Pattern Formation at Interfaces

SpringerWienNewYork

CISM COURSES AND LECTURES

Series Editors: The Rectors Giulio Maier - Milan Jean Salençon - Palaiseau Wilhelm Schneider - Wien

The Secretary General Bernhard Schrefler - Padua

Executive Editor Paolo Serafini - Udine

The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.

INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 513

PATTERN FORMATION AT INTERFACES

EDITED BY PIERRE COLINET UNIVERSITE LIBRE DE BRUXELLES, BRUSSELS, BELGIUM ALEXANDER NEPOMNYASHCHY TECHNION-ISR. INST. OF TECHNOLOGY, HAIFA, ISRAEL

This volume contains 113 illustrations

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2010 by CISM, Udine Printed in Italy SPIN 12821907

All contributions have been typeset by the authors.

ISBN 978-3-7091-0124-7 SpringerWienNewYork




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26

Pierre Colinet

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Interfacial Patterns and Waves in Liquid Layers and Thin Films

27

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Interfacial Patterns and Waves in Liquid Layers and Thin Films

53

YCC F= FV F YV=M CM C  DG(M : Z(Y F=6
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70

Alexander A. Nepomnyashchy

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0,1*2'-,* -*4 '*'27 -,"'2'-,

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Thin Film and Droplet Patterns Shaped by Surface Forces

181

: GBM> K>@BHG  ;HNG=>= ;R : L ;HMA MA> :K>: BGM> @K:E :G= @K:EL 2A> :K>: BGM>@K:E BL >O:EN:M>= NLBG@ BGM>@K:MBHG ;R I:KML    

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182 

Len M. Pismen -2'-, "3# 2- 17++#207 -$ -,2!2 ,%*#1

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
  0   5> A:O> GHMB= MA:M MA> =BIHE> GM =H>L GHM :><M MA> LA:I> H? MA> =KHIE>M ?HHMIKBGM ;>LB=>L BML =BLIE:F>GM .G> A:L MH K>JNBK> MA>K>?HK> 0   A>G MABL BGM>@K:E O:GBLA>L 2A> K>F:BGBG@ ;HNG=:KR ?HK BGM>@K:E BL >O:EN:M>= NLBG@ MA> B=>GMBMR
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

     %    EG ' K P:RL H? >EBFBG:MBG@ MA> LBG@NE:KBMR >@ NLBG@ $J   RB>E= LBFBE:K K>LNEML =B>KBG@ HGER ;R MA> GNF>KBK MA> EH@:KBMAF 2A> K:MBH H? MA> F:EEM:E> LB@G H? MA> K>LHEO>= LBG@NE:KBMR

 

$"$# $ ' $ "%"#" -4',% 0-.*#2 -,  0#!301-0 '*+

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        0 .0  0  =0  0 =0             K>E:M>L MA> I>KMNK;:MBHG H? MA>  MH MA> I>KMNK;:MBHG H? =BL CHBGBG@ IK>LLNK>  0        0  =0     

184

Len M. Pismen

.G MA> HMA>K A:G= MA> BGM>@K:E  BL MK:GL?HKF>= MH : @K:E ;R BGM>@K:MBG@ BG MA> =BK><MBHG GHKF:E MH MA>  B> :EHG@ MA> K:=BNL = 



 



 = : ==  : =:  :  0  0 =       0  0 =0   =0  0 
 




2A> BGM>@K:G= H?  BL MK:GL?HKF>= :LLNFBG@ MA:M MA> K:=B:E =>I>G=>G H? MA> =BLCHBGBG@ IK>LLNK> BL =>M>KFBG>= ;R MA> EH EH IKHI>KMB>L P>:DER =>I>G=>GM HG MA> :K< E>G@MA : :><M I:K:F>M>KL H? MA> ?NG<MBHG  0  2A> E:LM >QIK>LLBHG BL H;M:BG>= ;R BGM>@K:MBHG ;R I:KML MA> ;HNG=:KR O:EN>L O:GBLA ;> MA> =BLCHBGBG@ IK>LLNK> O:GBLA>L ;HMA :M 0  :G= :M 0  0  ;R =>GBMBHG H? MA> IK>K MABLL (G OB>P H? $J   MA> KLM A:KFHGB< H? $J  ?KB<MBHG ?:<MHK  BL = BG MA> L:F> F:GG>K :L BG 1><MBHG  2A> =B>K>G BL BG >O:EN:MBG@ MA> BGM>@K:E   5BMA  0 =>G>= ;R $J   MA> BGM>@K:G= O:GBLA>L BG MA> IK> LBG@NE:KBMR :M 0  BL GH EHG@>K IK>L>GM LH HG> MA> LM:G=:K= 1MHD>L FH;BEBMR ?NG<MBHG   2A> K>@BHG B> : KBG@ PBMA MA> PB=MA 4 L:MBL?RBG@ MA> BG>JN:EBMR %  4   0 MH MA> =BLLBI:MBO> BGM>@K:E LAHNE= ;> >O:EN:M>= NLBG@ MA> :<MN:E LM:MBHG:KR IKHE> 0 = = ;R LHEOBG@ $J  HK      %







% 4 0  0  =0  EG    > 0 0 , 0



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

 
  0 % 0  
  %  0 PA>K> 0 BL MA> IK>JNBEB;KBNF PBMA : :M E:R>K H? ;NED NB= 2A> IK>:K E:K@>K =KHIE>ML PABK> ?HK> @KHP :M MA> >QI>GL> H? LF:EE>K HG>L 2ABL BL :G :G:EH@ H? MA> &B;;LT 2AHFLHG >><M PA>K> F:LL >Q PBMA MA> IK>IE:L >O:IHK: MBHG 2A> IK>OHENMBHG :L P>EE :L =KHIE>M FHMBHG K>= JN:LBLM:MBHG:KR PA>G BGM>K:<MBHG BL P>:D 1BG MA> H? MA> IK> @EB@B;E> $J  K>=NL MH MA> =BNLBHG >JN:MBHG PBMA O:KB:;E> >><MBO> =BNLBOBMR  0  
 0  

 0  8 0  0  



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

186

Len M. Pismen

MA> LBFIE>LM H? : I:BK H? =KHIE>ML L>I:K:M>= :M : =BLM:G 9 FNK MA:G MA>BK K:=BB %  HG> MA> +:IE: >JN:MBHG NLBG@ MA> ;BIHE:K LRLM>F PBMA MA> ?H =KHIE>M GM>KL 2A> L   K>LI><MBO>ER K>E:M>= MH MA> ":KM>LB:G L = > :L =

9 LBGA    L F:KD MA> BGBMB:E IHLBMBHGL :G= MA> LG >O>GML =HML F:KD >QMBG<MBHG >O>GML

L= ;R : EBG>:K DBG>MB< >JN:MBHG =-=;  3 - 3- PA>K> - BL MA> ;NED DBG>MB< E:MM>K BL :LLNF>= ?HK LBFIEB MA> L:F> BG MA> =KHIE>M :G= MA>  2:DBG@ BGMH :M MH ;> G>@EB@B;E> P> PKBM> MA> :=LHKIMBHG=BNLBHG >JN:MBHG ?HK MA> LNK?:<M:GM K:@> HG MA> LN;LMK:M> BG MA> =BF>GLBHGE>LL ?HKF -   - -    



PA>K>   >JN:EL MH  HNMLB=> :G=  BGLB=> MA> =KHIE>M ?HHMIKBGM 2A> LNK?:<M:GM K:@> - BL L= ;R MA> K:@> BG >JNBEB;KBNF PBMA MA> LNK ?:<M:GM  3 - 3 MBF> ;R MA> BGO>KL> =>LHKIMBHG K:M> G@MA ;R 3 PA>K>  BL MA> LNK?:<M:GM =BNLBOBMR HG MA> LN;LMK:M> M E:M>K LM:@>L H? MA> IKHLL PA>G LNK?:<M:GM : =KHIE>M ;NED HG> MA> L:F> >JN:MBHG M:DBG@ BGMH

Thin Film and Droplet Patterns Shaped by Surface Forces

191

:K>G H? :=LHKIMBHG K:M>L HNMLB=> :G= BGLB=> MA> =KHIE>M BL BFIHKM:GM :G= K>IE: =B>K>G H? MA> K>LI><MBO> O:EN>L  2A> KBLMB< O>EH K:MBH H? MA> 8FBEH KBLMB< 8AR=KH=RG:FB< O>EHKFBG>L MA> BG N>G H? OBLLL>L HG MA> =KHIE>M LA:I> LNLM:BG>= ;R LNK?: M>GLBHG 2ABL BFIEB>L MA:M MA> K BL MA> MKN> LF:EE I:K:F>M>K H? MA> IKH;E>F =>OB:MBHGL H? MA> LAHNE= ;> H? " ": MH CNLMB?R MA> I>KMNK;:MBHG :IIKH:K K>:EBLMB< >Q I>KBF>GM:E LA:I> H? FBEE>= =KHIE>ML BL HGER P>:DER =BLMHKM>= ;R OBLLL>L $JN:MBHG  MK:GL?HKF>= MH MA> ?K:F> FHOBG@ PBMA : =BF>GLBHGE>LL  O>EH = :QBL BL LHENMBHG H? MABL >JN:MBHG >QIK>LL>= PBMA MA> A>EI H? :G :IIKH IKB:M> &K>>GL ?NG<MBHG MAKHN@A :G BGM>@K:E HO>K MA> =KHIE>M ?HHMIKBGM :K>: :G= LN;L>JN>GMER MK:GL?HKF>= BGMH : @K:E PBMA MA> A>EI H? MA> &:NLL MA>HK>F /BLF>G    %HK : E> FH=NENL +  % 3 MA> KFBG>L MA> IKHI:@:MBHG LI>>= BL = BG MABL P:R :L  

   
        + > K>  :G=  ;>EHP :K> FH=B>= !>LL>E ?NG<MBHGL LLNFBG@ MA> MH ;> : EBG>:K ?NG<MBHG H? MA> LNK?:<M:GM K:@>  
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

    = +    +   + LBG  =  LBG   + =+ 

     =  =  LBG  + LBG  +     =+  LM:KMBG@ ?KHF  +   +  +  /EN@@BG@ MA> K>LNEMBG@ >QIK>LLBHGL BG $J  RB>E=L MA> HGL>M H? FHMBHG ! 

+ 7 +  +  +  + 9  



2A> = BG %B@  1BG MA> K:=B:E =>I>G=>G BG $J  L:MNK:M>L PA>G MA> =KHIE>M K:=BNL ?:K >Q>=L MA> =BNLBHG:E K:G@> LH MA:M !  :M +  GH =KHIE>M ;>EHP MABL EBFBMBG@ O:EN> !> H? MA> EH@:KBMAFB< =>I>G=>G H? ! HG MA> =KHIE>M K:=BNL MA> LBS> =>I>G=>G H? MA> MK:O>EBG@ MAK>LAHE= BG $J  LMBEE K>F:BGL BFIEBQIEBI>G=>G >QMK:<M>= :?M>K K>PKBMBG@ $J  :L   
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194

Len M. Pismen 1
M0 0.25 0.2

1
M0 0.005

0.15

0.001 0.0005

0.1

0.0001 0.00005

0.05

0.00001 0.02 2

4

0.05 0.1 0.2 6

a

8

a

'%30#  2A> =BF>GLBHGE>LL =KHIE>M K:=BNL + (GL>M ;EHPNI G>:K MA> HKB@BG HG EH@:KBMAFB< L 2A> =KHIE>ML :K> FH;BE> ;>EHP MABL 

MA> K:=BNL H? FH;BE> =KHIE>ML BL ;HNG=>= ;HMA ?KHF ;>EHP :G= :;HO> :L BM BG=>>= ?HEEHPL ?KHF MA> >QBLM>G H? : F:QBFNF BG MA> K:=B:E =>I>G=>G H? MA> I:K:F>M>K   LN>G BG %B@  !>RHG= MA> EH= NLBG@ ?NKMA>K M>KFL BG MA> >QI:GLBHG   2A> =BIHE> GM H? MA> M>KF JN:=K:MB< BG < O:GBLA>L :G= MA>K>?HK> MA>K> BL GH K 2A> =BIHE> GM H? MA> MABK=HK=>K M>KF BL  <  PA>K>  

 +   +  +  +  + +  +  +  



2ABL GM BL G>@:MBO> A>G MA> ;B?NKKOB:MBHGL !  ! !   MA> O>EH =BF>GLBHGE>LL  =KHIE>M K:=BNL + ?HK     H;M:BG>= =BK><MER ;R BGM>@K:MBG@ :EHG@ MA> =BK><MBHG H? FHMBHG PBMA MA> BGBMB:E :=O:G K>LNEMBG@ K>=BG@  -   >   



=>I>G=L HGER HG MA> K:MBH 

+ 3%    < ' ":

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PA>K>   
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196

Len M. Pismen Ca 0.006 0.0055 0.005 0.0045

0.01 0.02 0.03 0.04 0.05 0.06 0.07




'%30#  2A> =>I>G=>G H? MA> K  HG MA> =BF>GLBHGE>LL K:=BNL ?HK        2A> =:LA>= EBG> LAHPL MA> :LRFIMHMB< =>I>G=>G  

PA>K>  = BL : 1MKNO> ?NG<MBHG 2A> ?NG<MBHG   BG:L>L FHGHMHGB =>I>G=>G H? MA> K HG MA> =BF>GLBHGE>LL =KHIE>M K:=BNL H;M:BG>= :G:ERMB NGL:MNK:M>= :G= L:MNK:M>= K>@BF>L K>LI><MBO>ER :M LF:EE :G= E:K@>   (G MA> ?HKF>K  HG> MA> :IIKHQBF:MBHG       "   MH H;M:BG    ":    EG  (G MA> HIIHLBM> EBFBM       :G=   EG  ":  



2ANL MA> O>EHL PBMA =KHIE>M LBS> BG MA> NGL:MNK:M>= :G= => :L>L BG MA> L:MNK:M>= K>@BF> BG :@K>>F>GM PBMA >QI>KBF>GM +>>     :G= GNF>KB      %HK BGM>KF>=B:M> O:EN>L H?   MA> =>I>G=>G H? O>EH= ;R LHEOBG@ $J  GNF>KB= BG %B@ 

Thin Film and Droplet Patterns Shaped by Surface Forces 

197

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ZB+ JG+4 JW+ O+U B += GOJ+ M+
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Interfacial Phenomena in Materials Science

heat flows away here faster freezing

heat accummulates here slower freezing

235

MELT

CRYSTAL


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236

Alexander A. Golovin

B JGBO O= . B.JGBO B JWGZ =+O= GJ+ JG. JWJ B Z JW+
ZGZ B JW+ WB+ =+O= GJGM ZJ 8MJ8 + [+J 8Z +O+ GC+ JW+ . B
+ B   BGO Z.W+ GM O8M+8Z =GZM8ZZ+= GO D+MJGBO - O= MBOZG=+ JW+  BJW B  M UZJ B O 
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Z!2WBZBO +3+MJ B JW+ Z8 M+ +O+ U BO JW+ +8GG
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+ +8 JB JW+ +8GG
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+ "#/# O= +8 JB  4 ZGOM+ BJW+ GZ+4 W+J ZB8 M+Z B ZGO"Z B8=
+ . +Z+OJ GOZG=+ JW+ M UZJ 2W+ . B
+ MO JW+ +B +
+ =+ZM G
+= MB.+J+U
U MBOZG=+ GO JW+ J+.+ J8 + ?+=   + GO JW+ +J4 O= JW+
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Interfacial Phenomena in Materials Science

237

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244

Alexander A. Golovin

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Interfacial Phenomena in Materials Science

245

D8
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+Z.BO=GO JB JW+ [.MGO B JW+ +O M8 %J8 + 2W+ =+ G%JGBO B JW+ Z8 M+!=G38ZGBO +8JGBO O= JW+ ZB8JGBO B JW+  GO!
B8O= U  BB%+ . B
+ Z ? ZJ B
JGO+= GO JW+ MZZGM ..+


U K8GOZ K8GOZ 4 @Y74 WGMW JW+ =+ G%JGBO . +Z+OJ+= GO JWGZ Z+MJGBO MBZ+U BBZ

 ( (!  ( )
 (  ()"(()!   ( /O JWGZ Z+MJGBO + ZW =GZM8ZZ O G.B JOJ GOJ+ MG GOZJ
GGJU JWJ GZ

+J+= JB JW+ ?+= B OOBJ+MWOBBU O= +Z.BOZG
+ B JW+ B JGBO B GOJ+ +ZJGO OOB!ZM+ Z8 M+ ZJ 8MJ8 +Z M+= 8OJ8 =BJZP 6BOZG=+  ? B ZBG= M UZJGO+ J+ G =+.BZGJ+= BO  Z8 M+ B  Z8
ZJ J+ =+ B OBJW+ M UZJGO+ J+ G DBG=!BO!ZBG= =+.BZGJGBO GZ M+= +.GJU4 O= W+O JW+ =+.BZGJ+= J+ G GZ =G3+ +OJ  B JWJ B JW+ Z8
ZJ J+ GJ GZ M+= W+J+ B!+.GJU 2W+ =+.BZGJGBO . BM+ZZ GZ BJ+O =BO+
U +OZ B 
+ B JBZ B B+M8+Z WGJJGO JW+ Z8
ZJ J+4 JW+ ZB!M+= B+M8


+ +.GJU KH W+O JBZ  + =+.BZGJ+= BO  Z8
ZJ J+ JW+U ZJGM" JB JW+ JBZ B JW+ Z8
ZJ J+ ZB JWJ JW+ JBZ GOZG=+ JW+  BGO +.GJG ?  + 

O+= MMB =GOU DGOM+ JW+ M UZJ JJGM+ Z.MGOZ GO JB =G3+ +OJ J+ GZ 8Z8U =G3+  B BO+ OBJW+ "1 /",4 JW+ ?  BZ GO O +ZJGMU ZJ +ZZ+= ZJJ+4 O= WZ +ZJGM +O+ U ZJB += GO GJ /4 Z  +Z8J B ZB+ ,8MJ8JGBO4  Z .+ J8
JGBO GO JW+ B  B  Z WG ..+ Z BO JW+ ? Z8 M+4 JW+ + G
+ B + BB GOZG=+ JWGZ WG B JW+ JBZ B JW+ ? JB =58ZJ JW+G GOJ+ JBGM Z.MGO JB JW+ OB  +8GG
G8 %8+4 WGMW G += JB JW+ =+M +Z+ B JW+ +ZJGM +O+ U 2WGZ

246

Alexander A. Golovin

. BM+ZZ B JW+ WG B JGBO G JW+ +B +
+ +O+ +JGMU . ++ 
+4 WGMW G +Z8J GO O GOZJ
GGJU B  .O ? JWJ G =+MB.BZ+ GOJB  ZUZJ+ B GZO=Z 2W+ J OZ.B J +MWOGZ
U WGMW JW+ ? Z8 M+ +MBOZJ 8MJZ GJZ+ GOJB  ZUZJ+ B GZO=Z GZ Z8 M+ =G38ZGBO =GZM8ZZ+= GO JW+ . +%GB8Z Z+MJGBO 2WGZ +MWOGZ B JW+ GZO= B JGBO GZ ZMW+JGMU ZWBO GO G@@ Ge FILM Ge FILM

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GJ GOJ+ +ZJGO 8OJ8 . B.+ JG+Z JWJ MO
+ 8Z+= B 
GMJGBO B O+ ++MJ BOGM =+%GM+Z B JWGZ +ZBO Z8MW GZO=Z  + M+= # / #Z B +%G+Z B JW+ B JGBO O= . B.+ JG+Z B #Z Z++ DWMW8"GO O= HG
+  @Q HG
+  + -NN Q DJO + -NN  /O B =+ JB =+ZM G
+ JW+ =UOGMZ B JW+ B JGBO B #Z GO +.GJG ?Z BO+ ZWB8= 8Z+ JW+ Z8 M+ =G38ZGBO +8JGBO =+ G%+= GO JW+ . +%GB8Z Z+MJGBO AB+%+ 4 BO GJW JW+ Z8 M+ +O+ U4 JW+ Z8 M+ MW+GM .B! J+OJG ZWB8= GOM8=+ ZB JW+ +ZJGM +O+ U MM88J+= GO JW+ ? 2W8Z + W%+ ;  0   F )

@N- @ F ; W+ +  GZ  MBOZJOJ . B.B JGBO JB JW+ Z8 M+ =G38ZG%GJU B JBZ4 ) GZ JW+ Z8 M+ +O+ U4  GZ JW+ +O M8 %J8 +4 O=  GZ JW+ . J B Z8 M+ MW+GM .BJ+OJG MB

+Z.BO=GO JB JW+ +ZJGM +O+ U ZJB += GO JW+ +.GJG ? /J GZ MB.8J+= Z  BB W++Z O= BWOZBO 4 -NN   0

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Interfacial Phenomena in Materials Science

247


   .+Z B 8OJ8 =BJZ 8..+ +J S+ #Z BO DGNN@ GGZ + @$  +. GOJ+= GJW .+ GZZGBO  B GGZ + @$4 M @$
U JW+ X+ GMO 6W+GM DBMG+JUQ 8..+ GWJ 
D+ #Z BO 
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G + -NN  +. GOJ+= GJW .+ GZZGBO  B M XMW
G + -NN4 -NN
U JW+ X+ GMO WUZGM DBMG+JUQ B+ +J /OXZ #Z BO SXZNN@ S O=BZ + -NN  +. GOJ+= GJW .+ GZZGBO M  B S O=BZ + -NN4 -NN
U JW+ X+ GMO /OZJGJ8J+ B WUZGMZQ B+ GWJ MB Z+OGO B DGS+ #Z BO DGNN@  ?8 +
 MB

+Z.BO=Z JB J+ JG+ JWO  B B + -NNN  +. GOJ+= GJW .+ GZZGBO  B B B M + -NNN4 -NNN
U JW+ X+ GMO WUZGM DBMG+JU T+. GOJ+= GJW .+ GZZGBO  B D. GO+ 

248

Alexander A. Golovin

GO 8Z+= /O JW+ .. BGJGBO B GO+ +ZJGMGJU JW+B U4 , O=   + MBOO+MJ+=
U JW+ BBGO +JGBO [O=8 O= [GZWGJZ 4 @$@  
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@N  @F W+ +  GZ JW+ ZW+ B=88Z4  GZ JW+ BGZZBO*Z JGB4 O= . GZ JW+  BO+"+

=+J 2W+ ZJ GO J+OZB GZ =+J+ GO+=
U JW+ MB.BO+OJ B JW+ =GZ.M++OJ %+MJB  JWJ MW MJ+ GC+Z Z =+B JGBOZ B  ZBG=
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@ /  F /   -

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U JW+ +.GJG ZJ +ZZ M8Z+=
U JW+ JJGM+ GZJMW
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+J++O JW+ ? O= JW+ Z8
ZJ J+ GZ .O O= JW+ !GZ GZ OB  JB GJ4 GJW   N MB

+Z.BO=GO JB JW+ Z8
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+Z.BO=GO JB JW+ ?Q  0 ; ? + =+ZM G
+Z JW+ ZW.+ B JW+ ?  ++ Z8 M+4 O= ?  + JW+ MBB =GOJ+Z GO JW+ .O+ . + JB JW+ Z8
ZJ J+ DGOM+ Z8 M+ =G38ZGBO . BM+ZZ+Z  + 8MW ZB+ JWO JW+ Z.++= B ZB8O= GO  M UZJGO+ J+ G JWJ =+J+ ! GO+Z JW+ MW MJ+ GZJGM JG+ B +ZJGM +JGBO4 + MO ZZ8+ JWJ J +MW B+OJ B JG+ JW+ + GZ +MWOGM +8GG
G8 GO JW+ ? O= GO JW+ Z8
ZJ J+ WGMW GZ =+ZM G
+=
U JW+ +8JGBO / , 0 N

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+ ZWB8= ZB Z+J JW+ BBGO
B8O= U MBO=GJGBOZ G ZJ +ZZ! ++ ? Z8 M+4 , 7 0 N

@N7

W+ + 7  + JW+ MB.BO+OJZ B JW+ OB  JB JW+ ? Z8 M+Q GG MBOJGO8GJU B =GZ.M++OJ ?+= GO JW+ ? O= JW+ Z8
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Interfacial Phenomena in Materials Science W+ + 90







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ZGM ZJJ+  + =+J+ GO+=
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+ C+ B4 , 0 N 2W+O  B JW+ ZJ +ZZ! ZJ GO +JGBO @N  + ?O= JW+ %+ JGM MB.BO+OJ B JW+ ZJ GO GO JW+ ?4 -9    0  @@ @   2W+O4 GO  B @N  + ?O= JW+ WB GCBOJ MB.BO+OJZ B JW+ ZJ GO J+OZB 4

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0 , 0 -9 @   . +ZZGBOZ @@-!@@  + M+= +.GJG ZJ GO O= @@  GZ M+= +.G! JG ZJ +ZZ + MO Z++ JWJ
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250

Alexander A. Golovin

9BJ+ JWJ JWGZ +O+ U =B+Z OBJ =+.+O= BO JW+ ZGO B JW+ JJGM+ GZJMW4 G+ GJ =B+Z OBJ =+.+O= BO W+JW+ JW+ +.GJG ZJ GO GZ MB. +ZZG%+ B

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+ 8OZJ
+ GJW +Z.+MJ JB JW+ 8O=8JGBOZ B JW+ ?  ++ Z8 M+ JWJ MO +Z8J GO JW+ B JGBO B B8O=Z O= GO JW+ =+M +Z+ B JW+ +ZJGM +O+ U ZJB += GO JW+ ? /O B =+ JB ZWB JWJ + O++= JB .+ B   GO+ ZJ
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ZGM ZJJ+ =+ZM G
+= 
B%+ 2WGZ OUZGZ GZ 8GJ+ M8
+ ZB+ O= JW+ =+JGZ MO
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+ JW+ GO ZJ+.Z B JWGZ OUZGZ + MBOZG=+ GO?OGJ+ZG .+ J8
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+ GJW +Z.+MJ JB Z8 M+ 8O=8JGBOZ 2W+ =GZ.+ ZGBO +JGBO @@$ GZ ZWBO GO G@ 2W+ +ZJGM +O+ U WZ =+ZJ
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JGBOZ 2W+ MB.+JGJGBO B JW+ JB +3+MJZ

Interfacial Phenomena in Materials Science

251

W

+=Z JB JW+ Z++MJGBO B  MW MJ+ GZJGM %++OJW B JW+  BGO ZJ 8M! J8 +4 6 0 -14 4 W+ + 4 MB

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U +.GJG ZJ +ZZ =8+ JB JJGM+ GZJMW
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GGJU JWJ Z ? ZJ ZWBO JB BMM8 B  ZJ +ZZ+= Z+G! GO?OGJ+ ZBG= GJW   ++ Z8 M+ XZ B O= 2G+ 4 @7-Q S GO+= 4 @$I 2W+ ZJ
GGJU OUZGZ =+ZM G
+= GO JWGZ Z+MJGBO Z ? ZJ =BO+ GO D.+OM+

+ 4 @@4 @ /J =+ZM G
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+ G.B JOJ B JW+ B JGBO B #Z4 B +.+4 +JJGO GOJ+ MJGBOZ
+J++O JW+ ? O= JW+ Z8
ZJ J+ O= Z8 M+!+O+ U OGZBJ B.U &O+ MO += 
B8J JW+Z+ +3+MJZ Z + Z 
B8J OBOGO+

+%B8JGBO B JW+ 

UZ B #Z GO SBB%GO + 4 -NNI4 -NN Q [+%GO+ + 4 -NN7 O= GO ++ +OM+Z JW+ +GO

252

Alexander A. Golovin

 
&!  XMW
G4 # )GGO4 S BZJB C4 O= A )B D+!ZZ+
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BZGBO M M"GO 1 #/4 @7$@7I4 @7- # HG
+ 4 K S 8O=OO4 O= 99 [+=+OJZB% # ( 1& 1/"1/4 6WGMW+ZJ+  G+U4 @ DA #%GZ ,1%  "#4 6
G=+ OG%+ ZGJU  +ZZ4 -NN@ X B B4 KH DGOMG 4  6WZBO4 [H  +8O=4 T# 2+ZJ+O4 T AO4 O= SX [8M=B 9B%+ DGS+ GZO= MB Z+OGO "GO+JGMZ &ZJ! = G.+OGO O= +ZJGM GOJ+ MJGBOZ ,%/ '1* 014 $ 7N@7N 4 -NNN K SG"ZO O= D K ZW 2W+ =+O= GJ+ /O #2 A8 +4 +=GJB 4 #)  %/ $,4 Z+%G+ 4 @ 6 SB= +MW+4 +=GJB  /     6
G=+ OG%+ ZGJU  +ZZ4 @- XX SBB%GO4  BB W++Z4 O= DA #%GZ D+!ZZ+
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Interfacial Phenomena in Materials Science

253

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