The force on a bubble, drop, or particle in arbitrary time-dependent ...

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unsteady portion is small. A very similar derivation can be performed here. <strong>The</strong> interested reader is referred to the original work for the details. <strong>The</strong> result is FH (t=7 a(Z,+2Uj(t)+!Re[1+2U,(t)]) ± 2lrpa 3 U 1 (t) ±S8Tfa e vts/ FA(t) -8ei" t (1/3 2/3A + 5/9 6irftaU (A+l± (A+ 1)2 ( 1 +a) 2 f(a13) 2Ag(af3) +(3±a)f(af3)) -Re 5e-M- Z+2/3 ) 2 - R e ~ e ~ ' )+ with Xeric -T-- U(s) ds 8-irjia ft U S ds TTJ_ 0 , T9v(t-s) Ia 2 GWt =etU 2 /4v tU/ r X 3 /' 2 -xtU 2 /4v dx, J (l+ijI~ e (69) (70) where the imposed flow U' (t) = U[1 + U 1 (t)] has the condition U 1 (t) Re. At low frequency (e
1/3 1 3 (A23 2 1 1 (74a) 4 Afla 3 ReA+2/3 ) 2 1 1 (74b) _'A+2/3 2a 1e
Page 1 and 2: The force<
Page 3 and 4: =fSd L -(r' d ,) J d d Tn-(,-o* Pd-
Page 5 and 6: = fV", (-Vp*).- (M*..)dV = .fVh -V
Page 7 and 8: govern the flow when the time scale
Page 9: sion for a bubble, (60), and with t
Page 13: where mf is the mass of the exterio

The force on a bubble, drop, or particle in arbitrary time-dependent ...

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