Study and simulation of the interaction between two drops under shear flow and its relation to coalescence

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(14) !"#$% &'() *+, -%.,$/012% -$,34 4#15%67%- 7, 48%0$ 9,+ +!78 0: !:!7!02 -!470:6% .$,/ 1,78 6%:7%$4 ;%270 <= *8% 3$,6%-#$% 7, -%>%2,3 78%4% %?#07!,:4 0$% .#$78%$ %@320!:%- 1A B,C$!D!-!4 E=F #:7!2 78% >%2,6!7A ,170!:%- 07 0 3,!:7 x0 ,: 78% -$,3 !4) Uj (x0 ) =. 2 ∞ 1+λ [Uj 1 + 8π. 1 8πµs. PR. 4fi (x) Gij (x, x0 )dS (x) Sm R PV m P (1 − λ) Sm Ui (x) Tijk (x, x0 )nk (x)dS (x)] (x0 ) −. G&'(H. m. I8%$% λ = µµ !4 78% $07!, 1%7+%%: 78% 30$7!62% >!46,4!7A µe 0:- 78% 4#43%:-!:" /%-!#/ >!46,4!7A µs J U ∞ !4 78% >%2,6!7A ,. 78% 4#43%:-%- 9#!-J Sm !:-!607%4 78% 4#$.06% !: +8!68 78% !:7%"$02 ,: 78% /78 30$7!62% !4 1%!:" 6026#207%- 0:- nk (x) !4 78% ,#7+0$- :,$/02 >%67,$ ,: 0 "!>%: 3,!:7 ,: 78% -$,3' *8% K$47 !:7%"$02 ,: 78% $!"87 80:- 4!-% ,. %?#07!,: GLH !4 D:,+: 04 78% M!:"2%N20A%$ 8A-$,-AN :0/!6 3,7%:7!02 0:- 78% 4%6,:- ,:% !4 D:,+: 04 78% -,#12%N20A%$ 8A-$,-A:0/!6 3,7%:7!02 ,. 47,D%4 9,+ E=F' *8!4 2047 !:7%"$02 >0:!48%4 !: 78% 604% +8%: λ !4 %?#02 7, ( 04 60: 1% %04!2A 4%%: .$,/ %?#07!,: GLH' ,$ 78% 3#$3,4%4 ,. 78!4 -,6#/%:7 +% +!22 6,:4!-%$ 78% 604% ,. λ = 1 .,$ 4!/32!K607!,: ,. 78% 02",$!78/' O. 30$7!6#20$ !:7%$%47 !: 78% 4!:"2%N20A%$ !:7%"$02 !4 78% .#:67!,: Gij (x, x0 ) +8!68 !4 78% P$%%: .#:67!,: 7807 !4 -%K:%- 04 78% 4,2#7!,: ,. 78% M7,D%4 %?#07!,: .,$ >%2,6!7A -#% 7, 0 3,!:7 .,$6% 0332!%-' *8% .#:67!,: 804 78% .,22,+!:" .,$/) e s. Gij (x, x0 ) =. he. ij. r. +. ri rj i r3. G&'=H. I8%$% eij 0$% #:!7 >%67,$4 !: 78% -!$%67!,: ,. i 0:- j ,: 0 Q0$7%4!0: .$0/% 0:- $ !4 -%K:%- 04) r = x − x0. G&'&H. !:022AJ 78% 7%$/ 4f !4 78% 5#/3 !: 47$%44 -#% 7, 78% 7$067!,: 07 78% !:7%$.06% ,. 78% -$,3' B,C$!D!-!4 E=F -%K:%4 78!4 5#/3 !: 78% .,22,+!:" +0A) R.

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