The Viscosity of Liquids under Pressure

VOL. 11, 1925

PHYSICS.- P. W. BRIDGMAN

603

THE VISCOSITY OF LIQUIDS UNDER PRESSURE BY.P. W. BiumxAw JSFItZRSON PHYSIcAL LABORATORY, HARVARD UNIvERSITY

Communicated September 10, 1925

A method has been developed by which the relative viscosity of liquids may be determined over a wide range of pressures at various temperatures. The method has been applied to 43 liquids in the pressure range between atmospheric and 12,000 kg./cm.2 and at 30° and 75°C. The results are summarized in tables 1 and 2. The results will be given in much greater detail elsewhere. In the detailed account will also be found certain data incidentally obtained, such as a number of new freezing points under pressure and the compressibility of glycerine to 12,000 kg. In table 1 are the results for all the liquids except water. The viscosity increases so rapidly with pressure that it is convenient to tabulate log (viscosity), rather than viscosity itself. Opposite each substance in the table are two lines of data; the upper'line gives data for 30°C. and the lower line for 75°C. The data tabulated are the logarithms of the ratios of the viscosity at the pressure and temperature in question to the viscosity at atmospheric pressure at 30°C. The frequently missing dta in the table correspond to the fact that the substance is not liquid under the conditions in question, but is frozen by the high pressure. Frdm the data tabulated the change of temperature coefficient of viscosity with pressure may be found. In table 2 are the data for water; the chang* of viscosity under pressure is comparatively small, so that it' is convenient to tabulate' directly relative viscosity rather than log viscosity. Water is unique among the substances investigated in that, at low temperatures and pressures, its viscosity decreases with rising pressure instead of increasing. At low temperatures the viscosity passes through a pressure minimum and then increases. With increasing temperature the minimum flattens out, eventually disappears, and at temperatures above approxiimately 25° the viscosity increases with rising pressure from the beginning. This anomalous behavior of water has been already suspected from previous measurements of viscosity at low pressures. The anomaly is doubtless connected, as are many of the other anomalies of water with a high degree of association, which changes rapidly with pressure and temperature. The viscosity of all the other 42 liquids itcreases uniformly with rising pressure. At low pressures the viscosity increases linearly with pressure, but beyond a pressure of the order of a thousand kilograms the rate of increase rapidly increases, so that a logarithmic curve is necessary to represent the entire course of the curve. The curve of log viscosity against' pressure is at first concave toward the pressure axis, but above a few thou-

604

PHYSICS: P. W. BRIDGMAN

PROC. N. A. S.

TABLR 1 LOG RELATIVS VISCOSITY AS A FUNCTION OF PRISSURI AT 300 AND 75°C. SUBSTANCS

ATMOS.

Methyl Alcohol Ethyl Alcohol n-Propyl Alcohol n-Butyl Alcohol n-Amyl Alcohol i-Propyl Alcohol i-Butyl Alcohol i-Amyl Alcohol n-Pentane

' ,OG10/1O I/sS 1/1 2000 6000 12,000 KG.

KO.

AN

KG.

N

.000 .286 .616 .998 i-Pentane 9.769 .043 .334 .655 .000 .363 .829 1.390 i-Amyl 9.657 .045 .473 .919 Decane *000 .494 1.131 1.915 Ethylene 9.598 .074 .610 1.223 Dibromide .000 .554 1.289 2.208 Ethyl 9.548 .089 .690 1.396 Chloride .000 .607 1.448 2.495 Ethyl 9.540 .105 .722 1.562 Bromide .000 .591 1.318 2.311 Ethyl 9.505 .087 .701 1.424 Iodide .000 .696 1.655 2.898 Acetone 9.444 .075 .838 1.459 .000 .686 1.636 2.952 Glycerine 9.424 .065 .848 1.780 I .000 .524 1.112 1.846I Ethyl 9.811 .380 .908 1.493 Acetate .000 .561 1.224 n-Butyl n-Hexane 9.803 .379 .961 1.646 Bromide .000 .641 1.487 n-Octane Cineole 9.810 .390 1.080 Diethyl.000 Oleic Acid aniline 9.419 .255 Nitroben.000 CC14 zene 9.760 .349 .884 .386 .000 Chloroform Toluene 9.858 .251 .691 .674 1.189 o-Xylene .000 .307 CS2 9.875 .180 .527 .946 i .000 .514 1.042 1.670 m-Xylene Ether 9.878 .344 .806 1.311 n-Amyl .000 .708 1.685 p-Xylene 9.736 .364 1.125 2.007 Ether .000 Cyclohexane p-Cymene 9.723 .3411 Methyl .000 .710 1.804 Eugenol Cyclohexane 9.747 .434 1.335 2.582 .000 Benzene 9.765 .308 Chloroben.000 .478 1.223 zene 9.814 .245 .852 Bromoben.000 .486 .874 9.801 .228 , zene .709 000 * Aniline 9.551 .102 I At 1500 kg. 2 At 1000 kg. ' At 10,000 kg. I

2

ATXOS.

KG.

.000 .559 9.821 .408 .000 .772 9.772 .463 .000 9.756 .203 .000 .405 9.850 .285 .000 .387 9.806 .235 .000 .385 9.837 .227 .000 .373 9.895 .245 .000 .497 8.810 9.204 .000 .463 9.836 .253 .000 1.474 9.832 .273 .000 9.654 .575 .000 .761 9.690 .259 .000 .2642 Deconnposes .000 .497 9.796 .267 .000 .577 9.767 .2g2 .000 .529 9.799 .286 .000 9.797 .315 .000 .626 9.800 .335 .000 1.081 9.429 .143

000 KG.

12,00 KG.

1.175 1.947 .960 1.586 1.334 .837 .683 .854 .653 .888 .672 .804 .610 1.346 9.818 1.120 .761 1.115 .811

1.323 1.111 1.400 1.123 1.549 1.200

1.031 .628 1.974 1.416 2.018 1.484

1.250

1.285 .896 1.832 1.087 .983

1.859 1.168 2.1648 3.007 1.520

.Vor. 11, 1925,

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PHYSICS: P. W. BRIDGMAN

sand kilograms the curve becomes nearly straight for most liquids, and for a number even .reverses curvature slightly. The increase of viscosity under 12,000 varies from 10-fold for methyl alcohol to at least 107 fold (extrapolated) for eugenol. It thus appears that the effect of pressure on viscosity is greater than on any other physical property hitherto measured, and varies more with the nature of the substance. The temperature coefficient of viscosity increases with rising pressure; the increase is of the order of several fold under 12,000, and varies much with the liquid. In general the results show a correlation between the increase of viscosity under pressure and the complication of the molecule. The increase is obviously less for such simple substances as methyl alcohol and CS2, and is greatest for substances with such complicated molecules as Cineole. This effect is particularly well marked in the various series of homologous compounds, such as the alcohols. TABLE 2

RULATIVR VISCOSITY OF WATEMR rnssuas X0./CM.2

1

500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10,000 11,000

RELAV VISCOSITY 00

1.000 .938 .921 .932 .957 1.024 1.111 1.218

1.347

10.30

.779 .755 .743 .745 .754 .791 .842 .908 .981 1.064 1.152

300

.488 .500 .514 .530 .550 .599 .658 .720 .786 .854 .923 .989 1.058

750

.222 .230 .239 .247 .258 .278 .302 .333 .367 .404 .445 .494

1.126

Theoretically the viscosity of liquids is not well understood. It is, of course, well recognized that the mechanism of viscosity in a liquid is entirely different from that in a gas, as is shown by the fact that changes of pressure or temperature produce opposite changes in the viscosity of liquids and gases. Such theoretical discussions as there are, have placed special emphasis on the relation between viscosity and volume. Thus PhillipsI has viscosity a function of volume only; that is, at 750 a liquid under a pressure sufficiently high to reduce its volume to the volume at atmospheric pressure at 30° would have the same viscosity as at 300 at atomspheric pressure. The data of this paper show that this relation is far from being satisfied. Brillouin2 in his theory does not make viscosity a volume function only, but makes it vary under changes of temperature at constant

606

PHYSICS: H. B. WAHLIN

Pfoc. N. A. S.

volume very much less than under changes of temperature at constant pressure. He finds an expression for (n/br) in terms of the compressibility and the velocity of sound in the substance. Tested against the data of this paper this expression fails by a factor which may amount to thousands of fold. The very large pressure effects, the great variability of the pressure effect with the nature of the material, and the fact that the pressure effect is high in substances with complicated molecules suggests that there may be a very important element which is neglected in the usual explanations of the viscosity of liquids, namely an actual interlocking effect between the molecules. A complicated molecule may be thought to have geometrical projections which interfere with its free motion with respect to its neighbors. The restraint offered by such an interlocking will evidently be decreased by rising temperature, even at constant volume, and would be expected to be increased to a smaller or a very large extent (depending on the particular geometrical configuration) by decreases of volume under increasing pressure. 1 H. P. Phillips, these PROCUEDINGS, 7, 172-177 (1921). 2 L. Bri11ouin, Jour. Phys. Rad. (VI), 3,326-340,362-383 (1922).

THE AGING EFFECT IN THE MOBILITY OF POSITIVE IONS By H. B. WAEaNw DgPARTM1NT OiF PHYSIcS, UNIVRSITY OF WISCONSiN

Communicated August 21, 1925

In an article entitled "Ionic Mobilities in Ether as a Function of Pressure;" which appeared in these PROCE3DINGS for July, 1925, Loeb questions the results on the aging in the mobility of the positive ions obtained by the writer' using the Franck modification - of the -Rutherford alternating potential method. The writer found, in agreement with results obtained by Erikson2 using a blast method, that if the mobility was measured soon after the ion was formed, the value obtained was 1.80 cm./sec./volt/cm. while if the* ions were aged the mobility dropped to the normal value, viz., 1.35 cm./sec./volt/cm. Loeb found that, due to the interaction of the alternating and the auxiliary field, a change in the auxiliary field alone will produce a change in the mobility which he could not ascribe to any aging effect and for this reason contends that the author's results are approximate only. That this effect, due to the gauze, was absent in the writer's results will be seen from the following considerations. It was found that at a pressure of 30 mm. and with an auxiliary field of