field or the flow of electric charge in an electric field. Hence we refer to potential flow. Despite the idealised nature of its underlying assumptions, potential flow solutions have many practical applications relevant to industrial hygiene. For e x a m p l e , they have been widely (and successfully) used to describe the flow around aerosol sampling devices and the hoods of local exhaust ventilation systems.

31

Aerosol science for industrial hygien&ts

Stagnation In addition to the features already described, a moving fluid is also characterised by static pressure and velocity pressure. The first of these is associated with the potential energy of the flow, and the second with its kinetic energy. The sum of these two pressures is the total pressure, associated with the total energy in the system. These are concepts which are familiar in relation to the design and characterisation of ventilation systems. They relate in particular to what happens along a streamline of the fluid motion. One important property of a streamline is that, everywhere along its length, the sum of the local static pressure and the local dynamic pressure remains constant. This is the well-known Bernouilli theorem. In a given streamline pattern, it is not inconsistent that an individual streamline may intersect with a solid flow boundary. This does not imply that there is any flow into the surface. Rather it describes the limiting case where the fluid comes to rest at that point. Here, therefore, all the energy in the flow is converted into potential energy in the form of static pressure and so the dynamic pressure falls to zero. The value of the static pressure therefore becomes a maximum, and so the point where the streamline intersects with the surface is known as the stagnation point. To an industrial hygienist, this has two aspects of practical interest. The first is that stagnation points on surfaces (e.g., near the entrances to samplers or to ventilation ducts) are where there tends to be maximum aerosol deposition. The second ~ and incidentally as far as this book is concerned ~ is that it provides the principle of operation of the pitot-static tube which is widely used in velocity measurement. A typical example of the phenomenon of stagnation is given in Figure 2.8.

Separation The phenomenon of boundary layer separation is particularly important for flow about a body and is associated with the distribution of static pressure

Stagnation point (velocity falls to zero) /

Dividing streamline (or streamsurface) Figure 2.8.

Illustration of the phenomenon of stagnation.

32

The properties of air and gases

over the body surface. For idealised frictionless inviscid flow, there is no net loss of energy along a streamline as it approaches the body, diverges to pass around it, and then recovers on the downstream side. This is because it is assumed that there is no velocity shear (and hence no energy losses due to viscosity) near the boundary. There is just the transformation of potential energy to kinetic energy (as the streamlines get closer together and, hence, the velocity increases) and back to potential energy again. However, for a streamline which passes close to the surface and where there are friction losses due to viscosity (the real situation), not all of the initial potential energy is recovered. The result is that the fluid in the boundary layer close to the surface of the body (on its downstream side) comes to rest prematurely. When and where this occurs, the flow breaks away from the body, enclosing a negative-pressure recirculating region which may or not be turbulent (depending on the characteristic Re-value for the flow, as discussed below). Some typical separated flows are illustrated in Figure 2.9.

(a) Sphere with stable wake cavity

(b) Surface-mounted block

///////////

////

/7// Q

|

-------Stagnation points

Region of separated flow

Figure 2.9. Illustration of some typical separated flows: (a) sphere with a relatively stable wake 'cavity' ('doughnut-shaped' region of recirculating flow); and (b) surface-mounted block (e.g., as for a building in the atmospheric wind). (From Vincent, J.H., Aerosol Sampling: Science and Practice, Copyright 1989, adapted by permission of John Wiley and Sons Limited)

33

Aerosol science for industrial hygienists Turbulence

No discussion of fluid mechanics relevant to practical applications, no matter how elementary, would be complete without mention of the p h e n o m e n o n of turbulence. This was first identified by the aforementioned Sir Osborne Reynolds in the nineteenth century during his classic experiments with fluid flow in pipes (which led directly to the formation of the Reynolds' number concept). This complex and fascinating phenomenon is certainly relevant to many aspects of air flows in the context of industrial hygiene. The starting point for a qualitative discussion is the ideal, non-turbulent case known as laminar flow, in which ~ as stated earlier ~ the layers of the fluid (i.e., between the streamlines) slide smoothly over one another. However, from the Navier-Stokes equations it can be shown theoretically that, if inertial forces are large enough in relation to viscous forces (i.e., Re is large enough), then a disturbance in velocity of sufficient amplitude introduced into the flow can lead to overall instability. Such a disturbance might arise, for example, due to the passage of the flow around some sort of flow blockage and the resultant flow separation. Fluid mechanical amplification of the resultant triggering disturbance leads to a state of overall instability which appears as randomly-fluctuating motions superimposed on the mean flow. Two of the consequences are: (a) an apparent increase in the viscosity of the fluid (which, in the example of flow through a pipe, would appear as an increase in resistance to the flow); and (b) an accompanying sharp rise in its mixing properties. In the light of the latter, it is necessary to qualify the earlier comment about the inability of fluid to be transported across streamlines. Strictly speaking, this applies only to laminar flow. For turbulent flow, the resultant turbulent mixing provides a mechanism for the exchange of fluid elements across streamlines ~ in both directions. However, it remains that there can be no net transfer of fluid when transport is averaged over time. Turbulence itself is an extremely complex phenomenon and cannot be treated in detail in this book. However, industrial hygienists need to be aware of its existence and recognise where it can play a role, not just in aerosol aspects but also in relation to ventilation and air movement in general. The macroscopic properties of turbulence are especially important. For a given turbulent flow, if it is visualised at an instantaneous point in time, its streamline pattern will appear to be highly chaotic. However, averaged over time, the more-familiar streamline pattern is restored. Once a disturbance has occurred and turbulence has been established, it is important to recognise that the consequences referred to are associated with the properties of the turbulence and are not intrinsic properties of the fluid per se. So the apparent increase in fluid viscosity is just that ~ apparent. It is an externally observed property of the bulk fluid motion. Meanwhile the basic internal viscosity of the fluid, determined by the individual molecular motions of the gas as 34

The properties of air and gases described by kinetic theory, remains the same. From practical observation, it becomes clear that, in a given flow system, turbulence usually occurs when Re exceeds a certain value. That value depends on the flow system in question, whether it be the flow in a pipe or duct, flow in a boundary layer, or around a bluff flow obstacle (e.g., a small particle), etc. For each such system, Re can be calculated from the characteristic dimension and velocity, using either Equation (2.27) or the easy-to-remember Equation (2.28). Typically, for most practical systems like those listed, the threshold value of Re for the onset of turbulence is around 2000-3000. At the microscopic level, the origin of the turbulence has already been described as a small initial disturbance. Clearly, this in itself cannot provide the energy which drives the intense turbulent motions like those usually encountered. This must derive from the mean flow itself. Once the flow has been rendered unstable by the action of the mean flow, the initial and relatively large-scale ~ fluctuating motions (i.e., eddies) created by the triggering disturbance are stretched and distorted, and so are broken down successively into smaller and smaller eddies. The energy from the mean flow which goes into the turbulence is therefore handed down ~ in a so-called 'cascade' process ~ through the resultant range of eddy sizes until, eventually, the eddies become very small. At that point, when the Re-values for the eddies themselves become very small, viscous forces take over inside the eddies and the energy is therefore finally dissipated as heat. From this qualitative description, there emerges a physical picture of turbulence as an irreversible spectral phenomenon, characterised by a continuous distribution of eddy sizes and associated velocity fluctuations (superimposed on the mean flow). One important feature of this picture is that the energy that goes from the mean flow into the turbulence can never be recovered as useful kinetic energy. This is a consequence of the second law of thermodynamics, one of the most important laws of physics. For many working purposes relevant to industrial hygiene, the picture of turbulence may be simplified so that the phenomenon can be described in terms of two 'bulk' properties; the characteristic intensity of the fluctuations (U', the root-mean-square value of the fluctuating velocity) and the characteristic mean length scale of those fluctuating motions (l). The degree of mixing increases with both, and a fair estimate of the diffusivity of a turbulent fluid (Dft) is given by Dft ~ lU'

(2.29)

which, as can be seen by inspection has the correct dimensions of [L2T-1], or [m 2 s -1] in the SI system of units. The scale and intensity of turbulence can vary greatly from one situation to another.

35

Aerosol science for industrial hygienists

Example 2.8. Estimate the diffusivity of turbulent air moving in a pipe of diameter 10 cm at mean velocity 1 m s -1 and where the intensity of turbulence is given as 3%. Note that the intensity of turbulence is given by U

t

- 0.03 U where, as before, U is the mean velocity. The characteristic length scale (l) cannot exceed the diameter of the pipe. A rough estimate is 3 cm. From Equation (2.29), we get Oft ~ 3 X 10 - 2 [m] • 0.03 [m s -1]

*

Dft ~ 1 0 - 3 m 2 s - 1

It is i n t e r e s t i n g to n o t e t h a t Dft as c a l c u l a t e d h e r e is t w o o r d e r s of m a g n i t u d e g r e a t e r t h a n the classical diffusivity of gas m o l e c u l e s q u o t e d e a r l i e r ( = 10 -5 m 2 s - l ) . In m o s t practical s i t u a t i o n s in w o r k p l a c e s , the scale a n d i n t e n s i t y of t u r b u l e n c e will be c o n s i d e r a b l y g r e a t e r still.

REFERENCES Schlichting, H. (1968). Boundary Layer Theory, 6th Edn. McGraw-Hill, New York. Vincent, J.H. and Mark, D. (1982). Application of blunt sampler theory to the definition and measurement of inhalable dust. In: Inhaled Particles V (ed. W.H. Walton). Pergamon Press, Oxford, pp. 3-19.

36

CHAPTER 3

Properties of aerosols 3.1 AEROSOL GENERATION IN WORKPLACES Many industrial processes generate aerosols in one form or another, usually as a side effect of the process itself and by a wide variety of physical and chemical means. The list of possibilities outlined below is far from exhaustive, but serves to indicate the range of types of aerosol that need to be recognised and dealt with in the field. Mechanical generation of dry aerosols Mechanical generation of dry aerosols in the form of airborne dust particles occurs as a consequence of many industrial processes. For example: In the mineral extraction industries (e.g., coalmining, iron ore mining, quarrying, etc.), during the excavation and cutting of rock and during subsequent crushing, grading, sieving, riddling, transportation, handling, bagging, etc; In the textiles industries (e.g., cotton, flax, asbestos) during bale and bag opening, and subsequently during various processes such as carding, spinning, winding, weaving, etc; In the chemical industries (e.g., silica gel, fertilisers) during the processing, handling and transportation of bulk powders and aggregates, etc; In foundries during moulding, sand blasting, etc; In the wordworking industries (e.g., furniture) during the cutting, working and sanding of hard and soft timbers, etc; and many others. In these, the principl~ physical processes of aerosol generation are associated with the fracture, breaking and cutting of large pieces of bulk material objects into smaller ones (and the creation of new 37

Aerosol science for industrial hygienists surfaces), abrasion, agitation, the breaking of adhesive forces (e.g., van der Waals, electrostatic) holding primary particles together in aggregates, entrainment into the air, etc. Of course, the amount of aerosol generated by such means varies with the nature and condition of the bulk material in question. But, for a given material, it tends to increase with the energy given to the dispersal process. It is also strongly sensitive to whether the material is hydrophilic (i.e., can absorb water), influencing the surface binding forces which hold the bulk material together. In turn, it is dependent on the previous history of the material (i.e., processing, additives, etc.) and on the humidity of the atmosphere in which it is held. Other factors include the friability of the bulk material ~ that is, its ability to be broken or crumbled. The actual process of aerosol generation and dispersal is also ultimately dependent on the movement of the surrounding atmosphere. As indicated in Chapter 2, there is in principle no upper limit on the size of individual particles produced in this way. The industries given as examples above are well-known to be 'dusty' and have long been the subject of industrial hygiene interest. For materials like those described, it is therefore relevant to discuss the question of 'dustiness'. This term refers to the dust-generating capacity of certain types of bulk material when handled mechanically under specified conditions. Over the years, a variety of technical laboratory methods have been proposed which enable quantitative assessments to be made of relevant (and consistent) indices of dustiness, with the aim of enabling materials to be tested and placed in rank order with respect to this property. Two of these are illustrated in Figure 3.1. The one shown in Figure 3.1a is the gravity dispersion method, involving the dropping of known masses of sample bulk material from a given height into an enclosed space under defined conditions, and assessing the resultant dust cloud (e.g., by gravimetric sampling or optically). This is intended to simulate an industrial process by which bulk aggregated material undergoes a single drop (e.g., as in emptying a bag into a hopper). The version shown in Figure 3.1b is the mechanical dispersion method whereby the sample is dispersed by agitation. This is intended to simulate an industrial process where the aggregated material undergoes multiple drops or continuous agitation (e.g., as in a mixer, or during conveying). The version shown employs a rotating drum for this purpose. Another approach (not shown) is the gas dispersion method, involving the passage of a stream of compressed gas through the sample. In these (and other devices not shown), the concentration of the airborne dust resulting from the mechanical agitation is measured, either gravimetrically by weighing samples captured by aspiration and collected by impaction or filtration, or by remote optical sensing methods (the physical means of which are are described in later chapters). Inevitably, such dustiness estimation methods differ in important physical respects, and so it is not surprising to find that they tend to give differing results. Indeed, they do not necessarily even

38

Properties of aerosols

Figure 3.1. Illustrations of technical methods that have been proposed for measuring indices of 'dustiness' for bulk solid materials" (a) the gravity drop method; and (b) the rotating drum method.

place materials in the same rank order of dustiness ~ although, it might be argued, each might be a valid test for a particular class of industrial dust generation process. For many industries, and hence for many industrial hygiene situations, dustiness is a useful index upon which primary control strategies might be based. Therefore some move towards standardisation is required ~ and, in fact, is taking place. In recent years, a working party of the Technology Committee of the British Occupational Hygiene Society has carried out important work on dustiness estimation (Hammond et al., 1985). Based on this work Table 3.1 gives, by way of illustration for each of the methods shown in Figure 3.1, the relative dustiness index (using the average for all the 'dustiness' values obtained for each method as the basis of normalisation) and the rank order of dustiness. In this table, for each estimation method indicated, the original raw data (e.g., the figures obtained from the optical detector in Figure 3.1a, or from the aerosol sampled mass in Figure 3.1b) have been normalised by

39

Aerosol science for industrial hygienists Table 3.1. Relative 'dustiness' for a range of c o m m o n industrial materials as o b t a i n e d using the gravity dispersion and rotating d r u m m e t h o d s (see Figure 3.1) (based on data r e p o r t e d in H a m m o n d et al., 1985).

Material

Method

Rubber 'E' Rubber 'F' Rubber 'G' Sulphur Oil absorber Chalk Silica Charcoal

Gravity drop

Rotating drum

0.04(1) 0.36(3) 0.72(4) 0.20(2) 0.95(5) 1.39(6) 1.41 (7) 2.92(8)

0.02(1) 0.04(2) 0.14(4) 0.20(5) 0.05(3) 0.22(6) 2.81(7) 4.55(8)

Note: The figures given are tor the ratio of the dustiness for the material in question and the average of the values measured for all eight materials shown. The figures in parentheses are the rank orders of 'dustinbss' as measured by the two methods.

dividing each by the average for that method. It is seen that not only are the magnitudes of the relative dustiness different but so too (in parentheses) is the rank ordering between the two methods. Thus, the methods described are very empirical. Work is continuing on this important problem. Lyons and Mark (1994) have further extended the rotating drum method and determined the dustiness of a wide range of aggregated materials in terms of their abilities to generate aerosol falling within defined health-related particle size fractions (described in Chapter 8). In addition, at the time of writing this book, laboratories from a number of European countries are planning Pan-European research to investigate factors such as humidity, electrostatic charge, wall losses, adhesion, friability, particle size, and so on (C.M. Hammond, Michelin Tyre plc, U.K., personal communication). Similar efforts have been taking place in the United States (e.g., Heitbrink et al., 1990).

Mechanical generation of liquid droplet aerosols Mechanical generation of droplet aerosols can be achieved for any liquid provided that enough mechanical energy is provided in disrupting the surface of the original bulk liquid. Liquid droplet aerosols are less common in workplaces than dry dusts, but are found in some types of industry; for example: Processes where liquids are involved as the primary working material (e.g., paint spraying, crop spraying, etc.);

40

Properties of aerosols Processes where liquids are involved as the auxiliary material (e.g., machining fluids, electroplating, etc); and so on. They may also be found, perhaps ironically, as a side effect of certain technical measures (e.g., wet scrubbers in the underground mine environment) which are sometimes employed for the control of dry dusts. Physically, the droplet formation process involves the mechanical breaking of the surface tension forces which hold the bulk liquid together. This may be achieved, for example, by simply splashing or otherwise mechanically agitating the liquid surface; or more vigorously by virtue of the shearing forces associated with passing the liquid under pressure through a nozzle, by mixing the liquid with a compressed gas jet, or by the action of centrifugal forces, electrostatic forces, etc. The process is variously described as nebulisation, atomisation and spraying, the actual terminology employed usually reflecting the size of the resultant droplets (e.g., from small to large for the processes in the order indicated). The size of droplets produced is dependent on the energy that goes into aerosol generation, with the smallest particles usually being generated by the most energetic mechanisms. As mentioned in the previous chapter, the ultimate upper limit of size of droplet sustainable once the aerosol has been formed is governed by the balance between surface tension forces (tending to hold the molecules of the droplet together) and gravitational and shearing forces (tending to distort and, ultimately, disrupt the droplet). Formation by molecular processes

The other class of basic aerosol generation processes involves the formation of particles by the aggregation of molecules, by physical condensation and/or chemical reactions. Physical formation by this means is usually known as nucleation, and involves the kinetics of molecular transfer from the gas to the liquid phase and thereafter, possibly, the solid phase. Heterogeneous nucleation refers to the most common version of the process, involving the condensation of molecules onto pre-existing surfaces in the form of very small (sub-micrometre) aerosol particles known as condensation nuclei. Normal atmospheric air contains sufficient numbers of such particles to enable this process to occur readily if the physical conditions are favourable. In particular, the atmosphere needs to be supersaturated so that the saturation ratio (SR) is greater than 1 (see Chapter 2). This requires the cooling of air that is already saturated, as occurs for example in the atmosphere prior to the formation of the water droplets that go to make up clouds and fogs. Here, therefore, the surface of any insoluble solid nucleus will have a layer of adsorbed vapour molecules, thus providing the starting point for the arrival of more molecules, in turn leading to droplet formation and growth. Whether

41

Aerosol science for industrial hygienists or not that growth can proceed ~ and how far it can proceed ~ will depend on the physical conditions required for such evolution. This is discussed later in this chapter. For a soluble solid nucleus, the process is somewhat different. For such substances which have a strong affinity for water, the conditions for the condensation of water molecules is more favourable than for insoluble nuclei, and so droplet formation can take place at lower values of S R. Homogeneous nucleation is less common, and refers to the spontaneous formation of liquid droplets by the transfer of molecules directly from the gas phase. It does not require the pre-existence of small particulate nuclei. Here, however, the conditions for nucleation are less favourable. So considerably higher values are required for the supersaturation ratio, with typically S R > 4. Much of the preceding discussion is focused on the common example of the formation of water droplets in humid air. But the same processes can occur with other materials; for example, in the condensation of hot metal vapours to form the primary particles which are the 'building blocks' of metal fume (e.g., during the cooling of the plasma in arc welding). Here the processes leading to the formation of aerosol particles recognisable as being associated with the processes in question are very complicated, involving the production of very fine primary particles of nanometre dimensions and their subsequent aggregation into complex structures which, although they are much larger than the original primary particles, are still relatively fine (micrometre-sized). Such processes are characterised by the involvement of heat energy, and so conditions may sometimes be favourable for chemical reactions also to occur. This, therefore, leads to another version of the molecular formation process, chemical formation. This occurs when certain types of free radical species present in the air act as nuclei upon which other molecules may interact and react chemically. Examples include the formation of soot particles during the combustion of hydrocarbons (e.g., as in the burning of fossil fuels) and the formation of oxides in a metallic arc (e.g., as in welding). The complicated kinetics of the processes described require detailed discussion which is beyond the scope of this book. A more rigorous discussion appears in several texts, including that by Friedlander (1977).

3.2 T H E E V O L U T I O N OF A E R O S O L S It should not be assumed that an aerosol, once it has been dispersed, will necessarily retain the properties with which it began. Depending on the material in question, the initial generation process and the concentration of the aerosol, and other conditions in the surrounding air, a number of possibilities exist for evolutionary changes. These include" (a) growth by coagulation, agglomeration, coalescence and condensation; and (b) diminution by disintegration and evaporation. 42

Properties of aerosols Coagulation, agglomeration and coalescence If particles in an aerosol can come into contact with one another and, in so doing, remain joined together, then the total number of airborne entities in the aerosol is reduced whilst the effective entity size is increased. At the same time, however, the mass concentration remains the same. One mechanism by which the particles come into contact is thermal in origin, derived from their random (or Brownian) motions governed by collisions with gas molecules whose own random velocities are a function of gas temperature as described by the classical kinetic theory of gases. Another mechanism is so-called kinematic coagulation, where particles are brought together as a result of their different migration velocities under the influence of an externally-applied force field. One example of this mechanism involves gravity, in which particles of different sizes in still air fall at different velocities. Here the slowly-falling small particles are overtaken by the faster-falling larger ones, and so become engulfed by them. Whatever the actual mechanism, this process is commonly referred to in general as coagulation, although it is also sometimes called agglomeration or more appropriately for liquid droplets where the joining of two or more spherical droplets results in a single larger spherical droplet ~ coalescence. For thermal coagulation, the dynamics of the process is continuous and its full description complicated. However, a simplified collision model can shed useful light, indicating that the rate at which the process occurs depends on the size of the particles, their thermal velocities and their instantaneous airborne concentration. The process is discussed more fully in Chapter 4. The converse to the process of coagulation is disintegration. This occurs when a system of particles which has previously combined together to form a single particle is subjected to external forces such that the adhesive and cohesive bonds which hold its individual elements together are broken. In particular for systems where the individual elements are small, such binding forces are strong and they are not readily overcome. For example, therefore, fine fume or smoke aggregates of nanometre-sized primary particles are not prone to break-up. However, in strongly sheared flows (e.g., in some types of sampling device such as an impactor) or in strong turbulence, shear forces can be encountered which are sufficient in magnitude to cause the break-up of dusty agglomerates and the shattering of large droplets. Such particles can also be broken up during high velocity impaction onto surfaces.

Condensation and evaporation We have already discussed the subject of condensation in connection with the initial aerosol formation out of the vapour phase. Depending on the ambient conditions, condensation may continue after formation, with molecules 43

Aerosol science for industrial hygienists entering the particle from the vapour phase, leading to particle growth, and hence changes in the particle size distribution of the aerosol (towards larger particles) and an increase in its airborne mass concentration. Alternatively, the ambient conditions may be such that evaporation predominates, with molecules leaving particles and entering the vapour phase. Now particles become smaller and the aerosol mass concentration decreases. The basis for a physical discussion of these phenomena has been given in Chapter 2. However, it should be noted that the description there assumed the liquid surface to be flat. For the case of the curved surface of a liquid droplet, the kinetics of the transport of molecules inside and outside of the surface is modified by the change in geometry. Specifically, for given pressure and temperature, the smaller the droplet the greater the partial pressure which is required to maintain equilibrium at the liquid surface. This is known as the Kelvin effect, and is important to the discussion about the growth of droplets by condensation ~ or conversely diminution by evaporation. For the droplet to maintain a constant size, the equilibrium value of the saturation ratio (S R = eqSR) is given by eqSR = exp

(

}

pRdeqT

(3.1)

deq is the equilibrium droplet size, 13 the coefficient of surface tension for the liquid in question, M is its molecular weight, p is its density, and R is the universal gas constant. Note here that S R = Pv/P~v as before (Chapter 2). But now, whereas p~ is the equilibrium partial pressure at the liquid droplet surface, p~,, is the saturation vapour pressure corresponding to a flat liquid surface. where

Example 3.1. For a water droplet of diameter 0.01 txm in air at 20~ saturation ratio required to maintain it at that size?

what is the

Note that 13 = 7 2 . 7 x 1 0 - 3 k g s - 2 M = 18 g m o l e - 1 = 0 . 0 1 8 k g m o l e - 1 p = 103 k g m - 3 R = 8 . 3 1 4 k g m 2 s - 2 ~ -1 m o l e - 1

From Equation (3.1) we get (4 x 72.7[kg S -2]

X

O.O18[kg mole-l])

ln{eqSR} = (103[kg m -3] x 8.314[kg m2s -2 o K - l m o l e -1] x 10-8[m] x 293[~ = 0.2148

44

Properties of aerosols *

eqSR = 1.24

Note that, similarly, for a water droplet in equilibrium at diameter 1 I~m, we obtain eqSR about 1.002 F o r a d r o p l e t of g i v e n d i a m e t e r a n d for a n y v a l u e of S R less t h a n t h e e q u i l i b r i u m v a l u e c a l c u l a t e d f r o m E q u a t i o n ( 3 . 1 ) , t h e d r o p l e t will s h r i n k by e v a p o r a t i o n . H o w e v e r , if S R is g r e a t e r , t h e d r o p l e t will g r o w b y condensation.

1.008

~R

0.1

1.0 d (p,m)

1.008

/

/

~R 1.000

0.996 0.1

1.0

I0

d (p,m)

Figure 3.2. (a) Equilibrium saturation r a t i o (eqSR) as a function of droplet diameter (d) for pure water (at 20~ The curve derives from the Kelvin equation (Equation (3.1)) so that a droplet described by conditions in the hatched area above the curve will grow while one in the hatched area below will shrink. (b) Equilibrium saturation r a t i o (eqSR) as a function of droplet diameter (d) for sodium chloride solution (at 20~ where the figures on the curves relate to the mass of sodium chloride present in the droplet. (Note that the concentration of sodium chloride decreases as the size of the droplet increases.)

45

Aerosol science for industrial hygienists From Equation (3.1), it is seen that each equilibrium droplet size (for a given liquid) is uniquely associated with a given value of eqSR. The effect is illustrated for droplets of pure water in Figure 3.2a. In this figure, the region above the curve represents conditions (S R, d) where droplet growth will occur; the region below the curve is where droplets will shrink. One important practical result is that, in a polydisperse system consisting of different-sized droplets and for a given value for SR, larger particles may grow by condensation while the smaller particles shrink by evaporation. So we have a situation where larger droplets can become even larger at the expense of smaller droplets. In many practical cases of heterogeneous nucleation, the starting nucleus is made up of a solid material which is soluble in the liquid in question (e.g., salt in water). Here, as the droplet grows by condensation, the composition of the droplet changes, and this in turn influences the kinetics of molecular motion and hence of particle growth. This is shown for sodium chloride in Figure 3.2b, where it is seen that the effect is towards the potential for enhanced growth (i.e., the region above the curve is enlarged). The effect is the most marked for smaller droplets. An excellent fuller description of the evolution of droplets by condensation and evaporation is given by Hinds (1982). Such considerations are certainly important in extreme situations (e.g., inside some industrial processes) and are relevant to aerosol long-term behaviour in the atmosphere. But they may also be relevant to some workplace exposure situations where droplet aerosols are formed. They can be particularly important in relation to health effects for some types of particle which, when inhaled into the lung where the air is further humidified, can subsequently grow by condensation during transport inside the respiratory tract. This in turn can lead to significant effects on regional deposition.

3.3 P A R T I C L E M O R P H O L O G Y Particle shape classification Particle shape can have a significant bearing on effects relevant to industrial hygiene; for example, on the way particles behave in the air, and how they behave after they have been deposited in the respiratory tract. Particle shape falls into a number of categories, some of which are illustrated in Figure 3.3. Firstly there are aerosols in which particles are spherical, including liquid mists, fogs and sprays (unless, of course, the droplets are so large that they become distorted by the effects of gravity and shearing forces) and some dry aerosols (e.g., glassy spheres condensing out of some high temperature 46

Properties of aerosols

Figure 3.3. Illustrationof typical shapes of particles found in the industrial work environment.

processes). Idealised spheres (e.g., of polystyrene latex) are also artificially produced in the laboratory for some aerosol research applications. Secondly, there are non-spherical, angular particles which have no preferred dimension or whose aspect ratio cannot be said to be substantially different from unity. These are referred to as regular or isometric. Thirdly, there are essentially two-dimensional, flat platelet particles. Finally there are long, thin, rod- or needle-shaped particles, referred to as fibrous or acicular. Particles typical of aerosols at mineral extraction industry workplaces (such as coalmining or quarrying) are usually angular but tend to be isometric in shape, not exhibiting any obvious difference between length and breadth. But there are some exceptions. For some dusts arising, for example, during extraction of anthracite or minerals from mica-bearing rock, there are substantial populations of platelet-like particles. Particles from aerosols in the atmospheres of textiles factories exhibit a variety of morphological properties, ranging from isometric like those just described to elongated ones (see the examples in Figure 3.4). For the cotton, flax and jute industries, most of the finer particles tend to be irregular but not obviously fibrous. These tend to be fragments which may not necessarily be intrinsic to the basic textile material itself but which may have become attached to the bulk material during its previous history (e.g., dirt, detritus, biological entities, etc.). On the other hand, there do tend to be fibrous entities amongst the coarser particles, and these are more likely to be of the basic textile material. In the case of asbestos aerosols, most of the particles tend to be both very fine and elongated, and are therefore markedly fibrous. The same is true for aerosols found in the man-made mineral fibres industries.

47

Aerosol science for industrial hygienists

Figure 3.4a

Figure 3.4b

48

Properties of aerosols

Figure 3.4c

Figure 3.4d

49

Aerosol science for industrial hygienists

Figure 3.4e Figure 3.4.

Photographs of actual dust particles typical of those actually found in workplace atmospheres in the textile industries.

The welding fume example illustrated in Figure 3.5 reveals another morphological property exhibited by some aerosol particles. Here, as already mentioned, the particles of the aerosol exist in the form of complex structures, each one made up of a large number of very much smaller (nanometre-sized) primary particles formed during condensation from a hot metallic vapour. This property leads to the concept offractal geometry which has only relatively recently been applied to aerosol particle morphology. As first introduced by Mandelbrot (1983), the main property of an object exhibiting fractal properties is the fact that its detailed structure repeats itself when viewed at progressively larger magnifications, a phenomenon sometimes referred to as 'self-similarity'.

Figure 3.5. Picture of a typical welding fume particle.

50

Properties of aerosols Fibres

No discussion of workplace aerosols can be conducted without drawing special attention to the morphological properties of fine fibrous aerosols (of which asbestos is the most widely-discussed example). For such particles, significant adverse health effects are known to be associated with inhalation exposure, and the two dimensions of particle length and diameter, respectively, are both independently relevant to the risk. On the one hand, it is the particle's diameter which (largely) governs its aerodynamic motion and hence its ability once inhaled ~ to penetrate far down into the deep lung (see Chapter 4). On the other hand, it is the particle's length which mainly influences how well the lung's defence mechanisms can cope with the particle after it has been deposited (see Chapter 7). The morphology of asbestos fibres is further complicated by the fact that, for some types (e.g., chrysotile), the fibres are not straight, but tend to be flexible and curly. In addition, closer inspection of chrysotile fibres under the electron microscope reveals that they are made up of bundles of even finer fibrous elements (or fibrils). Under certain conditions (e.g., under the action of lung fluids after deposition in the respiratory tract), such particles may be broken down into their much finer fibril constituents. Although serious interest in the health effects associated with the inhalation of fibres began with asbestos, attention in recent years has also turned to other materials from which airborne fibres can be generated, including glass and carbon fibre. From this has emerged the concept of a 'durable fibre': that is, one that can persist for a long time in human tissue. 3.4 A E R O S O L C O N C E N T R A T I O N Interest in aerosol measurement by industrial hygienists is stimulated by the practical need to assess the exposures of people at work to potentially harmful particles, to use the information gained to assess risks to health, and to provide a basis for the setting and maintenance of standards. For workplace aerosols, such concentration is usually expressed in terms of particulate mass per unit volume of air, most commonly in units of milligrams per cubic metre (mg m-3), in contrast to atmospheric aerosols for which concentrations tend to be orders of magnitude lower and so are usually expressed in terms of micrograms per cubic metre of air (Ixg m-3). A related property of practical interest for some particles (e.g., durable fibres, bacteria) is the number concentration (particles m-3). It is fair to say that, although such concentration indices might not always be the best in relation to a given aerosol-related health risk, the choice in practice is often dictated by practical measurement considerations. A good example of this dilemma is the case of fibres. Here, because the health risk is known to be associated with very small

51

Aerosol science for industrial hygienists fibre concentrations which are usually present with much larger amounts of other non-fibrous particles, the selection and counting of such particles when viewed under the microscope is the only realistic practical approach currently available. Generally speaking, aerosol concentration is analogous to a gas density. Thus, it may be described in terms of its spatial distribution, implying in turn that it can be described mathematically by a continuous function. In reality, this view needs to be qualified since each 'point' can only be defined in the limit as the volume in space with dimensions no smaller than the mean distance between particles. For most practical purposes, it is indeed a reasonable starting assumption that the spatial distribution of concentration is continuous. But caution is required when the concentration of the aerosol of interest is very low ~ for example, in the case of an aerosol which, because of the known extreme hazard to health, is controlled to very low levels by stringent technical measures (e.g., radioactive aerosols, certain biological aerosols, asbestos, etc.). In such cases, in interpreting results for measured aerosol concentration from sampling exercises, statistical problems could arise from the lack of continuity in the aerosol's spatial distribution. This is a potential trap for the unwary industrial hygienist. How should he (or she) interpret the result in the case, for example, where an apparently large concentration may be due to the collection during an 8-hour sampling shift of a single very large, but potentially dangerous, particle?

3.5 P A R T I C L E SIZE Particle size is a property which has already been mentioned as being extremely important in virtually all aspects of aerosol behaviour. But it is a property whose definition is not always as simple as might at first appear, and can be elusive. The simplest case is that of a particle which is perfectly spherical. By definition, this has only one dimension ~ its true geometric diameter (say, d). This is what would be obtained if the spherical particle were to be sized under a microscope. But in nearly all practical situations, particles are not spherical, as shown in most of the examples given in Figures 3.4 and 3.5. For these, because of the particle geometric non-uniformity, no single geometric dimension can be assigned. Therefore, another index must be found to enable 'size' to be defined. This leads to definitions described in terms of one or more 'effective' or 'equivalent' diameters not true diameters as such but dimensions derived from knowledge of some other property (or combination of properties) of the particle. Firstly, if we were to examine a two-dimensional picture of a non-spherical particle, a 'characteristic' effective geometric diameter could in principle be identified. There are a number of ways of achieving this, as shown in Figure 3.6. For example, the Feret diameter (dr) is the width of the particle 52

Properties of aerosols

Figure 3.6.

Illustration of how the Feret and Martin diameters are defined as indices of particle size for a non-spherical particle.

contained within a pair of parallel tangents to its image when viewed in two dimensions. The Martin diameter (dM) is the length of the chord which divides the two-dimensional picture of the particle into two equal areas. Such measures of particle size cannot be unique for an individual particle, since the choice of orientation of the defining line in each instance is arbitrary. But provided that the measurement ~ notably with respect to the placement of the microscope cross-wires ~ is always made in the same direction, useful results can be obtained for ensembles of particles. However, these approaches are rarely used nowadays in industrial hygiene. In general, for more quantitative purposes, other definitions are generally more appropriate. For example, the equivalent projected area diameter (dp) is the diameter of a fictitious sphere which, in two dimensions, projects the same area as the particle in question. This too, however, is dependent on the orientation at which the particle is viewed, and so is most appropriate for ensembles of particles. But there are two other definitions which are unique for a given individual particle. First we have the closely-related equivalent surface area diameter (dA). Both dp and d A a r e relevant to many aspects of the visual and optical appearance of aerosols. Then there is the equivalent volume diameter (dv), the diameter of a sphere that has the same volume as the real particle in question, and is relevant to the drag force the particle experiences as it moves through the air. These three concepts are illustrated in Figure 3.7.

53

Aerosol science for industrial hygienists

Figure 3.7. Illustration of how the equivalent projected area, surface area and volume diameters are defined as indices of particle size for a non-spherical particle. E x a m p l e 3.2. Calculate the e q u i v a l e n t surface a r e a d i a m e t e r for a 10 I~m • 10 txm • 10 txm cube. The cube has 6 sides, each of area 100 Total surface area = 600

ixm 2

Surface area of the equivalent sphere By definition,

7rdA2 --

p~m 2

600

= ~dA2

p~m 2

600 So d A = V'

) = 13.8 ixm

7/"

E x a m p l e 3.3. Calculate the e q u i v a l e n t v o l u m e d i a m e t e r for a straight cylindrical fibre o f l e n g t h (L) e q u a l to 50 Ixm and d i a m e t e r (d) e q u a l to 2 txm.

7rd2L The fibre has volume =

= 157 ixm 3

54

Properties of aerosols rrdv3 V o l u m e of the e q u i v a l e n t s p h e r e -

By definition, 7rdv3/6 = 157 txm 3 *

So d v = 3~/' (942/rr) = 6.7 Ixm

For embodying many aspects of the airborne behaviour of particles, however, none of the above definitions of particle size is sufficient. More appropriately for many applications, d v may be combined with knowledge of particle density and shape in order to arrive at the aerodynamic diameter (dae). As will be seen as this book progresses, this last definition is one which is the most widely used in the industrial hygiene context. There are some types of particle where further considerations need to be invoked. This is the case, for example, for fibres where, for a full description of particle size, both diameter and length should be defined. Complex aggregates such as those (e.g., smokes) formed during combustion also pose special problems. As already mentioned, these are made up of large numbers of very small primary particles and the degree of complexity is such as to render difficult the definition of size in relation to any of the measurable geometrical properties like those described above. So, although aerodynamic diameter can be usefully applied to describe aerodynamic behaviour, and a geometrical diameter can be applied to describe aspects of visual appearance of individual particles or aerosols as a whole, these do not always properly convey the full nature of the particles. Here, therefore, Mandelbrot's concept of fractal geometry can convey additional information. As already stated, this applies to the properties of some types of particle which reflect the tendency to exhibit self-similar structure. This means that, when viewed at increasing magnifications, the structure of the particle appears in greater and greater detail ~ but that at each scale the structure appears to be geometrically similar. Application of fractal geometry to a particle of complex shape leads to a relationship of the form N ~- Rgf

(3.2)

where N here is the number of primary particles making up the aggregate and f is the fractal dimension. In this expression, Rg is the radius of gyration of the particle, another measure of particle size (not used elsewhere in aerosol science), given by Moment of inertia

) 1/2 (3.3)

Rg =

Mass

55

Aerosol science for industrial hygienists Typical particles in smoke aerosols generated during combustion may contain from 102 tO 105 primary particles, and f may take values ranging from 1.4 upwards. As already stated, fractal considerations are relatively new in aerosol science. However, many aerosols of the type having fractal properties (e.g., combustion aerosols) also have important occupational health implications. So it is quite likely that, one day, such fractal properties might become of more direct interest to industrial hygienists. Meanwhile, the general fractal concept is finding increasing application not only in relation to particle morphology in aerosol science but also elsewhere to the structure of turbulence, filters, the lung, and so on.

3.6 E L E M E N T A R Y P A R T I C L E SIZE STATISTICS Only rarely in practical situations ~ usually under controlled laboratory conditions ~ do aerosols exist that consist of particles of all one size. Such aerosols are referred to as 'monodisperse'. More generally, however, in workplaces and elsewhere, aerosols consist of populations of particles having wide ranges of sizes, and so are termed 'polydisperse'. For these, particle size within an aerosol needs to to be thought of in statistical terms. The importance of this, as will be seen later, is that particles falling within specific size ranges (or aerosol size fractions) may be associated with different types of health effect. The first assumption that is usually made is that, for a polydisperse aerosol, its particle size characteristics can be described in terms of a distribution function that is continuous. That is, all particles sizes within the overall range of interest are possible, although not necessarily with equal probability. For most practical purposes, a rudimentary outline of the statistics is sufficient. Consider an ensemble of particles whose sizes can be represented in terms of a single dimension (say, d). The fraction of the total number of particles with size falling within the range d to d + d d may be expressed as

dn = n(d)dd

(3.4)

where oo

f

n(d)dd = N

(3.5)

0

in which n(d) is the non-normalised number frequency distribution function sometimes referred to as the number probability density function ~ and N here is the total number of particles in the ensemble under consideration.

56

Properties of aerosols Alternatively, we may consider the particle size distribution in terms of the mass frequency distribution function, m(d), where

dm = m(d)dd

(3.6)

and O0

f m(d)dd 0

= M

(3.7)

where M is now the overall mass of particles contained in the ensemble. Similar relationships may be written for other forms of the frequency distribution (e.g., in terms of surface area). They are all interrelated. Which form is actually used in practice depends on how particle size is measured. For example, if we were to count and size particles under a microscope, then the distribution would be obtained in terms of n(d). On the other hand, if we weighed samples which have been classified and collected according to size, then the distribution would be obtained in terms of m(d). It is often helpful in particle size statistics to plot distibutions in the alternative cumulative form. For example, for the distribution of particle number this is given in terms of the number with diameter less than d, thus d

Cn(d ) - j n(d)dd

(3.8)

0 In terms of mass, the

mass

with diameter less than d is given by d

Cm(d) - I m(d)dd

(3.9)

0 Either of these can be expressed fractionally; so, for example, the of mass with diameter less than d is given by

fraction

d

f m(d)dd 0 M

57

(3.1o)

Aerosol science for industrial hygienists A typical mass distribution for a workplace aerosol is shown in Figure 3.8, both in the frequency and cumulative forms. Note here that the cumulative distribution describes the mass (e.g., in units of [mg]) contained in particles below the stated size. Since the cumulative distribution is obtained by integrating the frequency distribution, it follows conversely that the frequency distribution derives from differentiating the cumulative distribution. Thus, it is seen that the frequency distribution represents the mass fractions of particles contained within narrow size bands, and so may be expressed as d M / d d (e.g., in units of [mg ~m-1]). Figure 3.8 contains a number of important features. Firstly the mass median particle diameter (dmm), at which 50% of the mass is contained with smaller particles and 50% is contained within larger ones, can be read off directly from the cumulative plot. Secondly, the frequency distribution shown exhibits a strong degree of asymmetry such that the peak lies at a value of d which is substantially smaller than dram, and there is a long 'tail' in the distribution that extends out to relatively large particles. This characteristic is very common in practical polydisperse aerosol systems like those found in workplace

1.0r 0.8 m(d)

I 106 0.4 0.2 0

5

10

15

20

25

30

35

40

45

50

12-

Cm(d) [mg]

dm~ (or MMD) 0

5

l0

I

15

I

I

20

25

I

30

I

35

I

40

I

45

I

50

d (l~m)

Mass-based particle size distribution for a typical workplace aerosol, shown in: (a) the non-normalised frequency distribution form; and (b) the non-normalised cumulative distribution form. Note that the normalised versions of these curves are obtained if their vertical axes are divided by the total mass sampled. Figure 3.8.

58

Properties of aerosols e n v i r o n m e n t s . Very often, the overall distribution may be r e p r e s e n t e d to a fair first a p p r o x i m a t i o n by the log-normal m a t h e m a t i c a l function M

{

m(d) =

exp

(lnd-lndmm) 2 ) -

(3.11)

d V(2r;) ln~rg

2(lnerg)2

w h e r e O'g is the geometric standard deviation, reflecting the width of the distribution. This is given by d84% O'g - "

dmm =

dmm

(3.12)

d16%

Example 3.4. For the particle size distribution shown in Figure 3.8, estimate by graphical methods the median particle diameter and the geometric standard deviation. Firstly, the cumulative distribution function is normalised and plotted on log-probability axes. This is shown in Figure 3.9 Here we see that the plot is linear, confirming that the particle size distribution is indeed log-normal *

It may be read directly from the graph that Also from the graph,

d84 %

= 21 p~m and

dram --

dl6 % =

9 ~m

4.1 i~m.

From Equation (3.12) 21 - 2.30

O'g

9 or

9 = 2.20

O'g -"

4.1 indicating an accuracy which, from such graphical methods, is usually sufficient for practical purposes.

For a perfectly m o n o d i s p e r s e aerosol, O'g = 1. M o r e typically for aerosols f o u n d in the workplace e n v i r o n m e n t , O'g ranges from a b o u t 2 to 3. T h e

59

Aerosol science for industrial hygienists

E

,.,,,.,,i

l

d84~, = 21 I~m

9

dmm = 9 I~m di6 % = J [ 4.1 I~m / o-

o~ I

~1~1 i i/ 2

5

! 11 1

10 20 50 80 90 95 98 Percentage of mass with diameter less than stated d.

Figure 3.9. Cumulative particle size distribution (by mass) for a typical workplace aerosol, plotted on log-probability axes to illustrate the property of log-normality.

property of log-normality (or even a reasonable approximation to it) which is so often found in practice in workplace aerosols provides some additional useful aspects. In particular, it enables conversions between relationships for distributions based on particle number, mass, surface area, and any other aerosol property. As long ago as 1929, Hatch and Choate developed a set of equations for this purpose, each equation having the form qMD - NMD exp(qln2org)

(3.13)

where NMD is the number median particle diameter and qMD is the median diameter weighted by dq. We note, for example, that the link between particle number and volume (and hence mass) for particles of diameter d is d3, based on simple geometrical considerations. This, therefore, leads to the choice of q = 3 if we wish to use Equation (3.13) to convert distributions from number to mass . . . . . . . . . . , for particle surface area, q = 2. Note that, in such conversions, O'g does not change. The appearance of a log-normal particle size distribution is usually associated with a single aerosol generation process. But in many workplaces there may be more than one type of aerosol. In such cases, therefore, it is not unusual to find two or more particle size distributions superimposed. These are referred to as multi-modal. Figure 3.10 shows an example of a clearly bimodal aerosol like that found in an underground mining environment where there may be both relatively coarse dust (generated by the extraction process itself) and relatively fine diesel particulate (generated by underground transportation) (e.g., Cantrell and Rubow, 1990). We have already mentioned that fibrous aerosols represent a special

60

Properties of aerosols 0.3 I m(d)

Dust

0.2 -

l 0.1

0 0.01

0.1

1.0 d (Izm)

I I00

I0

Figure 3.10.

Illustration of the frequency distribution (by mass) for a typical bimodal aerosol (e.g., like that found in underground mining where diesel vehicles are being used).

case in o c c u p a t i o n a l health terms. B e c a u s e of the i n t r o d u c t i o n of the additional d i m e n s i o n , particle size statistics for such aerosols n o w r e q u i r e the c o n s i d e r a t i o n of three distributions; d i a m e t e r (d), length (L) and aspect ratio (d/L). E x a m p l e s for a typical s a m p l e of w o r k p l a c e a i r b o r n e asbestos dust are s h o w n in Figure 3.11, where each of the two c u m u l a t i v e distributions s h o w n is seen to be log-normal.

|.0

100

'

IO

E :L 0.1

0.01

I

I

I

5

20

50

I

i

80 95 Percentage of particles less than stated size

E :L

l

~9

Figure 3.11. Illustration of the cumulative size distributions (by number) for both length and diameter for airborne asbestos fibres. The ones shown are typical of an amosite asbestos fibre generated in a laboratory chamber during animal (rat) inhalation experiments (e.g., reference aerosol as defined by the Union Internationale Contre le Cancer [UICC]).

61

Aerosol science for industrial hygienists

3.7 E L E C T R I C A L P R O P E R T I E S In aerosol science, both in industrial hygiene applications and elsewhere, the electrical properties of aerosols have frequently tended to be ignored, or ~ at b e s t occasionally invoked to provide qualitative explanations of unexpected, or otherwise implausible, observations. However, in recent years, a growing body of experimental work has indicated that the state of static electrification (i.e., particle charge) in an aerosol may be of significant practical relevance in a number of industrial hygiene areas. For example, it has now been established that it can affect the behaviour of particles in the lung after inhalation (leading to enhanced deposition in some cases). It can also influence sampling and filtration. In recent years, instrumentation has been developed which has enabled the measurement of the electrical properties of workplace aerosols, in terms of both the magnitude of the charge carried by individual particles and how that charge is distributed between positive and negative polarity and over populations of particles of different sizes (e.g., see Figure 10.17 in Chapter 10). An example of a particle charge distribution from an aerosol typical of those found in workplaces is shown in Figure 3.12. From comprehensive measurements made on workplace aerosols of widely-varying types (Johnston et al., 1985), two main features were found which appear to be common to all the workplaces surveyed, irrespective of the type of aerosol generated and how it was generated. Firstly, each particle is charged either net positive or negative and, for the aerosol as a whole, the charges on individual particles are distributed almost symmetrically between positive and negative

I:I

-100

I

0

!00 Plus

Minus

qle Figure 3.12. Illustration of the electric charge distribution for particles of a given size in a typical workplace aerosol, in which the vertical axis represents the probability of finding a particle carrying charge q/e (where e is the charge per electron, 1.6 • 10 -19 C).

62

Properties o f aerosols 100o

oy IOO

Z/

10-

1

0.1

J

l

1.0

.,

I

10

d (~m) Figure 3.13. Typical data for the median magnitude of particle charge, expressed in terms of Iqm/el as a function of particle size (d) for a typical workplace aerosol (where e is the charge per electron, 1.6 • 10-19 C). The data shown are based on results obtained at a rock crushing operation in a quarry (from Johnston, A.M. et al., Annals of Occupational Hygiene, Copyright 1985, adapted by permission of the British Occupational Hygiene Society). polarity. Secondly, the median magnitude of charge per particle for each given workplace aerosol (Iqml) may be represented by the simple empirical relation (see Figure 3.13) qlTl = Ad n

(3.14)

e where n is a constant coefficient and, if particle diameter (d) is in [~m], A is the number of charges equivalent in magnitude to one electron (e) carried by a 1 ~m-diameter particle. From the above, a given aerosol might appear to be of neutral polarity even though individual particles might be very highly charged. In many aspects of particle behaviour (including effects of particle deposition in the lung), it is individual particle charge which is important. But this notwithstanding, in practice there is no such thing as an aerosol where all the particles are truly neutral. For an aerosol exposed to the naturally-occurring airborne charges of both polarities (e.g., air ions, cosmic rays, etc.), such 'neutrality' is defined in terms of Boltzmann equilibrium, for which, in Equation (3.14), A ~ 3 and n ~ 1/2 (Liu and Pui, 1974). This is what would be achieved for an aerosol that has been in existence for a long time (which, under normal conditions, would in practice be upwards of about 1 hour). Thus it is seen that, for most long-lived aerosols encountered in the ambient outdoors atmosphere, they are likely to be in a state of Boltzmann neutrality. In workplaces, however, due to the more confined environment together with the turnover of air due to ventilation, aerosols to which workers are exposed are 'fresher'. So 63

Aerosol science for industrial hygienists

particles will usually carry charge above that corresponding to Boltzmann equilibrium. The level of charge is associated with the process with which they were made airborne. For dry aerosols produced by mechanical dispersion, charging occurs as the result of the creation of new surfaces, contact charging (the making and breaking of contacts) and triboelectric charging (associated with friction). For liquid droplets, charging may be the result of the reorganisation of the surface energy of the original bulk liquid. For Table 3.2. Typical summary data for particle charge for a range of typical workplace aerosols, based on the coefficients A and n in E q u a t i o n (3.14) for aerosols with isometric particles and on the coefficient or for fibrous asbestos aerosols in E q u a t i o n (3.15). Industry

Location

Jute

Cotton Flax

Glass fibre

Chemicals

Rubber Batteries Quarry Coal mine Asbestos 1

Asbestos 2

A

n

Batching Spreading Carding Drawing Spinning Winding Weaving Weaving Hackling Carding Weaving Spinning Winding Slivering Spinning Winding Weaving Silica A Silica C Silica D Mixing Rolling Oxide production Soldering Primary crusher Secondary crusher Return roadway

22.3 27.8 28.6 20.7 13.2 13.0 35.3 33.2 22.6 49.8 29.2 10.3 13.7 3.6 4.8 4.3 4.4 11.2 10.1 24.1 6.2 5.1 2.9 2.1 22.0 4.0 25.0

1.03 0.80 1.19 1.18 1.44 1.16 1.25 1.24 1.77 1.12 1.23 1.84 1.84 1.34 1.04 1.19 1.44 1.01 1.21 0.72 1.69 1.91 0.90 0.98 1.50 1.43 1.20

Carding Spinning Weaving Carding Spinning (dry) Spinning (wet) Weaving

13.0/~m length 10.1 9.6 8.4 11.0 4.9 6.0

64

Properties of aerosols

such aerosols, it is reasonable to expect that A in Equation (3.14) will be substantially greater than 3. In fact, values as high as 40 have been found for workplace aerosols, tending to be higher the greater the amount of energy that went into the aerosol generation process. In addition, since the ability of a particle to retain electrical charge should be approximately proportional to its surface area, we might expect n ~ 2. In practice, values were found ranging from 1.2 to 2.5, tending on the whole to be less than 2. By way of illustration, Table 3.2 shows some results for the states of static electrification of some typical workplace aerosols, most of them expressed in terms of the quantities A and n contained in Equation (3.14) (from the Johnston et al. study). Example 3.5. For particles made airborne during the carding process in the manufacture of flax textiles, estimate the median magnitude of charge (in Coulombs) carried by particles of diameter 7 Ixm. C h a r g e p e r p a r t i c l e is given by E q u a t i o n (3.14)

F r o m T a b l e 3.2, n o t e t h a t A = 49.8 a n d n = 1.12. So

qm = 49.8 x 71-12 e

N o t e that e l e c t r o n i c c h a r g e , e = 1.6 x 10 -~9 C

T h u s Iqm]

= 49.8 x 71-12 •

1.6 x 10 -19 C

= 7.04 x 10-17 C

Once again, fibres (e.g., asbestos) present a special case which is worthy of mention. Results have shown that, as a result of their large overall physical dimensions, the level of charge carried by long, thin fibres can be significantly larger than for isometric particles of corresponding aerodynamic diameter. For such particles, charge per particle has been found to be relatively independent of fibre diameter, but increases approximately linearly with fibre length. Thus qm -

cr L

(3.15)

e

where cr here is the charge per unit length of fibre. This is a feature which could have significant effects on some aspects of airborne behaviour, including deposition in the lung after inhalation (see Chapter 6). Typical results for workplace aerosols are shown in Table 3.2. 65

Aerosol science for industrial hygienists 3.8 M I N E R A L O G I C A L A N D C H E M I C A L P R O P E R T I E S As already described, the raw material from which aerosols are derived, and the processes by which many are formed and subsequently evolve, are often very complicated. So too, therefore, are their chemistry and mineralogy. Particle composition features significantly in the cellular reactions that are stimulated once an aerosol is inhaled and particles subsequently come into contact with biological tissue. Therefore, it clearly has an important bearing on possible toxic effects to exposed workers. Discussion of particle composition brings us close to the question of toxicity, a subject which is usually considered to lie outside aerosol science itself. The mechanisms by which inhaled particles of a given substance can provoke biological responses are varied. Even a relatively insoluble particle can appear to the cells of the lung as a undesirable 'foreign body' and so stimulate a whole range of defence processes which relate to mineralogical composition as well as to other factors such as particle size and morphology. Here the surface properties are particularly relevant so that one insoluble mineral particle might appear to the cells as more toxic than another. For example, on the one hand, crystalline silica (e.g., quartz) has been shown to be relatively toxic to cells, although uncertainty remains as to the exact mechanisms. Here, biological responses to the presence of a quartz particle can be so severe as to lead to permanent pathological changes in the lung (e.g., fibrosis). On the other hand, other insoluble materials such as titanium dioxide and fused alumina are considered to be relatively inoccuous. Other substances may be soluble in the lung environment. For these, when they come into contact with the lung, material be transferred into the blood whereupon it may be transported to other parts of the body, possibly leading to adverse health effects in regions remote from the lung itself (e.g., kidneys, liver, bone, etc.). Some metal-containing aerosols (e.g., lead, cadmium) come into this category. In workplaces, aerosols are often made up of complex mixtures of compounds and mineral types. Therefore, even though the mass concentration, size distribution and morphology of particles in the aerosol as a whole may be known, it often remains difficult to assess exposure to such aerosols in a truly meaningful way. Ultimately, the choice of a limit value which is assigned to a particular workplace aerosol as a basis for controlling exposures to within 'safe' limits comes down to considerations of composition. Here, therefore, we have the concept of an aerosol fraction in terms not just of its particle size distribution but also of its chemical and mineralogical composition. Again, the case of quartz is a good example to illustrate some of what is involved since it is frequently present ~ together with other minerals in workplace dusts, in particular those found in the extraction industries. Even in relatively small proportions (e.g., 10% or less) it can present a significant risk to the health of exposed workers if the overall dust level is high enough. So, in 66

Properties of aerosols

assessing exposure in a manner which reflects the magnitude of that health risk, it is important to be able to measure not just the overall dust in the fine particle size fraction relevant to particle deposition in the alveolar region of the lung (the region at risk) but also the quartz content within that fraction. Another complicating factor, however, is that the quartz content of the dust does not behave in isolation. Evidence from epidemiology and animal inhalation studies has suggested that the response may be modified by the presence of certain other minerals. Metal-containing aerosols represent another interesting class of problem. Whereas it is currently common practice to determine exposure in terms of the airborne concentration of the metal atoms that are present (e.g., by atomic absorption spectrophotometry), it is known that certain molecular forms are more harmful than others. For example, in the production of nickel, epidemiology has suggested that although water soluble, sulphidic and oxidic forms might be associated with lung and possibly nasal cancer, there is no such evidence for the metallic form (Doll et al, 1990). In such cases, the question of which chemical species is the most relevant to ill-health is therefore an important issue. It is a significant challenge to analytical chemistry to develop quantitation techniques that can be used for aerosol speciation in the industrial hygiene setting.

3.9 B I O L O G I C A L P R O P E R T I E S The science of aerobiology ~ the study of airborne particles of biological o r i g i n - is one of the oldest branches of aerosol science. But it is perhaps fair to say that, in the development of what we might now call 'mainstream' modern aerosol science (in particular physics and chemistry), aerobiology has tended to be excluded. Or perhaps it was not specifically included. So it has continued over the last two decades to develop somewhat independently. Now, however, in the mid-1990s, there is sharply renewed interest in the whole range of what we now term as 'bioaerosols' ~ particularly by those concerned with occupational and environmental health. This is stimulating increased involvement in aerobiology by aerosol scientists and by industrial hygienists and other health professionals, bringing to the subject a wider range of backgrounds and expertise. So a new multidisciplinary approach to the problems associated with bioaerosols is emerging. This in turn is bringing the subject of aerobiology back into the mainstream of aerosol science. Bioaerosols are complex and highly diverse. They include particles in the forms of bacteria, viruses, fungal spores, endotoxins, allergenic and toxic substances of plant and animal origin, protein aerosols, and others. Their airborne concentration may be expressed in more than one way, depending on the type of particle. Bacteria and fungal spores, for example, may be

67

Aerosol science for industrial hygienists expressed in terms of the number of bacterial entities of a given type per unit volume of air (i.e., number m-3). On the other hand, such particles, if they are viable, may be expressed in terms of their ability to reproduce that is the number of 'colony-forming units' per unit volume of air (i.e., cfu m-3). For endotoxin and allergenic material, it is appropriate to express concentration in terms of the mass of the active component per unit volume of air (i.e., >g m-3). Such diversity presents many difficulties in sampling and measurement methodology for exposure assessment. This is an area which has not been well developed in relation to industrial hygiene. However, the new awareness of the importance of bioaerosols in many occupational settings is leading to new efforts to develop appropriate procedures. This is discussed in Chapter 9. A comprehensive review of these aerosols, their properties and their health effects in occupational settings like those found in agriculture, sawmills, textiles manufacture, meat and other food processing, biotechnology, research laboratories, waste disposal, construction, health care, etc. has been given by Lacey and Dutkiewicz (1994). A short summary is presented in Table 3.3. Some examples are shown in Figure 3.14.

Table 3.3. Some bioaerosols found in occupational environments. Category found (particle size)

Type/description

Occupational setting

Viruses etc. ( > mfp, and (b) d < mfp.

73

Aerosol sciencefor industrial hygienists random thermal motion. On the one hand, if the particle is large enough (i.e., much greater than the mean free path between gas molecules, mfp), it experiences the air as a continuum. This is because it cannot 'recognise' individual collisions with gas molecules. On the other hand, for particles which are so small that d is of the same order of magnitude or less than mfp, the nature of particle motion may be envisaged as 'slip' between successive collisions with the gas molecules. These contrasting scenarios are illustrated in Figure 4.2. To account for particle slip, it is now necessary to modify the expression for the drag force by the introduction of a correction factor know as the Cunningham slip correction factor (Ccun). Thus

- 3~rd~xv FD =

(4.3)

Ccun where, according to Cunningham (1910)

2.52mfp ) Ccun

-

1 +

(4.4)

d

(.)

(055d)

for d down to 0.1 ~m. The more complicated empirical expession

Ccu n = 1 +

{2.514 + 0.8exp

d

}

(4.5)

mfp

has been shown experimentally to work well for d down to 0.01 ~m. Typically, as stated in Chapter 2 for air at STP, mfp = 0.066 p,m. So it is seen that consideration of the effects of the slip correction starts to become important for aerosol particles with d less than about 1 ~m. This means that, for many practical industrial hygiene situations involving mineral dusts and other such relatively coarse aerosols, it may be neglected. But for other, finer, aerosols (e.g., welding fume, diesel fume), it must be taken into account. The second modifying factor concerns departures from Stokes' law at Rep values exceeding about 1. To discuss this, it is useful here to introduce the concept of the dimensionless drag coefficient (C D). Thus for a spherical particle

CD

(

projected area of the sphere

) (4.6)

( 1/2 Pair V2) 74

The motion of airborne particles

where the denominator on the right-hand side serves to normalise the force per unit frontal area of the sphere with respect to the velocity pressure in the approaching flow. For Stokesian particles, Equation (4.6) gives 24 (4.7)

C D --

Re P From Equations (4.4) or (4.5) - (4.7), the general expression for drag force is therefore FD =

( coRep) ( 24

)

(4.8)

Ccu n

where the term inside the first bracket on the right-hand side is the correction to allow for 'non-Stokesian' behaviour. The general shape of the relationship between C D and Rep over a wide range of Rep for spherical particles is shown in Figure 4.3. The Stokesian region, corresponding to Equation (4.7) is described by the straight portion (on the log axes shown) to the left. The curve tends to become less steep for Re -> 1, levelling out for Re -> 2000. In the intermediate range, the empirical expression CD =

(24) ( RERJ3) ~ Re

{1 +

}

6

has been found to agree with experimental data to within 2%.

Figure 4.3. Curve showing the relationship between the drag coefficient (CD) and Reynolds' number (Rep) for a spherical particle. Note the linear region (on the log axes) for the Stokes region where Rep < 1. (From Vincent, J.H., Aerosol Sampling: Science and Practice, Copyright 1989, adapted by permission of John Wiley and Sons Limited).

75

(4.9)

Aerosol science for industrial hygienists So far we have considered only spherical particles. However, experience has shown (as described in Chapter 3) that particles like those encountered in the industrial hygiene context are rarely so idealised. This, therefore, leads to the third modifying factor. It is reasonable to expect that particle shape will influence particle motion, and so a further correction to the drag equation is needed. Now the drag force is written in the form CDRe p ) D

m

3~rdv~xV+

__

24

(4.10) Ccun

where d is now replaced by d v, the equivalent volume particle diameter as described earlier, and + is the dimensionless dynamic shape factor. The latter is usually determined experimentally from observations of the falling speeds of particles settling in air under the influence of gravity. It should be noted that + for an irregular particle will depend on the particle's orientation with respect to the flow during its motion. Since this is usually difficult to define in an experiment, then d~ is usually obtained for motion which is averaged uniformly over all possible orientations. Some values of + for typical workplace aerosol particles are shown in Table 4.1, where it is seen that + ranges from 1.0 for perfect spheres to about 1.4 for non-spherical particles of quartz, and 2.0 for platelet-shaped particles of talc. In Equation (4.10), Ccun should also be adjusted for particle shape, but the value of Ccu ~ for a spherical particle serves reasonably well for most practical situations.

Table 4.1. Values for the dynamic shape factor (+ of typical aerosol particles. Shape/type

Shape factor, +

Sphere Fibre (L/d=4)

1.00 1.32 (axis perpendicular to motion) 1.07 (axis parallel to motion) 1.36 1.04- 1.49 2.04

Quartz dust Fused alumina Talc (platelet)

In summary, Stokes' law describing the aerodynamic in air. However, a number be important under certain

has been identified as the basic starting point for drag forces acting on an aerosol particle moving of corrections have been identified which could conditions. These are:

76

The m o t i o n o f airborne particles

'slip' for d _ 1, and non-spherical particle shape, respectively. These corrections should never be completely ignored. But in many industrial hygiene situations, they may be considered small enough that to a first approximation ~ Stokes' law is a reasonable working approximation.

4.3 P A R T I C L E M O T I O N

Equations of motion

As in the case of fluid mechanics, the starting point for all considerations of particle transport is again Newton's Second Law (mass • acceleration = net force acting). This leads to a general equation of particle motion. For the forces acting, the drag force describing the resistance of the fluid to the particle's motion has already been described. In addition, there may be an external force (e.g., gravity, electrical, etc., or some combination of forces), the effect of which is to generate and sustain particle motion. So long as the particle is in motion relative to the fluid, the drag force will remain finite. The proper relationship for describing the particle motion is a vector equation, embodying the relative motion of the air and the particle and the forces acting for each of all three available dimensions. The 'shorthand' vector notation used for expressing this mathematically appears deceptively simple. But the resultant set of equations which need to be solved for particle motion in specific cases can become quite complicated. However, the important principles involved can be illustrated by reference to some simple - - but nonetheless relevant - - examples.

Motion under the influence of gravity

The first example is for a particle falling still air. Here, as shown in Figure 4.4, the linear motion in the single vertical (y) illustration we neglect the effects of slip, particle non-sphericity. Then the equation

under the influence of gravity in problem reduces to one involving dimension. For the purposes of departures from Stokes' law and of particle motion is given by

dpy m

= -

3TrpMVy + ( m g -

dt 77

FB)

(4.11)

Aerosol science for industrial hygienists Drag force

Bouyancy force ('upthrust')

elocity, v

I y-direction

Gravitational force

Figure 4.4.

Schematic to illustrate the problem of a particle falling in air under the influence of gravity, indicating the forces acting.

where Vy is the particle's velocity in the downwards y direction, m is its mass and g is the acceleration due to gravity. The term F B is included to allow for the upwards buoyancy force arising from the mass of air that is displaced by the particle (as described by Archimedes' principle). But since the density of air (1.29 kg m -3 at standard temperature and pressure) is so much less than the density of a particle (usually greater than 103 kg m-3), this term may usually be neglected for practical purposes. With this in mind, Equation (4.11) may be re-organised to give dvy + dt

(Vy) ~

-g=0

(4.12)

T

where d2p -r =

(4.13) 18Ix

78

The motion of airborne particles in which p is particle density. In E q u a t i o n (4.13), closer inspection of its units reveals that -r has dimensions of time, the significance of which we shall see shortly. E q u a t i o n (4.12) is a simple first-order linear differential e q u a t i o n of the type familiar in almost all areas of science and engineering. Its solution is very straightforward. In terms of the particle velocity at time t, it has the well-known exponential form

Vy-- g-r

[

1 - exp

(

(4.14)

- -T

for the case where the particle starts from rest (Vy = 0) at time t - 0. This shows that particle velocity under the influence of gravity tends exponentially towards a terminal value, as shown in Figure 4.5. The sedimentation or falling speed is given by v ~ - g-r

(4.15)

for which the corresponding mechanical mobility (B), defined as the velocity per unit of applied mechanical force, is Vs

B -

(4.16)

mg As stated above, E q u a t i o n (4.15) relates for illustrative purposes to the simple case where slip, non-Stokesian conditions and particle non-sphericity are neglected. More generally, we should write

lYs = g T

v y

0.63

9

vs

I

/ 0

T t (secs)

Figure 4.5.

Form of the function describing a particle's settling (or falling) speed (Vs) as a function of time (t), starting from rest at t = 0.

79

Aerosol science for industrial hygienists

v~ -

(Ccun)(24) +

g-r

(4.17)

CDRep

R e g a r d l e s s of particle size (but again u n d e r the b r o a d g e n e r a l a s s u m p t i o n of S t o k e s i a n c o n d i t i o n s ) , particle velocity rises to 6 3 % of its final t e r m i n a l value at t = -r. T h e q u a n t i t y -r is t h e r e f o r e r e c o g n i s e d as b e i n g the t i m e c o n s t a n t (or, inversely, the rate) of the e x p o n e n t i a l process. F o r the e x a m p l e given, it is s m a l l e r the faster the particle r e a c h e s its t e r m i n a l velocity. M o r e g e n e r a l l y , f r o m E q u a t i o n (4.13), it is seen to be a f u n d a m e n t a l p r o p e r t y of the particle itself, relating to the rate at which the particle c o m e s into d y n a m i c a l e q u i l i b r i u m with its s u r r o u n d i n g s a n d the forces acting (i.e., w h e r e it is n e i t h e r a c c e l e r a t i n g or d e c e l e r a t i n g ) . A e r o s o l scientists t h e r e f o r e r e f e r to it as the particle relaxation time. It is a v e r y i m p o r t a n t q u a n t i t y which occurs time a n d t i m e again in c o n s i d e r a t i o n s of particle m o t i o n . Example 4.1. Calculate the falling speed of a spherical particle of diameter 0.01 txm and density 1 x 103 kg m -3. Assume that the viscosity of air is 18 x 10-6 N s m -2 (as mentioned in Chapter 2), and that the mean free path for molecular motions is 0.066 txm Also note that, for a spherical particle, the dynamic shape factor, r = 1 Also note that the Cunningham correction factor for a particle of the size indicated is given by Equation (4.5), thus

C = 1+

(O.O66)(

I).55 x 0.01

2.514+0.8e(

0.066

0.01 = 22.45 Also note that Stokes' law is obeyed for such a small particle Now from Equation (4.17) 22.45 x (10-8)2[m 2] x 103[kg m -3] • 9.81[m s -2] VS ~-

18 X 18 X 10-6[N s m -2] in SI units, so that *

vs = 6.80 x 10- S m s -1

80

The motion of airborne particles E x a m p l e 4.2. C a l c u l a t e t h e falling s p e e d of a q u a r t z p a r t i c l e w i t h e q u i v a l e n t v o l u m e d i a m e t e r 150 Ixm a n d d e n s i t y 2.7 • 103 kg m -3. .....

Note here that, for such a large particle, we may neglect the slip correction, so that Ccu n = 1. But it is likely that we may have to make a correction for non-Stokesian conditions First, for a particle of quartz, Table 4.1 gives the dynamic shape factor cb = 1.36 In Equation (4.17) we see that we cannot assign Rep until we know the falling speed. Therefore, since vs depends on Rep while Rep depends on vs, the calculation is less straightforward than for the low Rep case. First, begin by assuming that Stokes' law applies. Then, initially, we get (150 x 10-6)2[m 2] x 2.7 x 103[kg m -3] • 9.81[m s -2] k'sl

=

18 x 18 x 10 -6 x 1.36[N s m -2] = 1.35 m s -1 Now check Rep, recalling that this is given quite accurately for workplace conditions by 7 • 104dVsl . We get Rep = 7 x 104 x 150 x 10-6[m] x 1.35[m s -1] = 14.18 = 14 which is well outside the range for Stokes' law to apply So now recalculate a new value for v s using Equation (4.17) with this value for Rep. H e r e

(143)

we need to calculate a value for the drag coefficient from Equation (4.9), thus

CD =

{1 +

~

} = 3.37

6

(24)

We can use this to calculate a new value of v S, giving

Vs2 = Vsl x

=1.35 x 0.5

(3.37 x 14) = 0.68 m s-1

81

Aerosol science for industrial hygienists Now we have to go back and check Rep again, thus R e p - - 7 • 104 • 150 • 106[m] • 0.68[m s -1] = 7.08 -~ 7 Now

CD=

~

{1 +

~

} = 5.52 6

So

Vs3

= Vsl •

(24)

= 1.35 • 0.62

5.52 • 7 = 0 . 8 4 m s -1 At this point, we are beginning to see that the process of converging towards the final m and correct m value for vS is iterative. So we may continue with the cycle of calculating vs,

Rep, calculating

calculating

CD, then recalculating v~, etc. until we get c o n v e r g e n c e -

that

is, where the calculated value of v~ does not change from one cycle of the calculation to the next. Conducted in the manner indicated above, it is clear that this can become laborious. However it becomes relatively simple with modern spreadsheets. For the present example, it so happens that the number of iterations to achieve this is quite small; namely (following the above nomenclature): Vs4

=

0.79 m s -1

Vs5 = 0.80 m s-1 Vs6 =

0.80 m S-1

We see that convergence has been achieved. So, for the example given, the final answer is *

vs = 0.80 m s -1.

Full calculations for vs for particles covering wide ranges of size and shape have

been

droplets

reported

with

p -

in t h e

literature.

103 k g m - 3

are

Some

shown

for falling speed shows the values calculated l a w is a s s u m e d ,

as g i v e n b y E q u a t i o n

examples in T a b l e

water

The

first c o l u m n

if slip is n e g l e c t e d

and Stokes'

(4.15). The second

82

for spherical

4.2.

column

shows the

The motion of airborne

particles

Table 4.2. Calculated values for the falling speed of a spherical particle of water, firstly assuming no slip and Stokesian conditions, then allowing for both slip and non-Stokesian conditions. v~ ( m s - ' )

Particle diameter (for spheres with p = 10 3 kg m -3)

Stokes' law, no slip

0.01

3.03 x 10 -'~

0.1

3.03 •

1

3.03 x 10 . 5

10

3.03 •

100 1000

10 -7

Actual

6.74 x l O - a 8.68 •

10 -7

3.50 x 10-5

10 -3

3.05 •

10-3

3.03 x 1 0 - '

2.48 •

10-~

3.03

3.86

actual value when the Cunningham slip correction is included and when the correction for non-Stokesian conditions is applied. Inspection of these results show that there is quite a wide range (--- 2 - 50 I~m) over which Stokes' law provides v~ to within about +10%. This is sufficient for many practical industrial hygiene considerations. Motion under electrical forces The same basic ideas may be applied to particles moving under the influence of other types of force, the only difference being in the way that the force itself is specified. Electrostatic precipitation is another example which is relevant to industrial hygiene. Here the electrical force requires that the particle carries some electric charge, either that which it has acquired during the process of being made airborne (as discussed in Chapter 3) or

Charge, q ,,

FE~

FD Velocity, v E

Figure 4.6.

Schematic to illustrate the problem of a charged spherical particle moving in an externally applied electric f i e l d .

83

Aerosol science for industrial hygienists d u r i n g s u b s e q u e n t artifical c h a r g i n g (as w o u l d be the case in an e l e c t r o s t a t i c p r e c i p i t a t o r air cleaning device). F o r a particle c a r r y i n g c h a r g e q, the p h y s i c a l p r o b l e m is s h o w n s c h e m a t i c a l l y in F i g u r e 4.6, w h e r e the electrical force (FE) is given by

F E - Eq

(4.18)

w h e r e E is the e x t e r n a l l y a p p l i e d electric field. U s i n g this e x p r e s s i o n to r e p l a c e the g r a v i t a t i o n a l force (rng) in E q u a t i o n (4.11), the result for the t e r m i n a l velocity (VE) of a S t o k e s i a n s p h e r i c a l particle ~ this t i m e k n o w n as the electrical drift velocity is

Eq VE =

(4.19)

3rrlxd a n d the c o r r e s p o n d i n g electrical mobility ( Z ) , d e f i n e d n o w as v e l o c i t y p e r unit a p p l i e d electric field, is VE

Z =

(4.20) E

Example 4.3. Calculate the electrical drift velocity for a spherical particle of diameter 5 Ixm, carrying a charge equivalent in magnitude to 500 electrons, and moving in a uniform electric field of intensity 10 kV cm -1. Note that E = 10 kV c m - 1 = 106 V m -1. Compare this with the electric field required to cause ionisation and breakdown of air at STP ~ 30 kV cm -1 (SO w e see that 10 kV cm -1 is not unusually high) Again, note that air viscosity (Ix) is 18 • 10-6 N s m -2 Since the magnitude of charge per electron is 1.6 • 10-19 C, particle charge is given by q = 500 [electrons] • 1.6 x 10 -19 [C electron -1] = 8 • 10 -17 C

From Equation (4.19), assuming Stokes' law applies, we get 10 6 [V m - 1 ] • 8 x 10 -17 [C] VE --

3 • 3.142 • 18 • *

10 -6

[N

VE = 0.094 m s -1

84

s

m -2] •

5

X 10-6 [m]

The motion of airborne particles I 0 0 --

I0

1.0

0.1

0.01 103

! 04

105

106

E (Vim) Figure 4.7. Calculated data for values of the electric drift velocity (VE) for charged particles moving under electric fields (E) typical of those which might be found in workplaces under certain conditions.

As indicated in Chapter 3, the natural charge on workplace aerosols tends to increase somewhat more rapidly than linearly with particle size. The same is true for artificial charging in, for example, the corona discharge of an electrostatic precipitator (see Chapter 10). For such levels of particle charge, Equation (4.19) indicates that the electrical drift velocity of particles will increase with particle size. The implication of this is that collection efficiency of particles by electrostatic forces will be greatest for the largest particles. Some results for the electrical drift velocity of typical workplace particles (using data for median particle charge taken from Table 3.2) are given in Figure 4.7. They are shown for a range of electric fields reasonably typical of what might be encountered in practical situations, where electrostaticallygenerated fields might locally be as high as 105 V m -1 (or even higher). With possible particle drift velocities of the order of a few centimetres per second, it can be seen that significant particle motion associated with electrical forces is possible. Motion in thermal gradients

The relevance to industrial hygiene of particle transport of aerosol particles under the influence of thermal forces should not be ignored. The visual appearance of the soiling of walls and other surfaces close to central heating radiators is clear enough evidence of the phenomenon of thermophoresis, a physical process derived from the thermal motion of the gas molecules surrounding a suspended particle (and hence based on the kinetic theory of gases). 85

Aerosol

industrial hygienists

science for

cold

Hot d >>

o

o

0 0 0

o

L~

o

oo

o

0

o o

0 0

0 0 o

0 _

0 0 0

0

O__o

mfp 0

o

o

~

~ o

o

O0 0

o o

O~ 0

~0~'~~0 ~

0

o

o

o

o

0

0

o

o ~

000 o

I

0 0

o

0

oWl/l/l/l,

o

0 dP 0

o

Net force

~176 0

0 0

I~

~ 0

0

0

d < 0 0 0

0 o

0

0

0

0

0

0

o

0

0 0

0

0 0

O0 0

0

0

0

~. X ~ ~

mfp 0 0

o

~0

0

0

O0

0

0 o

o

0 o

o

o

OI

I

~

Net force

0 0 0 0 00 0 0 O0 O0 0 0 0 000 I 0 0 0 0 0 0 0 0 0 0 0 0 0 O0 0 0 0 0 0 0 ~3 0 0 0 0 0 0 0 0 0 0 O0

I

Figure 4.8. Schematic to illustrate the problem of a particle moving under the influence of thermophoretic forces. Note that the net force arising from collisions of the particle with thermally-moving molecules acts in the direction from hot to cold.

The physical scenario is shown schematically in Figure 4.8. For a particle which is present in a thermal field where there is a temperature gradient, it receives more m o m e n t u m from collisions with gas molecules from the 'hot' side (the more energetic gas molecules) than from the 'cold' side (the less energetic gas molecules). The result is a net force in the direction down the temperature gradient (i.e., towards the cold region). For very fine particles which are small compared to the mean free path b e t w e e n gas molecules (d < < mfp), the problem is relatively simple, based on classical kinetic theory considerations. Here, the thermophoretic velocity (vT) has the form

vT

-

- klOT

(4.21)

where OT is the temperature gradient and the minus sign indicates the direction of the t h e r m o p h o r e t i c m o t i o n towards the colder side. The coefficient k a depends on the actual local temperature (T) but, significantly, not on particle size or composition.

86

The m o t i o n o f airborne particles

For larger particles where the particle 'sees' the gas as a continuum (d ~> m f p ) , the basic idea is the same, but the problem is now complicated by the

fact that there is a temperature gradient set up within the particle itself which, in turn, influences the temperature gradient in the region immediately outside the particle. In this region, therefore, the thermal conductivity of the particle (O'p) and of the surrounding air ( O ' a ) become relevant. Now (4.22)

v T -- - k20 T

where the new coefficient, k 2, contains the ratio ~p/ty a, as well as the local temperature. This time there is some dependence on particle size, but it remains relatively weak. Realistic order-of-magnitude calculations are difficult for thermal precipitation in practical situations because the temperature gradient is usually hard to specify or measure. But some hypothetical results are given in Figure 4.9 for some aerosols with contrasting thermal conductivity, typical of those found in industry, using equations for k I and k 2 collected from the literature by Hinds (1982). The results shown here are for hard wood dust and granite. But the calculations can be performed for any substance for which reasonable estimates of thermal conductivity are available. The results in Figure 4.9 are expressed in terms of thermophoretic drift velocity per unit temperature gradient. Here, for a very small particle (d < 0.1 ~m) at T 293 ~ vT ~ 2 x 10 - 4 cm S - 1 per 1 ~ c m - 1 , independently of what the particle is made of. But for larger particles with d > 1 I~m, vT falls markedly, the more so the greater the ratio Crp/~a. The magnitudes of the thermophoretic velocities (per unit of temperature gradient) are small enough to suggest that, in most practical situations, thermal contributions to particle motion would be much less than for other co-existing forces such as gravitational settling or electrostatic precipitation. Nevertheless, it can be an effective particle

_ H a r d w o o d dust O'P~ 5

"7 E 10 - 4 o

"7ra~

dust

E

Orp/tra -- 1O0

[--

~ 10-5 0.01

I 0.1

I 1.0

I 10

d (l~m)

Figure 4.9. Calculated results for the thermophoretic drift velocity (VT) as a function of particle size (d) for aerosols typical of those found in industrial workplaces.

87

Aerosol science for industrial hygienists

deposition mechanism in small confined spaces where high temperature gradients can be maintained. In particular, the fact that vT tends to be constant over quite wide ranges of small particle sizes is a very useful property in relation to certain applications. Indeed, it was exploited very effectively in some of the aerosol samplers based on thermal precipitation which ~ for a time ~ found favour in the British coal mining industry.

Motion without external forces

The concept of particle motion without the application of an external force is also important. For example, consider the simplest case where the air is stationary and a spherical particle is projected into it with finite initial velocity in the x direction. Motion is described by the equation db' x

= - 3zrlxdv x (4.23) dt where the particle now experiences only the drag force. As in the case of a particle falling under the influence of gravity, this differential equation also has a standard form. This leads to the simple exponential solution m

vx

= VxoeXp

(') - ~

(4.24)

T

where Vxo is the initial particle velocity relative to the fluid at time t = 0. This model portrays the situation where a particle is projected into a fluid with a finite initial velocity, analogous for example to a bullet shot from a gun into a water tank. Equation (4.24) has particular relevance to moving air since it describes the fact that, although a particle injected into the flow with zero velocity at first lags behind the flow, it is progressively pulled along by the drag force exerted by the fluid until it eventually 'catches up' with it. At this point, the particle is then transported along at the same velocity as the air itself, and may thereafter be considered to be 'airborne'. This state of being airborne is therefore seen to stem directly from the particle drag force. Further manipulation of Equation (4.24) yields a further important result. Simple integration provides the distance travelled by the particle relative to the air before it comes to rest ~ or, for the converse moving air case, catches up with it. Thus s -

where s is the

stop

Vxo 9

distance.

88

(4.25)

The motion of airborne particles

4.4 SIMILARITY IN P A R T I C L E M O T I O N We have already discussed the question of dynamical similarity in relation to fluid motion, and arrived at the Reynolds' number scaling concept. From the general equation of motion for a particle in the fluid, as expressed by the three-dimensional version of Equation (4.11), we may also examine the conditions under which its behaviour may be scaled. In this way it may be shown that, for systems which are geometrically and fluid-dynamically alike, similar particle motion (i.e., in terms of relative trajectories) occurs provided in the first place ~ that d2pU

St =

(4.26) 18~D

is constant. Here, as in the earlier fluid mechanical discussion, D and U are the characteristic dimensional and velocity scales, respectively. The dimensionless quantity in Equation (4.26) is known as the Stokes' number. For small enough particles, this definition needs also to include the Cunningham correction term to allow for the phenomenon of slip. Similarly, for nonspherical particles it also needs to include the dynamic shape factor. In addition, solutions for the motion of non-Stokesian particles will also depend on Rep. However, the simple form shown in Equation (4.26) is a fair working assumption for many workplace aerosols and the use of St alone for scaling purposes is usually adequate. The physical significance of St becomes apparent for situations where the flow is distorted (i.e., divergent or convergent); for example, near a bluff obstacle in the workplace, inside a bent tube or duct, or in the vicinity of a sampler. Equation (4.13) with (4.26) gives T

T

St =

= (D/U)

(4.27) "rd

where, if D is the dimensional scale of the physical system which is responsible for the distortion (e.g., the width of the bluff flow obstacle), it is also equivalent to the dimensional scale of the distortion itself. It follows that D / U reflects the length of time (Td) for a 'packet' of fluid to pass through the distorted flow region. St is therefore the ratio of the particle relaxation time to the timescale associated with the flow distortion, and so is a direct indication of how well the particle is able to respond to changes in the flow velocity and direction. Note, for example, that a very small particle with correspondingly small 9 will yield a small value of St in many flow systems. This indicates that the particle will tend to respond quickly to changes in the 89

Aerosol science for industrial hygienists flow and so tend to 'follow' the flow closely. A large particle, having large -r and a correspondingly larger St, will tend to respond less effectively to the changing flow. A very large particle will therefore tend to continue along in the direction of its original motion, and not to 'see' the changes in flow direction and velocity. The same concept can be viewed slightly differently. By combining Equations (4.25) and (4.26), we get another relation

St =

(4.28) D

where St is now expressed as the ratio of particle stop distance to the dimensional scale of the flow distortion. Similarly to the preceding argument, the particle will tend to follow the air flow when s is small compared to the flow distortion; and vice-versa when s is of the order of it or larger. From the preceding discussion, it is clear that St is an important measure of the ability of an airborne particle to respond to the movement of the air around it, and that particle trajectory patterns may differ to an extent dictated largely by the magnitude of St, the extremes being St < < 1 and St > > 1, with St ~ 1 representing some intermediate situation. Thus we have the concept of particle 'inertia', which is a function both of the particle itself and of the flow in which it is moving. This is illustrated in Figure 4.10, and embodies one of the most important concepts in the whole of aerosol particle mechanics. So far, we have assumed the absence of gravity. Of course, except in highly specialised working environments (e.g., space stations), gravity will

Air streamline

Particle St = 0 ~ ~ 0 ,

_

~ - , t . . . ~ ..~D- ' ~ ~ s O " ~ ~)..~r..O.- -0 s , . ,

D tjajectories

St increasing

Figure 4.10. Schematic diagram to illustrate the phenomenon of inertial motion of a particle in a flow field which is changing in direction. Note the role of Stokes' number (St).

90

The motion of airborne particles always be present and so must be borne in mind. In order to assess its possible contribution, we may introduce another dimensionless quantity, the

gravitational parameter

Vs G -

(4.29) U

which, in effect, compares the rate at which a particle moves towards a boundary by gravitational settling with that for it to leave the system by airborne convection. This is particularly relevant to particle transport in, for example, elutriators, filters, and the alveolar region of the human lung. In situations where inertial and gravitational forces are acting simultaneously, then to help assess which of the two mechanisms is predominant, we have the further dimensionless parameter, the Froude number St Fr -

U2 =

G

(4.30)

gD

which expresses the ratio of the magnitude of inertial forces to the magnitude of gravitational forces. The larger the value of Fr, the smaller the effect of gravity in relation to inertial effects. It should not be ignored so long as Fr is less than ~ or of the order of ~ unity.

4.5 P A R T I C L E A E R O D Y N A M I C D I A M E T E R For two spherical particles having different diameters (d 1 and d2) and different densities (Pa and P2), their falling speeds in air will be the same provided, from Equations (4.13) and (4.15), that

d21 [31- d22 P2

(4.31)

where for simplicity at this point the slip, Reynolds' number and particle shape corrections have again been neglected. Equation (4.31.) leads directly to a new definition of particle size based on falling speed; namely, the particle aerodynamic diameter (d~e). This is the particle size parameter which, as we shall see as this book progresses, is the most widely appropriate in relation to particle motion. It is defined as the d i a m e t e r of a spherical particle of density p - p* = 1 g c m - 3 -- 10 3 kg m - 3 (equivalent to that of water) w h i c h has the s a m e falling speed in air as the particle in question. T h u s for a g i v e n spherical particle w e h a v e

91

Aerosol science for industrial hygienists

p ) 1/2 dae = d

~

(4.32)

p*

So far, as stated, attention has been focused only on spherical particles. For non-spherical particles, and also restoring the corrections for 'slip' and non-Stokesian (Rep > 1) behaviour described above, the general form for aerodynamic diameter becomes

dae=dv{0CcunCRep))

112 (4.33)

(p* Cc*nCDRep+) where the terms marked * refer to the spherical water droplet. The overall concept of particle aerodynamic diameter is shown schematically in Figure 4.11.

Figure 4.11. Schematic diagram to illustrate the concept of particle aerodynamic diameter for a non-spherical particle.

92

The motion of airborne particles Example 4.4. For the quartz particle in Example 4.2, with equivalent volume diameter 150 Ixm, density 2.7 x 103 kg m -3 and dynamic shape factor 1.36, calculate its equivalent aerodynamic diameter. Again, neglect the slip correction for such a large particle From Equation (4.33) 2.7 X 103[kg m -3] ) dae = 150 x

12(x coRepC )12 Re

103[kg m3] x 1.36 ) 1/2

C;Rep = 211 x CDRep

Note from the calculation in Example 4.2 that the falling speed of the particle is 0.80 m s -1. So we can calculate its Rep and CD directly. Thus Rep = 7 x 104 x 150 x 10-6[m] x 0.80[m S-1] = 8.40 and

(24)(8.42,3)84 6 ,

CD

= 4.82 respectively Using Equation (4.9), we may now reduce dae to the form 211

}

dae =

• 24 (8.40•

1/2

That is (Re;)2/3 }

dae =

162

1+ 6

93

1+

(Rep)2/36 }

Aerosol science for industrial hygienists in which Rep* = 7 • 10 4 • dae[i~m ] • lO-6[m Ixm -1] x 0.80[m s -1] = 0.056 dae where dae is in [Ixm]. As in the earlier example for this particle, we again have a calculation problem since Rep* on the right-hand side of the above equation for dae is itself dependent on the unknown size of the hypothetical water droplet. Again this can be solved by iteration. An alternative is the graphical approach, in which both sides of this equation are plotted as a function of dae; that is y _. d a e

and

y=

162

{ o056dae,2/3 ( )} 1 +

6

with dae in [Ixm] From this plot, the aerodynamic diameter of the quartz particle of interest is estimated from the point at which the two lines intersect. Thus it is easy to show that

*

dae = 370 fxm

600

y = 162 { 1+(

500

O'056dae'~/ 2/36}

400 300 200

y=d~

100

0

k,"

I

I O0

!

I

I

200

300

I

1

I

400

500

I

600

Particle aerodynamic diameter, d~ (l~m) Note: This is clearly much larger than would be expected under the assumption that Stokes law applies. This is because the equivalent water droplet, being much bigger than the original particle of interest, lies even further outside the Stokesian regime, and so experiences a much greater drag force

94

The motion of airborne particles

Particles of extreme aspect ratio, notably long and thin fibres (e.g., asbestos), deserve special mention. The aerodynamic diameter of a fibre depends strongly on its orientation during motion. A number of theoretical models have been developed. In one of them, Cox (1970) derived equations for a cylindrical fibre with its axis perpendicular to and parallel to its direction of motion, respectively

(dae)2(d ) (9) (2L) =

and

-8

{ln

(dae)2(d ) (9) (2L) -

+ 0.193 )

(4.34)

+ 0.807 }

(4.35)

d

-4

{ln

d

where L is the fibre length and d is its diameter. For the long, straight fibres of amosite asbestos settling out in a spiral centrifuge (analogous to settling under gravity), St6ber (1972) obtained by experiment the empirical expression

(dae)2(d )

0.232

(4.36)

which by inspection is seen to be quite close to Equation (4.34). This suggests that, during settling under gravity, such fibres would fall with their axes horizontal.

4.6 I M P A C T I O N We now move on to discuss some aspects of particle motion which have particularly important implications in the industrial hygiene context (e.g., in particle deposition onto surfaces, in filtration devices and samplers, etc.). Consider again what happens in distorted flows, where the bluff body case serves as a useful illustration. Figure 4.12 shows for example a disc-shaped flow obstacle facing a wide aerosol-laden airstream. The air itself diverges to pass around the outside of the obstacle. The flow of airborne 'inertialess' particles would do the same. However, as described above, real particles exhibit the features of inertial behaviour, in particular the tendency to continue to travel in the direction of their original motion. This tendency

95

Aerosol science for industrial hygienists Limiting particle trajectory Streamlines

\

o.~

Impacting Non-impacting

particle trajectories

particle trajectories

Enclosed area, b"

Disc area, b'

Figure 4.12. Illustration of the phenomenon of impaction of particles onto the leading surface of a fiat disc placed normal to the airstream. Note that the efficiency of impaction is given by the ratio b"/b', which in turn is primarily a function of Stokes' number, St.

is greater the more massive the particle, the greater its approach velocity and the more sharply the flow diverges. Figure 4.12 shows a typical pattern of streamlines for the axially-symmetric flow in question, together with corresponding trajectory patterns for particles of given aerodynamic diameter (dae). Some trajectories intersect with the disc, which means that such particles will 'impact' onto its surface. Since particle trajectories, like streamlines in laminar flow, cannot cross one another, we may define a limiting trajectory (or dividing trajectory) surface, inside which all particles will impact onto the disc and outside which all will pass by. Impaction efficiency (E) is then defined as number of particles arriving by impaction E --

(4.37) number geometrically incident on the obstacle

which, for particles uniformly distributed throughout the oncoming flow, is equivalent to b

t!

b

!

E =

(4.38)

where b" and b' are the areas projected upstream by the limiting trajectory surface and the obstacle itself, respectively, as shown in Figure 4.12. 96

The motion of airborne particles If all the particles that impact onto the obstacle in the manner indicated actually stick and so are removed from the flow, then E is also equivalent to the collection efficiency. However, for real particles under real conditions, the situation is less ideal, and it is wise to be aware of the possibilities of particle bounce, rebound or blow-off, especially where dry, gritty particles are involved. This has been studied by several workers, including Vincent and Humphries (1978) who showed that, for gritty particles of fused alumina, the ability of particles to be retained following impaction onto a solid disc facing the wind is strongly influenced by particle size and microscopic morphology (especially in terms of the small asperities which go to make up the particle's surface), the size of the disc, the freestream air velocity approaching the disc, and the nature of the boundary layer flow over the front surface of the disc. The larger the particles, the more gritty and the greater the freestream air velocity, the greater the likelihood that such particles will be re-entrained after impaction. From the earlier discussion, it is a reasonable approximation that particle trajectories are determined largely by the Stokes number for particle flow about the obstacle (St) and, to some extent, by the particle Reynolds number (Rep). Also they will be dependent somewhat on the Reynolds number for the flow about the obstacle (Re) since this governs the shape of the streamline pattern. Thus, for a particle which is small compared to the size of the obstacle, E is a function of St, Rep and Re. That is E = f(St, Rep, Re)

(4.39)

if it is assumed that re-entrainment is negligible. It is obvious that E will take values close to zero for St close to zero and rise steadily as St increases, eventually levelling off towards E = 1 at large values of St somewhere exceeding unity. A large amount of experimental information is available in the literature, and a typical S-shaped trend exhibited by most of these is shown in Figure 4.13. Although the physics of what has been described is basically quite simple, there are no analytical solutions for impaction efficiency. Instead, calculations have to be carried out numerically, based on the determination of particle trajectories in a series of small steps from some starting point sufficiently far upstream of the obstacle where the particle is in dynamical equilibrium with the flow and so where the particle velocity is well-known. By such numerical models, provided that the correct flow field is used in the calculation, good agreement may be achieved between theory and experiment. Consider now what happens for a particle whose trajectory, as traced by the motion of the particle's centre of gravity, passes by outside the obstacle. If this trajectory passes close enough to the surface of the obstacle and if the particle is geometrically large enough, it may be collected by interception, as illustrated in Figure 4.14. Although for d < < D this effect on E is negligible,

97

Aerosol science for industrial hygienists

1.o

E

0.5

0 0.01

0. I

I 1.0

St

I I0

Figure 4.13. Typical S-shaped trend for the efficiency of impaction (E) as a function of Stokes' number (St) for a bluff flow obstacle like that shown in Figure 4.12.

Limiting particle trajectory for interception

Figure 4.14.

X~ d

Illustration of the phenomenon of interception by a bluff flow obstacle. Note that it is a function of the ratio d/D.

it becomes a significant influence if d becomes of the same order of magnitude as D. This might occur, for example, during particle collection in a filtration device made up of thin fibrous collecting elements. It is also relevant at this point to mention the contributions to particle deposition on the obstacle associated with other physical mechanisms. For example, particles may arrive at the surface of the obstacle under the influence of external forces such as gravity or electrostatic forces. They may also arrive under the influence of diffusion (see below). Although these are not based on inertia per se, they may be operating simultaneously with impaction and interception. When a number of deposition mechanisms (1, 2, 3 , . . . , n) are acting in such a situation, they combine in a very complicated way. But, to a fair working approximation, the overall efficiency of collection may be written in the form Eoveral 1 = 1

-

(1-E1)(1-E2)(1-E3)...(1-En) 98

(4.40)

The motion o f airborne particles Nozzle

/

/ Impactor collection plate Figure 4.15.

Illustration of the concept of an impactor.

where El... E n are the individual collection efficiencies associated with each of the mechanisms acting independently. If each of these individual efficiencies is small ( < < 1 ) , then Equation (4.40) reduces to Eoveral I = E 1 + E 2 + E 3 + . . .

+ E n

(4.41)

This picture is particularly relevant to the deposition of particles on the collecting elements of a filter where there is usually more than one physical collection mechanism operating. Again, although the example given has been concerned with deposition from a wide airstream onto a bluff flow obstacle, the same basic ideas apply in other distorted flow situations (e.g., at bends, expansions and contractions in pipes and ducts, etc.). In particular, much of the preceding provides the basis of a special class of device which finds application in particle size-selective aerosol sampling ~ the impactor. Here the particle laden flow is passed through a nozzle and the resultant jet is directed towards a plate (see Figure 4.15). The flow is deflected by the plate and so ~ by virtue of the mechanisms described above ~ particles may be deposited onto the plate. The nozzle may be cylindrical or slot-shaped. As expected, collection efficiency is governed in the first instance by a Stokes' number, this time one based on the air velocity in the jet nozzle and the width of the nozzle. With careful design with respect to nozzle width and depth, and nozzle-to-plate spacing, impactors can be achieved with very sharp and well-specified particle size 'cut' characteristics. The principles of such devices have been described in full by Marple and Willeke (1979) and others.

4.7 E L U T R I A T I O N As stated above, impaction refers to particle deposition under the influence of 'internal' inertial forces, without involving any external forces, gravity or

99

Aerosol science for industrial hygienists

otherwise. In this book, the general term 'elutriation' is used to refer to another mode of particle deposition relevant to industrial hygiene ~ from a moving air stream under the influence of an externally applied force. Traditionally, the term has been used mainly to describe the gravitational separation of particles carried along by smooth laminar flow through a narrow horizontal channel where particles are deposited onto the floor of the channel. A direct extension of this idea is the gravitational elutriation that occurs during aerosol flow vertically upwards (e.g., through a vertical tube, or into an inverted sampling device). Both aspects of gravitational elutriation were first described by Walton (1954). The general principle is the same if some other force (e.g., electrostatic) is the main agency of deposition. The process is relevant to aerosol behaviour not only in sampling devices but also in the airways of the lung after inhalation. The principle of elutriation is shown in Figure 4.16 where, for the purpose of illustration, the force bringing about deposition is that due to gravity. Particles are transported through a two-dimensional channel, conveyed along by the moving air. The flow is laminar so that, after a relatively short distance from the entrance, the boundary layer at each plate has grown to the stage where the flow is fully developed, at which point the velocity profile across the duct has stabilised and become parabolic. From simple solution of the Navier-Stokes equations (where, for the two-dimensional channel flow, an analytical solution is accessible), this velocity profile is given by

(y)2

ux=U~o{1-

~

(4.42)

}

b

Air flow velocity profile

~////////////////ff/////////////////////////////////////////////~////// t~'~~~~_~,o~_.__

- / / / / / /

/ / / ~ /

__ ~

/ / / / / / / / / / / / / / / / / / / / / / / / F I , , - / / / / / / / / / / / / / / / / / / / /

trajecto~_...

/

All particles contained within the shaded region are collected

Schematic to illustrate the phenomenon of elutriation for the transport of aerosol through a horizontal rectangular channel.

Figure 4.16.

100

The motion of airborne particles

where u x is the air velocity in the longitudinal x-direction at a distance y from the central axis of symmetry of the channel (plate spacing 2b) and Uxo is the maximum value at the centre. Particles entering the elutriator come under the influence of the drag force (acting longitudinally along the channel) and vertically (towards the floor). The result is that particles follow trajectories governed by both components. If the relaxation time (-r) of particles is small compared to the time that the particle would spend inside the channel, then it may be assumed that the particle is always in dynamical equilibrium with its surroundings. That is (a) its longitudinal velocity is always the same as the local air velocity corresponding to its position, and (b) its vertical velocity is always equal to its terminal settling velocity (Vs). Particle motion, in terms of its component velocities in two dimensions, may therefore be described by the pair of simple equations dx Px

-=

H x

--

dt

(4.43) dy Vy

"-

V s

--

dt which can be solved very easily to give the family of trajectories corresponding to various particle aerodynamic sizes and positions of particles (relative to the axis) on entry into the elutriator. Some are shown in Figure 4.16. Example 4.5. For air flowing at 1 1 min -1 through a channel of width 10 cm and height (2b) 0.5 cm, calculate the length of the channel which will be sufficient to prevent the penetration of particles with aerodynamic diameter 5 txm. For the channel, the mean air velocity is given by

10_3 ) [m3 s -1] 60

Uave -(0.1[m] • 0.005[m]) = 0.033 m s -1 so that Re = 7 x

10 4

• 0.005[m] X 0.033[m S-1] -- 12

from which we confirm that the flow through the channel is certainly laminar (since Re > 1), where an e l e m e n t a r y m o d e l based on H u y g e n s wave optics (as described in any e l e m e n t a r y text on classical optics)

122

The optical properties of aerosols may be used to estimate Q. Although somewhat removed from true reality, this approach enables the illustration of some of the important features of extinction. Consider a light beam of cross-sectional area S interacting with a single particle of projected area A. From the basic definition of Q, attenuation of the beam due to this one particle is expressed by -

QA

(5.10)

s If a detector is now placed as shown in Figure 5.3, and if the wave amplitude of the radiation per unit area of the beam is B then, without the particle present, the wave amplitude at the detector is BS and so the corresponding intensity is proportional to B2S 2. When the particle is present, the amplitude at the detector falls to B ( S - A ) and the corresponding intensity is proportional to B 2 ( S - A ) 2. Therefore I

{S 2 - ( S - A ) 2}

Io

S2

(5.11)

which, when A < < S, reduces to -

2A

(5.12) /o

s

Comparing Equations (5.10) and (5.12), it is seen that Q = 2. This is equivalent to saying (as stated in Babinet's principle of diffraction) that the amount of light removed from the beam by diffraction is equal to that which is lost by being geometrically incident on the particle. This is an important ,,,,.Area, S

r./ II Incident Light

i

I-.,Area. A f

!1

"J

tl

i!;,

v

I -

I I I_ I-v

I= Detector plane F i g u r e 5.3.

Schematic to describe a simple model for the phenomenon of light extinction by a single particle.

123

Aerosol science for industrial hygienists

result, but possibly ~ to some readers ~ a somewhat curious one. Why should the extinction coefficient as defined by Equation (5.4) exhibit a value which is greater than unity? This does not seem to be our experience from viewing 'every-day' large objects. However, the above model contains the implicit assumption that the detector must be a very long way away from the object in relation to the size of the object and the wavelength of the light. This can happen for a tiny aerosol particle at a relatively short distance, in which case we may feel comfortable with the result Q --~ 2 for aerosols. On the other hand, Q ---> 1 is more appropriate for much larger objects viewed under 'every-day' conditions. For particles which are small compared to the wavelength of the light (so that oL < < 1), Rayleigh obtained the following analytical expression for particle extinction by scattering

(8~ { 1,)2

ascatt

=

(m2+2)

3

(5.13)

where m is the particle refractive index as already defined. In addition, for absorption (m2_ 1) } Qabsorb

--

4~x

(5.14)

-

(m2+2)

Mathematically, in a manner consistent with Equation (5.1), the scattering result represents the real part of the light-particle interaction and the absorption result represents the imaginary part. From the above, it is seen that the extinction coefficient decreases with decreasing particle size or increasing wavelength of the light. The scattering component changes particularly sharply (as governed by or4). The important range between the two extremes of low and high ~ is most relevant to most aerosols found in workplace environments. This is where the Mie theory applies and for which, because of the mathematical complexity of the solutions, calculations for Q have been performed only for particles of relatively simple shape. Some typical results of such calculations over a wide range of ot are given in Figure 5.4. For the Mie range in the middle, the {Q,e~} curve, after its initial rise out of the Rayleigh region, exhibits strong oscillatory patterns. Physically, these oscillations may be regarded as the consequences of the 'constructive' and 'destructive' wave interference that takes place between the diffracted and refracted radiation. It is for the same reason that, for particles which are strongly absorbing (and where the refracted component is reduced), the oscillations are much less marked. Indeed, they may be damped out altogether.

124

The optical properties of aerosols 4

2 (b) m = 1.55 - 0.66i 0

I 5

1. 10

! 15

.

I 20

et = ' t r d l k

Figure 5.4. Typical results from calculations (using Mie theory) of the extinction coefficient (Q) as a function of particle size (d) and light wavelength (h) as embodied together in the particle size parameter ot = rrd/h (from Hodkinson, J.R. in Aerosol Science (ed. C.N. Davies), Copyright 1966, reproduced by permission of Academic Press Ltd, London). 5.5 E X P E R I M E N T A L M E A S U R E M E N T S O F E X T I N C T I O N Experimental extinction measurements are made in order to obtain values for Q, either for the purpose of validating theoretical calculations or for determining Q for aerosols where there are no calculated values. For workplace aerosols, for example, such information would be needed in order to enable the design and calibration of a suitable monitoring instrument based on the principles of light extinction. On the face of it, extinction measurements should be quite simple. To set up an appropriate optical system would involve a parallel light beam and a detector, between which the aerosol would be interposed. From measurements of I, I o and X we could proceed to determine Q (if we know CA) or CA (if we know Q). But, for the determination of Q, the provision of a test aerosol with well-defined concentration and appropriate particle size characterisation presents considerable difficulties. Then there are problems associated with the optics themselves. It is an in-built assumption that the light reaching the detector is only that which has not interacted with the aerosol and so has not been scattered or absorbed. However, for a light beam and detector of finite physical dimensions, the angular acceptance of the light measuring system will inevitably be such that some of the light scattered in the forwards direction will enter the detector and so be included in the measurement of I. As a result, I will be overestimated, suggesting an apparently low value of Q. The greater the angular acceptance of the detector system, the greater this error. For many practical instruments which have been built to operate on the principles of light extinction, there is a resultant uncertainty in characteristics such that calibration may be unreliable and performance may be inconsistent from one application to the next. In the best practical systems, this problem has been recognised and its effect minimised by careful design of the optics; for example, by the use of pinholes and lenses which prevent light leaving the aerosol at angles

125

Aerosol science for industrial hygienists Pin-holes

Light s ~ c e ~ l ~

..~.-_ ~..~:.,~2,.,~i~,,~~.Photodetector """ "" ' ~ : A:ero:o:l

lenses Figure

5.5.

Typical experimental set-up of the type required for the accurate measurement of extinction of light by an aerosol.

other than very close to the forwards direction from reaching the detector (shown schematically in Figure 5.5). Some good determinations of Q, obtained using an experimental system like that s u g g e s t e d in Figure 5.5, are shown in Figure 5.6. Here, for experimental convenience, Q is plotted as a function of the parameter 13 = 4ot(rn-1) which brings together both c~ and the particle refractive index m. Results are shown for non-spherical but reasonably isometric ~ particles randomly oriented with respect to the incident light. Such particles are quite representative of those found in many workplace aerosols. Figure 5.6 shows that the extinction coefficient tends to be quite constant at Q ~ 2 for 13 greater than about 15. But at smaller 13, Q exhibits only a single peak, higher for non-absorbing than for absorbing particles. From theory, backed up by good experimental data, there is a reasonable starting point for practical aerosol instrumentation based on light extinction principles. One area where there is particular interest is in the tomographic determination of aerosol in workplace atmospheres. This involves mapping the aerosol spatial distribution in a horizontal plane by means of a light

4

Irregular-shaped, 'real' particles

Q 2 ///

0

absorbing

5I

I I0

[3 = 4a (m-l)

I 15

I 20

Figure 5.6. Experimental data for the particle extinction coefficient (Q) as a function of the modified particle size parameter 13 - 4oL(m-1), obtained using apparatus like that described in Figure 5.5. The results are for non-spherical but reasonably isometric particles (from Hodkinson, J.R. in Aerosol Science (ed. C.N. Davies), Copyright 1966, reproduced by permission of Academic Press Ltd, London). 126

The optical properties of aerosols beam which is scanned through a workplace area and is transmitted to a succession of periphally-located detectors. Ramachandran and Leith (1992) have demonstrated that the extinction of light of multiple wavelengths (e.g., white light) for the various optical paths defined in such a system may allow the extraction of both the concentration and particle size distibution over the horizontal plane swept out by the scanning light beam. This is considered practicable because the optical path lengths can be made long. More generally, however, for extinction measurement where the path length is short or where the aerosol concentration is very low, the overall aerosol extinction coefficient (K) is likely to be low, so that I ~ I 0. Here therefore, since we are looking for small changes in light intensity, the sensitivity of measurement may be poor. For this reason, light extinction is not widely used today in workplace aerosol measurement instrumentation. Light scattering the converse of extinction ~ has many advantages, and so is much more widely used.

5.6 L I G H T S C A T T E R I N G Consideration of scattered light is based on the same physical principles as just outlined for extinction. However, because we now have the angular distribution of the scattering to take into account, the problem becomes yet more complicated. But, in terms of possibilities for instrument development, it does create more options. Now, instead of the extinction coefficient (Q) which was employed in the preceding section, the related particle scattering coefficient, S(O), is defined as flux scattered per unit solid angle at angle (O) from the forwards direction S(O) =

(5.15) flux geometrically incident on the particle

At the outset, it is assumed that the incident light is contained within a beam which is plane parallel and unpolarised. The physical scenario is shown schematically in Figure 5.7. Here, as before, I o is the intensity of the light incident on the aerosol. Now, for a detector which is being used to observe the aerosol through a slit detector placed at the angle O, it sees light coming from a scattering plane within the transmission path where the actual incident light, Ii, will be less than I o ~ due to extinction in the part of the beam before it reaches that plane. However, for simplicity, it is assumed here that the aerosol concentration is low enough such that I i = I o. From Equation (5.15), the total light flux received by the collecting optics in Figure 5.7 may be shown to be

127

Aerosol science for industrial hygienists

to

/

~.

" ~ Scattered light

Co

slit, w x h (Solid angle within which light is received, whlj~)

Figure 5.7. Physical scenario for assessing angular light scattering by an aerosol (from Hodkinson, J.R. in Aerosol Science (ed. C.N. Davies), Copyright 1966, reproduced by permission of Academic Press Ltd, London).

i:(

)( wh )

cploS(O )

(5.16)

sin 0

where w and h are the width and height, respectively, of the collecting slit which is placed at the focal point of a collecting lens of focal length f, and Cp as before ~ is the projected area aerosol concentration. In this expression, the first bracketted term on the right-hand side represents the volume (hatched area in Figure 5.7) from which the light is received by the collecting optics and the second represents the geometrical solid angle within which it is received. From this, as in the previous discussion about extinction, it is seen that there exists a basis upon which aerosol concentration measurement might be made. This time, however, instead of requiring knowledge of the extinction coefficient (Q), it is S(O) that needs to be defined and quantified. The application of light scattering principles in an instrument aimed at measuring aerosol concentration is referred to as 'aerosol photometry'. 128

The optical properties of aerosols 5.7 P A R T I C L E S C A T T E R I N G C O E F F I C I E N T As for the simpler case of extinction, the problem of determining the particle scattering coefficient may be broken down into three regimes ~ very fine particles, intermediate-sized particles and very large particles. For the reasons discussed earlier, there is no need to discuss the case of very large objects since these are not relevant to workplace aerosols. Again, for very small particles, Rayleigh's theory is applicable. For Rayleigh scattering, the total normalised scattered light flux from a particle into the angle O, as defined generally by Equation (5.15), is

s(o)

=

--

27r

{

( 1 "k-COS20) ~ ~) ( 1 + COS20)

(5.17)

(m2+

where the coefficient r replaces the two bracketted terms in the equation for S(O). Built-in to this equation, there is an additional concept, involving the degree of polarisation of the light. According to electromagnetic theory, light energy contains vibrations in the electric and magnetic vectors which are contained within the plane of the wavefront (i.e., transverse to the beam). For light where the vibrations are uniformly distributed throughout that plane, the light is regarded as unpolarised. But for light where the vibrations have a preferred direction, it is polarised. The degree of polarisation depends on the extent of this non-uniformity in the vibrations. Light which is initially non-polarised may undergo changes in degree of polarisation after it has interacted with some dielectric inhomogeneity. For example, reflected light may become polarised preferentially in a given direction, a phenomenon familiar to anyone who has used polarising sunglasses. In light scattering by aerosols, the same basic physics comes into play. Therefore, in Equation (5.17) which represents the total light scattered by a particle into the angle 0, there are two components Sa(O) = r and 32(0 ) ~-~ + COS20

(5.18)

where SI(O ) and $2(O ) are the components for scattered light polarised in and normal to the plane containing the incident and scattered light beams and the detector (see Figure 5.8), and

S(O) = 81(0 ) + 32(0 )

(5.19)

from Equation (5.17). The first component, $1(O ), gives an angular scattering pattern that is circular (and hence uniform in all directions). The second, $2(O ), gives a symmetrical figure-of-eight pattern indicating enhanced scattering in the forward and backward directions and zero scattering at 90 ~, 129

Aerosol science for industrial hygienists

•

Electromagnetic vibrations in the

tion of light beam (x)

Figure 5.8. Schematic to illustrate the two-component nature of polarised light. independently of particle size or wavelength of the light. The angular distributions of the two components of S(O) for Rayleigh scattering by fine particles are shown in Figure 5.9. As for extinction, the situation becomes more complex for larger particles of the order of or greater than the wavelength of the light. Some typical scattering patterns are shown in Figure 5.10, where S(O) is now replaced by the Mie intensity parameter, s(O) - 2rretzs(o). Here the general shape is $1

$2

s2(o)

Incident light

sl(0)

Small particle (d 1 0.418

)

1+ St (9.12) (R-l) A=I+

forR < 1 0.506R1/2 ) 1+ St

for wide ranges of St and R. Rader and Marple (1988) took into account the effects of particle interception at the tip of the sampling probe, and obtained

A = 1 + (R-l)

{ (

1

1-

)}

(9.13)

1+3.77STO.883 Effects of orientation

The situation becomes more complicated when the thin-walled probe is placed at an angle with respect to the approaching aerosol (i.e., is 'yawed'). This was first studied scientifically by Durham and Lundgren (1980), and later by Davies and Subari (1982) and Vincent et al. (1986). The physical picture is shown schematically in Figure 9.5, where the tube-shaped probe is placed at an angle 0 to the forward-facing direction. Here, as for the forward-facing sub-isokinetic case, the flow again diverges as it approaches the tube entrance. But, for the same value of the sampling ratio R, the divergence is less than for the forward-facing direction because the tube entrance projects upstream a smaller cross-sectional area. Now, the body of the sampler no longer imposes an infinitesimally small obstruction, but appears 'blunter' as more of the body of the tube presents itself to the flow, the more so as the angle 0 increases. In addition to these complications, the sampled flow has to change direction in order to enter the sampling 247

Aerosol science for industrial hygienists Vena c o n t r a c t a

Limiting streamsurface Figure 9.5. Schematic on which to base development of an impaction model for a thin-walled sampling probe aligned at an angle to the wind (from Vincent, J.H., Aerosol Sampling: Science and Practice, Copyright 1989, reproduced by permission of John Wiley and Sons Limited).

orifice. Therefore, the sampled flow not only undergoes divergence (or convergence for super-isokinetic flow) but also 'turns'. The net result of all these considerations is a more complicated expression for aspiration efficiency. Thus A = 1 + e~'(Rcos 0 - 1)

(9.14)

where the modified impaction parameter is

~x'= 1 -

(9.15) {1 + G(O)St(cos 0 + 4R1/2sin1/20)}

The coefficient G is now described as a function of orientation, although G - 2.1 has been found to provide a fair working approximation (Vincent et al., 1986). Physically, Equation (9.15) embodies considerations of the change in time associated with the passage of a particle through the distorted flow region as the contribution due to turning increases as 0 increases. It is now seen that A ~ Rcos0 for large St. Some typical trends for aspiration efficiency obtained using this model are shown in Figure 9.6. For the probe placed facing the flow, this expression reduces ~ as it should to the form of Equation (9.7). When Rcos0 = 1, then A = 1 for all particle sizes. So this is, in effect, the isokinetic condition for the yawed probe. Finally, when the probe is placed at 90 ~ to the flow, it yields the interesting result that

248

Aerosol sampling in workplaces 1.0 0=0

0 increasing

I

0

I

5

10

I

15

Particle aerodynamic diameter d~ (Ixm) Figure 9.6. Typical trends in aspiration efficiency for a thin-walled sampling probe facing at various angles to the wind (fixed R, varying dae and 0).

A - f { S t R 1/2}

(9.16)

which, on closer inspection, reveals that, for fixed volumetric flow rate, A is independent of the probe dimensions (Stevens, 1986). This is also consistent with the form suggested by Davies and Subari (1982) and Tufto and Willeke (1982). Finally, it is important to note that the preceding discussion applies for yaw angles only up to (and including) 90 ~. For backwards-facing orientations, the picture becomes complicated by the wake properties of the airflow about the sampler body, possibly accompanied by turbulence. Under such conditions, and on the basis of present knowledge, it is difficult to predict sampler performance. Example 9.1. A thin-walled tube of diameter 1 cm and sampling flow rate 20 1 min -1 is used to sample particles of aerodynamic diameter 25 txm from an airstream moving at 2 ms -1. Calculate the aspiration efficiency. The sampling velocity is given by ( 2 0 x 10-3/60) [m 3 s-1] • 4

Us =

= 4.24 m s-1 3.142 • 10 -4 [m 2]

From Equation (9.9), Stokes number is (252x 10-12) [m 2] • 103[kg m -3] • 2[m s-1] St = 18 • (18• 10-6 ) [N s m -2] • 10-2[m] = 0.386

249

Aerosol science for industrial hygienists The velocity ratio is

R =

- 0.472 4.24

From Equation (9.11), the coefficient G to be used in the impaction efficiency equation is 0.62 G=

)

2+ 0.472

= 3.32 So, from Equation (9.10), impaction efficiency is

1

)

1 + (3.32 • 0.386) = 0.561 This is now used in Equation (9.7) to give the aspiration efficiency A = 1 + 0.561 ( 0 . 4 7 2 - 1) = 0.704 *

Aspiration efficiency is 0.704 (or 70%)

E x a m p l e 9.2. F o r the p r e v i o u s e x a m p l e , c a l c u l a t e t h e a s p i r a t i o n efficiency w h e n the t u b e is p l a c e d at 90 ~ to the flow. Note that cos 0 = 0 and sin 0 = 1 Here we need a new impaction efficiency, oL', as given by Equation (9,15). Usiiag G(0) = 2.1 (the recommended working approximation), we get

{

1

)

or' = 1 (1 + (2.1 x 0.386 x 4 x V/0.472)) = 0.690

250

Aerosol sampling in workplaces Using this in Equation (9.14), we get A = 1 + 0.690(0-1) = 0.31 *

Aspiration efficiency now falls to 0.31 (31%)

9.4 A S P I R A T I O N E F F I C I E N C Y OF BLUNT SAMPLERS As already stated, thin-walled sampling tubes represent the simplest case of the general aspiration problem outlined in Chapter 4. But in reality, true thin-walled probes do not exist since the walls must have finite thickness, no matter how thin. Therefore, there must always be some aerodynamic blockage, even for forwards-facing 'thin-walled' probes, and the overall nature of the flow will contain features associated with both the convergence of the sampled air to enter the sampling orifice as well as the divergence to pass around the solid body of the sampler. In practice, however, it is possible to design thin-walled probes with walls sufficiently thin that such effects are negligible. This notwithstanding, thin-walled sampling probes enjoy only very limited application in industrial hygiene. Indeed, in spite of the considerable research which has gone into understanding their performance, application is still confined largely to aerosols in stacks and ducts. For most types of sampler used in practical aerosol measurement (and including, of course, the human head itself), the 'blocked-off' area projected by the body of the device is very much greater than the area projected by the sampling orifice itself. Under such conditions, sampler 'bluntness' becomes a very important factor. Attempts have been made to model the performances of so-called 'blunt' samplers along the same lines as described above for the idealised thin-walled probe. The physical picture for a sampler of simple shape facing the wind (e.g., an axisymmetric disc with a central sampling orifice) is shown in Figure 9.7. It is based on the flow pattern for the same system obtained by flow visualisation shown in Chapter 2 (see Figure 2.6a). The main goal in developing a physical model for the aspiration efficiency of this system is to evaluate the expression A = A 1A2

(9.17)

in terms of the relevant system variables. Here, A~ and A 2 represent the 'efficiencies' with which aerosol particles are conveyed towards the sampling orifice through the two distinct characteristic parts of the flow (assigned the subscripts 1 and 2, respectively). Each of these parts may be described in turn by an expression of the type shown in Equation (9.7), but with modified

251

A e r o s o l science f o r industrial hygien&ts

Limiting streamline Figure 9.7. Schematic of a simple blunt sampler facing the wind, on which to base development of an impaction model for aspiration efficiency (from Vincent, J.H., Aerosol Sampling: Science and Practice, Copyright 1989, reproduced by permission of John Wiley and Sons Limited).

Stokes' n u m b e r and velocity ratio terms derived from the local characteristics of the flow. The result is a set of working e q u a t i o n s which, for the simple axisymmetric case of a disc-shaped sampler facing the wind, is (Vincent, 1987, 1989)

St

--

2 dae p,

R

=

U/Us

(9.18.2)

r

=

8/D

(9.18.3)

r

=

r2/R

(9.18.4)

S

=

B ~1/3 D for 8 <
0.95 p r o v i d e d that St c R e E

00.1 -

0.01 0.1

0.1-

l 1

I 10

0.01 0.1

[ 1

I 10

Particle diameter (p.m)

Figure 10.12. Summary of the measured optical responses of the Royco and Climet optical particle counters (based on results reported by Mfikynen, J. et al., Optical particle counters: resolution and counting efficiency. Journal of Aerosol Science, 13, 529-535, Copyright 1982, and by Chen, Y.S., et al., Experimental responses of two optical particle counters. Journal of Aerosol Science, 15, 457-464, Copyright 1984, with kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington OX5 1GB, U.K.).

of operation is that airborne fibrous particles are subjected to a combined unidirectional and oscillating electric field. The larger unidirectional field aligns each fibre and the smaller oscillating component introduces a 'rocking' motion about its axes of alignment. The alignment and the rocking motion are dependent on the applied fields but are independent of fibre dimensions (Lilienfeld, 1985). In the physical arrangement of the instrument, the electric fields are arranged so that the rocking motion takes place in the plane at right angles to an incident light beam (see the optical arrangement shown schematically in Figure 10.13a). Light scattering associated with the rocking motion of the fibre is detected in this plane (Lilienfeld, 1987). It is greater for long fibres and becomes non-existent for the limiting case of spherical particles. Thus the opportunity exists for the selective detection of long fibres (e.g., those meeting the measurement criteria for 'respirable' fibres). The packaged instrument is shown in Figure 10.13b. Its performance capability is illustrated in Figure 10.14, where the scattered light intensity is plotted as a function of the cylinder roll angle + (see Figure 10.13a) for particles of fixed diameter and varying length. From this it is clear that particles can be discriminated according to their length and counted electronically. In practice, however, it has been found that the response of the instrument cannot be predicted theoretically. So it is necessary to calibrate it side-byside with one of the more conventional m e m b r a n e filter-based reference methods.

316

Direct-reading monitoring of workplace aerosols

Figure 10.13. The Fibrous Aerosol Monitor (FAM): (a) optical configuration (from Lilienfeld, P., Light scattering from oscillating fibres at normal incidence. Journal of Aerosol Science, 18, 389-400, Copyright 1987, with kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington OX5 1GB, UK), and (b) photograph of practical instrument (reproduced courtesy of P. Lilienfeld, MIE Inc, Billerica, MA).

317

Aerosol science for industrial hygienists

.,,-4

r~

O

L = 20 ~m

U

o,..

/

-IO

f

~-

10 i.Lm 5 ~m

o Fibre roll angle, 4) (degrees)

I

IO

Figure 10.14. Graph indicating the performance of the FAM in terms of its ability to discriminate between fibres of different length (from Lilienfeld, P., Light scattering from oscillating fibres at normal incidence. Journal of Aerosol Science, 18, 389-400, Copyright 1987, with kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington OX5 1GB, U.K.).

Apart from optical particle counters like those described where particle size is determined directly from the intensity of the scattered light pulse, there are also optically-based particle counting instruments which work on different principles. These include, for example, instruments where operation depends on the dynamic properties of particles as detected using phase-Doppler and imaging techniques (as reviewed by Rader and O'Hern, 1993). One instrument which is beginning to find increasing use in industrial hygiene, especially industrial hygiene research, is the 'Aerodynamic Particle Sizer R' (APS) (TSI Inc., St. Paul, MN). This was first proposed by Wilson and Liu (1980). The principle of operation of this instrument is shown schematically in Figure 10.15 and the instrument itself in Figure 10.16. The particles are introduced into the sensing zone through an acceleration nozzle, and each one is detected optically and its velocity relative to the surrounding air jet determined by laser Doppler velocimetry. The difference in velocity between the particle and the air is a direct measure of the particle's ability to respond to changes in the motion of the surrounding air, and so may be related directly to particle aerodynamic diameter. Since this index of particle size is highly relevant to particle inhalation and deposition in the human respiratory tract (see Chapter 6) as well as to aerosol sampling (see Chapter 9), this therefore links up strongly with the needs of industrial hygiene aerosol measurement. Baron et al. (1993) have provided a concise review of the

318

Direct-reading monitoring of workplace aerosols Aerosol in I Outer nozzle ~, ~ ~ . J 5 Imin-' ~'::.'*'.] Filter Inner nozzle ___~2, ~.~ ~ ["'] Flowmeter 1 1 min-I '. ":'"-. -..I'2Fr:T'Ng-"~ I x ~i":':~--~ ~

n

cus" g optics Laser

"" [7

"

'

1 ~

Shear4r ,valve nozzle min-I

Photomuitiplier

1

Pressure transducer

"Nx

If ~Filter I V Flowmeter [ I

I

II

I

Internal vacuum .... L.___ pump I

Figure 10.15. Schematic of the Aerodynamic Particle Sizer a (APS) (TSI Model 3310, schematic diagram courtesy of TSI Inc, St. Paul, MN).

Figure 10.16. Photograph of the Aerodynamic Particle Sizer R (APS) (TSI Model 3310A, photograph courtesy of TSI Inc, St. Paul, MN).

319

Aerosol science for industrial hygienists

APS, as well as other devices with related principles of operation such as the 'Aerosizer' (Amherst Process Instruments, Amherst, MA) (e.g., Dahneke, 1973) and the 'Electric Single Particle Aerodynamic Relaxation Time Analyser' (E-SPART) (e.g., Renninger et al., 1981). Although the optical response, reflecting the light-particle interaction, is a primary performance feature of optical particle counting instruments like those described, there are other important performance parameters that need to be taken into account. Firstly there is the question of defining the sensing zone into which the particles of interest may enter and from which the scattered light is received by the detector. This is determined by the design of the collector/detector optics. Here the problem lies in making the sensing volume large enough so that there is always a good chance of finding a particle there, but not so large that there will be more than one particle at any given time. This may be achieved firstly by constraining the aerosol flow as a thin particle beam in a sheath of clean air and then ensuring that the light-collecting optics receives light from a region which is small enough to contain only one particle. One difficulty is that, if more than one particle is present in the sensing zone at the ~ame time, they will be counted and sized together and recorded as if they were a single, larger particle. Thus, in some practical situations, aerosol concentrations may be great enough that, even at low sampling flow rates, such 'coincidences' may preclude the use of a particular instrument. In some instruments (e.g., for the APS), dilution of the sampled aerosol has been employed in order to alleviate this problem.

10.5 E L E C T R I C A L P A R T I C L E M E A S U R E M E N T The diverse physical properties of aerosols enable a range of further options for particle detection and characterisation. The electrostatic charge carried by aerosol particles, and which can be placed on particles in a controlled way through corona discharge techniques, provides a powerful alternative to the optical approaches discussed above. There are two primary objectives of electrical measurement, the electric charge distribution in an aerosol and the particle size distribution. The particle charge distribution is important in the industrial hygiene context since the charges carried by workplace aerosols may have a significant influence on the lung deposition of inhaled particles and on the performances of sampling and control devices (as reviewed by Vincent, 1986), it having been shown that relatively freshly-generated aerosols in workplace atmospheres are charged to levels significantly above that corresponding to Boltzmann equilibrium (Johnston et al., 1985). Those workplace studies were carried out using a 'split-flow electrostatic elutriator' of the type shown in Figure 10.17a (Johnston, 1983). In this device, particles are sampled into a rectangular duct between a pair of conducting plates, and are transported towards the upper or 320

Direct-reading monitoring of workplace aerosols lower plate d e p e n d i n g on the m a g n i t u d e and polarity of the charge carried and on the applied voltage between the plates. Particles of p r e - d e t e r m i n e d size are detected (using an optical particle counter set to the a p p r o p r i a t e particle size channel) at the exits of the upper and lower halves of the duct, respectively, for a range of applied voltages. By analysis of the two ' p e n e t r a t i o n ' curves using the ' m e t h o d of tangents' which has been described earlier for a simple electrostatic elutriator by H u r d and Mullins (1962) and Vincent et al. (1981), the distribution and m a g n i t u d e of the charge on the sampled aerosol m a y be determined. The p r o c e d u r e with the p r o t o t y p e apparatus used was found to

Figure 10.17. The 'split-flow' electrostatic elutriator: (a) schematic of the basic electrical arrangement, and (b) drawing of a fully-aut0mated version (where A is the parallel plate device, B is an Aerodynamic Particle Sizer (APS), C is a high voltage supply, D is a microcomputer, and E is a printer) (from Wake, D. et al. 1991, Crown Copyright is reproduced by permission of the Controller of HMSO).

321

Aerosol science for industrial hygienists be effective and reproducible. But it is rather laborious. This prompted Wake et al. (1991) to develop the fully-automated version shown in Figure 10.17b. However, at present, no commercial versions of this instrument have been developed. Hochrainer (1985) suggested that it is better to use a device where the aerosol is introduced into the inter-electrode space through an entrance slit whose location is well defined, thus rendering the 'method of tangents' redundant and so providing a direct measure of the electrical mobility of the particles (and hence their charge). Such instruments are referred to as electrical mobility spectrometers. Two versions have been developed, both based on cylindrical geometry. The first is the electrical aerosol analyser ( E A A ) shown schematically in Figure 10.18a. Here all the aerosol entering through the narrow annular slit at the top of the inter-electrode space and which is not deposited by electrical forces on either electrode passes through to a particle counter. The second is the differential mobility analyser ( D M A ) , shown schematically in Figure 10.18b, in which all those particles are detected which arrive at the central electrode exactly at the location of the exit slit

Clean air Clean air ,ll

~,

. ~

.

er

Charger

.:::.:...-:.:.:, 9

9.

-.:: ....:..:.. :

sampled

:..lliH..-i ..1l ..-. High voltage supply

~ [

{:.:.:

aerosol

/.~::{.

~ii-"~i'!"

Exit slit

supply

Excess

I:- 9 .'7-

Clean air

...

air

~..;:.:::: counter

To particle counter

(a)

(b)

10.18. Schematics to show the operation of two electrical mobility spectrometers: (a) the Electrical Aerosol Analyser (EAA), and (b) the Differential Mobility Analyser (DMA).

Figure

322

Direct-reading monitoring of workplace aerosols shown in the diagram. For both the E A A and the D MA, the electrical mobility distribution of the aerosol entering both instruments is provided directly from the curve of particle counts versus applied voltage. As for the electrostatic elutriator, the determination of the distribution of particle charge requires independent measurement of particle size. Conversely, however, if the charge on particles of given size is predetermined (for example by contact with air ions under controlled charging conditions), then either of the mobility spectrometers described can be used to determine the particle size distribution. Devices currently available commercially (e.g., from TSI Inc., St. Paul, MN) can provide this information only for very fine particles in the size range 0.01-1 Ixm.

10.6 C O N D E N S A T I O N NUCLEI P A R T I C L E C O U N T E R S (CNC or CPC) Instruments like those described in Section 10.5 require the detection of ultrafine particles. This has frequently involved another class of particle counters whose operation depends on the condensation of liquid vapour onto the particles acting as nuclei. This follows the theory of heterogeneous nucleation as outlined in Chapter 2 and particle growth as outlined in Chapter 3. The principle of operation of the condensation nuclei counter (CNC) ~ sometimes

Filter

~=~]P

'~ f~$[ Ill m

r

i

|

.

Filter

~

..-

Flowmeter 300 cm3/min 1

Pump exhaust 1500 cm3/min "n

/ o -tios I !

I I I I Cooled c o n d e n s e r 9 o

Vacuum pump

....... ]

Optional make-up air 0 or 1200 cm3/min "1

Heated saturator Optional bypass flow

Sample inlet 300 or 1500 cm3/min "n

Liquid-soaked felt

Figure 10.19. Schematic to show the operation of the Condensation Nuclei Counter (CNC) (TSI Model 3022A, schematic diagram courtesy of TSI Inc, St. Paul, MN). 323

Aerosol science for industrial hygienists

called the condensation particle counter (CPC) ~ involves firstly the sampling of aerosols and their introduction into a region which is saturated with water or some other appropriate substance (e.g., alcohol). The atmosphere is then made to supersaturate, preferably by convective cooling since supersaturation by expansion will require a non-uniform flow, usually considered undesirable from the sampling point of view. This causes molecules from the vapour phase to condense onto the small particles. The particles then grow to become large enough for detection by conventional optical particle counting techniques. A typical such device shown schematically in Figure 10.19 has been described by Agarwal and Sem (1980) and is now available commercially (TSI Inc, St. Paul, MN). It is widely used in fine-particle aerosol research. One particularly interesting version of this device, the TSI P O R T A C O U N T R, is frequently employed by industrial hygienists. As shown in Figure 10.20, this instrument is just about small enough to be used as a personal sampler for very fine particles. But perhaps its most common use is as a detector for personal respirator fit testing.

Figure 10.20. The PORTACOUNTR, a portable version of a CNC of the type shown in Figure 10.19 (photograph courtesy of TSI Inc, St. Paul, MN). 324

Direct-reading monitoring of workplace aerosols 10.7 M E C H A N I C A L A E R O S O L MASS M O N I T O R S For most of the direct-reading instruments described so far, the physics of the particle detection process is such that mass concentration of the aerosol of interest is usually not provided directly and unambiguously. This means that they may have somewhat limited application for routine industrial hygiene use. There are, however, some further direct-reading options which, in principle at least, can directly provide the mass concentration of the aerosol. These are generally referred to as 'mass balances', and share the common feature that the aerosol of interest must first be sampled and collected efficiently onto an appropriate surface. One such device is the piezoelectric mass balance, shown schematically in Figure 10.21. The main sensor is the piezoelectric crystalline material (e.g., so-called 'AT-cut' quartz). When an oscillating (or ac) potential is applied between the coated conducting surfaces placed on each face of the crystal, the crystal vibrates mechanically in its transverse mode. The resonant frequency for such mechanical oscillations is a strong function of the mass of the crystal (as, by analogy, for any physical spring-mass system). So any change in effective mass of the crystal will produce a change in resonant frequency of the form

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325

Aerosol science for industrial hygienists where Af is the change in frequency from its value at f corresponding to a change in mass Am, and where k is a coefficient which describes the sensitivity of mass detection and depends on the type of crystal, its geometry and size, etc. A summary of the piezoelectric mass balance concept and its applications has been given by Ward and Buttry (1990). From Equation (10.2), it can be seen that if Af and f can be detected and measured in the external driving circuitry, then Am may be obtained, provided that k is determined by means of appropriate calibration. Such a change in mass can occur as the result of aerosol particles which are deposited on the vibrating surface of the crystal. Therefore it follows that monitoring Af over a short time interval will provide information about corresponding changes in the mass present on the surface, and hence on the sampled aerosol concentration. So an instrument based on the piezoelectric mass balance concept can be seen as useful for providing direct-reading information (in close-to-real-time) about aerosol concentration. With all this in mind, an important part of a piezoelectric mass balance system is the efficient sampling and deposition of the particles. Electrostatic precipitation (see Chapter 11) has been shown to be effective for this purpose. In some versions of the device, impaction has also been employed. There are some basic practical limitations associated with this type of instrument. Firstly, the accurate detection of mass requires that the deposited particles are rigidly attached to the active crystal surface and are able to remain so during the rapid accelerations that are experienced during the mechanical oscillation of the crystal. Although this is usually the case for very fine particles for which the short-range adhesion forces are large, it may not be so for large particles (e.g., greater than a few micrometres). For the latter, particles may be less well detected, in which case significant undersampling of mass can occur. Secondly, if the crystal becomes heavily loaded, the response of the crystal as given by Equation (10.2) may become non-linear and unpredictable. These and other difficulties such as particle size effects, sampling losses, etc. have been widely reported (see Lundgren et al., 1976, and others). A related device is the Tapered Element Oscillating Microbalance (TEOM R) (first reported by Patashnick and Hemenway, 1969). Now the oscillating element is a tapered hollow glass tube (see Figure 10.22). One end of the tube is anchored, while the other end supports a filter through which the sampled air is drawn and on which the particulate material is deposited. Again, as the mass on the filter ~ and hence on the tapered element ~ increases, the frequency of electromechanically-generated oscillation decreases, and the rate of change can be related to the mass rate at which the aerosol is being sampled (and hence to aerosol concentration). This device has been considered for close-to-real-time sampling of respirable dust in mines. It is a promising technique provided that attention is given to limitations similar to those reported for the piezoelectric mass balance.

326

Direct-reading monitoring of workplace aerosols

Figure 10.22.

Schematic of the Tapered Element Oscillating Microbalance (TEOMR).

10.8 N U C L E A R MASS D E T E C T O R S Beta attenuation provides yet another alternative for the determination of deposited mass. Negatively-charged beta particles are emitted during the radioactive decay of isotopes such as ~4C or 147pm, and may interact with and so be attenuated by matter. The physical nature of the interaction between a beta particle and an individual atom in the attenuating medium is such that the efficiency (i.e., the 'cross-section') of the interaction is proportional to the ratio between the atomic number (i.e., the number of protons in the nucleus) and the atomic weight for the substance in question. This ratio does not vary much between the elements. So, to a good approximation, this means that the interaction relates uniquely to mass. For a beam of beta particles passing through an attenuating medium, the intensity falls according to the familiar exponential law, this time in the form I = Ioexp(-ixX)

327

(10.3)

Aerosol science for industrial hygienists

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Figure 10.23. Basis of the operation of an aerosol monitor working on the beta attenuation principle.

where Ix here is the mass absorption coefficient (e.g., in cm 2 g-l, the calibration coefficient for an instrument based on this principle) and X is the mass thickness (g cm -2, directly proportional to the mass present). In practice, the particles need to be deposited onto a collecting surface such as a filter or an impaction surface. Therefore, it is necessary to take into account the attenuation of the beta radiation not just by the collected particulate material itself but also by the collection substrate. This means that, in a direct-reading instrument, means have to be developed to remove the contribution of the latter, for example, by alternately scanning areas of clean and mass-deposited substrate (e.g., as described by Macias and Husar, 1970 and Vincent et al., 1982). Although from the preceding it might appear feasible to determine the mass directly from measurements of I and Io, the coefficient Ix contains a number of complicating factors, including the geometry of the beta source and detection 'optics'. So careful calibration against known gravimetrically-assessed reference samples needs to be carried out for each practical instrument based on the beta attenuation principle. The basis of a typical practical measurement system is shown schematically in Figure 10.23, and several practical instruments operating on this principle have been built and used in the industrial hygiene setting.

10.9 O V E R V I E W Direct-reading aerosol instrumentation very definitely has a place in the industrial hygienist's repertoire of tools and methods. However, here perhaps more so than for other measurement methods, where the scientific bases

328

Direct-reading monitoring o f workplace aerosols

for the m e t h o d s available are usually so complex, considerable caution is r e c o m m e n d e d in choosing an instrument to p e r f o r m a particular task. T h e r e are m a n y potential traps and pit-falls. Most of the direct-reading instruments described here detect the presence and quantity of airborne particles within a p p r o p r i a t e size ranges. H o w e v e r , none appears capable of also identifying particle species in the aerosol of interest. This appears to be a very i m p o r t a n t area for future work, and some basic research leading to the d e v e l o p m e n t of direct-reading instruments for aerosol chemistry (e.g., Carson et al., 1995) and for detecting the presence of certain bioaerosols (e.g., Evans et al., 1994) is currently u n d e r way and looking very promising. In addition, b e y o n d such particle characterisation by species, direct-reading i n s t r u m e n t a t i o n which can provide quantitative information a b o u t particle shape is now b e c o m i n g available (e.g., Clarke et al., 1994).

REFERENCES Agarwal, J.K. and Sem, G.J. (1980). Continuous flow, single particle-counting condensation nucleus counter. Journal of Aerosol Science, 11,343-357. Armbruster, L. and Breuer, H. (1983). Dust monitoring and the principle of on-line dust control. In: Aerosols in the Mining and Industrial Work Environments (Eds. V.A. Marple and B.Y.H. Liu). Ann Arbor Science Publishers, Ann Arbor, MI, pp. 689-699. Baron, P.A., Mazumder, M.K. and Cheng, Y.S. (1993). Direct-reading techniques using optical particle detection. In: Aerosol Measurement (Eds. K. Willeke and P.A. Baron), Van Nostrand Reinhold, New York, pp. 381--409. Carson, P.G., Neubauer, K.R., Johnston, M.V. and Wexler, A.S. (1995). On-line chemical analysis of single aerosol particles by rapid single-particle mass spectrometry. Journal of Aerosol Science, 26, 535-545. Chen, B.T., Cheng, Y.S. and Yeh, H.C. (1984). Experimental responses of two optical partical counters. Journal of Aerosol Science, 15, 457-464. Clark, J.M., Reid, K., Burke, J.S. and Shakeshaft, D. (1994). A performance assessment of a real-time instrument for the size and shape analysis of airborne particles. In: Proceedings of the Fourth International Aerosol Conference (Ed. R.C. Flagan) held in Los Angeles in August 1994, American Association for Aerosol Research, Cincinnati, OH, pp. 1059-1060. Dahneke, B. (1973). Aerosol beam spectrometry. Nature Physical Science, 244, 54-55. Evans, B.M.T., Yee, E., Roy. G and Ho, J. (1994). Remote detection and mapping of bioaerosols. Journal of Aerosol Science, 25, 1549-1566. Ford, V.H.W., Minton, R. and Mark, D. (1983). Comparative trials in coal mines of the TM-Digital and SIMSLIN dust monitors. In: Aerosols in the Mining and Industrial Work Environments (Eds. V.A,. Marple and B.Y.H. Liu). Ann Arbor Science Publishers, Ann Arbor, MI, pp. 759-775. Hering, S.V. (ed.) (1989). Air Sampling Instruments, 7th Edn. American Conference of Governmental Industrial Hygienists (ACGIH), Cincinnati, OH. Hochrainer, D. (1985). Measurement methods for electric charges on aerosols. Annals of Occupational Hygiene, 29, 241-249.

329

Aerosol science for industrial hygienists Hodkinson, J.R. (1966). The optical measurement of aerosols. In: Aerosol Science (Ed. C.N. Davies), Academic Press, London, pp. 287-357. Hurd, F.K. and Mullins, J.C. (1962). Aerosol size distributions from ion mobility. Journal of Colloid Science, 17, 91-100. Johnston, A.M. (1983). A semi-automatic method for the assessment of electric charge carried by airborne dust. Journal of Aerosol Science, 14, 643-655. Johnston, A.M., Vincent, J.H. and Jones, A.D. (1985). Measurements of electric charge for workplace aerosols. Annals of Occupational Hygiene, 29, 271-284. Leck, M.J. (1983). Optical scattering instantaneous respirable dust indication system. In: Aerosols in the Mining and Industrial Work Environments (Eds. V.A. Marple and B.Y.H. Liu). Ann Arbor Science Publishers, Ann Arbor, MI, pp. 701-717. Lilienfeld, P. (1985). Rotational electrodynamics of airborne fibers. Journal of Aerosol Science, 16, 315-322. Lilienfeld, P. (1987). Light scattering from oscillating fibres at normal incidence. Journal of Aerosol Science, 18, 389-400. Lilienfeld, P., Elterman, P. and Baron, P. (1979). The development of a prototype fibrous aerosol monitor. American Industrial Hygiene Association Journal, 40, 270-282. Lundgren, D.A., Cater, L.D. and Daley, P.S. (1976). Aerosol mass measurement using piezoelectric crystal sensors. In: Fine Particles (Ed., B.Y.H. Liu). Academic Press, New York, pp. 485-510. Macias, E.S. and Husar, R.B. (1970). High resolution on-line aerosol mass measurement by the beta attenuation technique. In: Proceedings of the 2nd International Conference on Nuclear Methods in Environmental Research (Eds. J.R. Vogt and W. Meyer). CONF-740701, p. 413. Mfikynen, J., Hakulinen, J., Kivisto, T. and I~ehtim~iki, M. (1982). Optical particle counters: resolution and counting efficiency. Journal of Aerosol Science, 13, 529-535. National Institute for Occupational Safety and Health (NIOSH). (1979). USPHS/NIOSH membrane filter method for evaluating airborne asbestos fibers. Criteria for a recommended s t a n d a r d - occupational exposure to cotton dust. NIOSH Technical Report. Patashnick, H. and Hemenway, C.L. (1969). Oscillating fibre microbalance. Review of Scientific Instruments, 400, 1008-1011. Rader, D.J. and O'Hern, T.J. (1993). Optical direct-reading techniques: in situ sensing. In: Aerosol Measurement (Eds. K. Willeke and P.A. Baron). Van Nostrand Reinhold, New York, pp. 345-380. Renninger, R.G., Mazumder, M.K. and Testerman, M.K. (1981). Particle sizing by electrical single particle aerodynamic relaxation time analyser. Review of Scientific Instruments, 52, 242. Rubow, K.L. and Marple, V.A. (1983). Instrument evaluation chamber: calibration of commercial photometers. In: Aerosols in the Mining and Industrial Work Environments (Eds. V.A,. Marple and B.Y.H. Liu). Ann Arbor Science Publishers, Ann Arbor, MI, pp. 777-795. Vincent, J.H. (1986). Industrial hygiene implications of the static electrification of workplace aerosols. Journal of Electrostatics, 18, 113-145. Vincent, J.H., Johnston, W.B., Jones, A.D. and Johnston, A.M. (1981). Static electrification of airborne asbestos: a study of its causes, assessment and effects on deposition in the lungs of rats. American Industrial Hygiene Association Journal, 42,711-721. Vincent, J.H., Mark, D., Gibson, H., Aitken, R.J., Bothyam, R.A. and Lynch, G. (1982). Development of a portable gravimetric dust spectrometer. Technical Memorandum No. TM/82/15, Institute of Occupational Medicine, Edinbrugh, Scotland, U.K. Wake, D., Thorpe, A., Bostock, G.J., Davies, J.K.W. and Brown, R.C. (1991). Apparatus for measurement of the electrical mobility of aerosol particles: computer control and data analysis. Journal of Aerosol Science, 22, 901-916.

330

Direct-reading monitoring of workplace aerosols Ward, M.D. and Buttry, D.A. (1990). In situ interracial mass detection with pizeoelectric transducers. Science, 249, 1000-1007. Wilson, J.C. and Liu, B.Y.H. (1980). Aerodynamic particle size measurement by laserDoppler velocimetry. Journal of Aerosol Science, 11, 139-150.

331

C H A P T E R 11

Control of workplace aerosols 11.1 I N T R O D U C T I O N Ultimately, the reduction of risk to workers associated with exposure to aerosol involves technical control measures. Inevitably, it is one of the jobs of the industrial hygienist to become involved in this process, liaising with the engineers who install and commission the necessary equipment and, afterwards, monitoring the workplace environment in order to check that the equipment is operating effectively. A number of technical approaches are available, including: Reducing the 'aerosolisability' (or, where appropriate, the dustiness) of the working material used in the industrial process in question; Modifying the industrial process such that the aerosol generation process is rendered less effective; General exhaust ventilation (GEV) to achieve sufficiently rapid turnover of the workplace air and so achieve effective dilution of airborne contaminants; Local exhaust ventilation (LEV) to remove the airborne contaminant directly at the source so that it does not become dispersed into the general workplace atmosphere; Effective transport of particulate material following its exhaust from the working environment; Separation of the particles from the air extracted by ventilation; Containment of the aerosol generating process; Localised aerosol suppression; As a last resort, the occupational hygienist might recommend: personal protective measures in the form of respiratory filtration equipment. 332

Control of workplace aerosols It is clear that ventilation is a major component, and this is applicable not only to aerosols but also to the control of contaminant gases and vapours. The general problem of ventilation is a broad field in its own right. Much of it falls outside the immediate scope of this book and is fully covered elsewhere (e.g., Burgess et al., 1989). But for aerosols, after air has been removed from the worksite by general or local exhaust ventilation, it is usually necessary to separate the particles from the air before the air can be discharged to outdoors or re-circulated to the workplace atmosphere. For this there are a wide range of physical air cleaning options which can be applied, and much of this chapter will be devoted to reviewing their underlying principles.

11.2 ADJUSTMENTS TO I N D U S T R I A L PROCESSES The first consideration in relation to the control of worker exposure to aerosols relates to the processes by which aerosols are generated in the first place. This involves both the industrial process as well as the materials which are used in that process. In Chapter 3, we discussed the question of 'dustiness', and how quantitative indices can be obtained by which materials may be ranked according to their dustiness. For industrial processes involving the use of dusty materials, the first control option is, where possible, to change to an appropriate alternative material which has a lower dustiness index. But for industrial processes where the material which is producing the aerosol is itself the primary industrial medium, this is not a real option. Then other options need to be explored, and there are a range of possibilities; for example: Modification of the mechanical process by which the material is being worked (e.g., in minerals extraction by the appropriate design of picks, speed of rotation of cutting heads, etc.); Reduction of the degree of agitation of bulk material (e.g., in powder handling by avoiding vibration and unnecessary drafts, reducing the 'roughness' of conveying, avoiding or minimising drops, etc.); Reduction of the number of friction points where abrasion of working materials can take place (e.g., in textiles manufacturing by modifying the paths of carded, spun, wound and woven material, etc.); The use of additives to reduce dustiness (e.g., water or other liquid media as used in mineral extraction, including both spraying onto working surfaces and infusion into rock strata, etc.); and Enclosure (or partial enclosure) of the industrial process (e.g., in processing particularly hazardous substances such a nuclear materials, asbestos, etc.);

333

Aerosol science for industrial hygienists and so on. Most of these adjustments are largely empirical, based on experience and on trial and error. In the mineral extraction industries, for example, there has been a large amount of engineering research to reduce the aerosolising capability at various stages of the winning, conveying and preparation processes by combinations of the above (e.g., Commission of European Communities (CEC), 1982).

11.3 B E H A V I O U R OF A E R O S O L S IN T H E W O R K P L A C E ATMOSPHERE After the aerosol has become airborne and dispersed, the behaviour of the particles in the macroscopic aerodynamic environment of the workplace atmosphere becomes important. Here, transport of particles is governed by many of the aerosol mechanical processes already referred to, including gravitational settling, inertia, Brownian and turbulent diffusion, thermophoresis and electrostatic forces. Particles are removed from the room air by such mechanisms and, in the absence of ventilation, the aerosol concentration that can build up depends on the balance between them and the rate of generation. For workplaces, the 'perfectly-mixed' scenario is an idealised but nonetheless appropriate ~ simple model to use as a starting point towards gaining some useful insight. For this, first consider aerosol in an unventilated room of horizontal cross-sectional area A and volume V (see Figure 11.1). Particles with aerodynamic diameter dae fall under the influence of gravity with a terminal velocity, v~. This motion is superimposed on the random motions associated with the mixing. The build-up of the concentration of particles of size dae as a function of time is governed by the expression /

Aerosol source, strength 13

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