The force on a bubble, drop, or particle in arbitrary time-dependent ...
The force on a bubble, drop, or particle in arbitrary time-dependent ...
The force on a bubble, drop, or particle in arbitrary time-dependent ...
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si<strong>on</strong> f<strong>or</strong> a <strong>bubble</strong>, (60), and with the aid of the frequency<br />
doma<strong>in</strong> expressi<strong>on</strong> (57) and the use of MATHEMATICA to<br />
carry out the appropriate <strong>in</strong>tegrati<strong>on</strong>s, we arrive at the<br />
follow<strong>in</strong>g expressi<strong>on</strong> f<strong>or</strong> the <str<strong>on</strong>g>f<strong>or</strong>ce</str<strong>on</strong>g> accurate to O(b) and to<br />
O(Re):<br />
FbH(t) 2 2 .rt1 . 4 t a<br />
6F =+5 e- @+l a2be-wt+ 5e-it a _a<br />
sierra U 3 3 3 9 (1+a/3 )<br />
10 -<br />
10-I<br />
(a)<br />
1 4 . 2"/ 2 (l-i)(ry+i) 312 -2i<br />
+6 Re±--Re.bee' t 4y<br />
6 94<br />
(64)<br />
<str<strong>on</strong>g>The</str<strong>on</strong>g> Reynolds number is def<strong>in</strong>ed by Re=aU/v and<br />
ry
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