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Thermocapillary migration of a bidisperse suspension of bubbles

Published online by Cambridge University Press:  26 April 2006

Y. Wang ,
R. Mauri  and
A. Acrivos
Y. Wang
Affiliation:
Levich Institute, T-1M, City College of CUNY, New York, NY 10031, USA
R. Mauri
Affiliation:
Department of Chemical Engineering, City College of CUNY, New York, NY 10031, USA
A. Acrivos
Affiliation:
Levich Institute, T-1M, City College of CUNY, New York, NY 10031, USA
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Abstract

We consider the thermocapillary motion of a well-mixed suspension of non-conducting spherical bubbles of negligible viscosity in a viscous conducting liquid under conditions of vanishingly small Reynolds and Marangoni numbers. Recently, Acrivos, Jeffrey & Saville (1990) showed that when all the bubbles are of identical size, the ensemble-averaged migration velocity $\bar{U}_{1}$ of a test bubble of radius a1 within the suspension equals $U^{(0)}_1[1-\frac{3}{2}c_1+O(c^2_1)]$, where c1 is the volume fraction of the bubbles and U1(0) is the thermocapillary velocity of single bubble given by Young, Goldstein & Block (1959). Here we extend this result to a bi-disperse suspension containing bubbles of radii a1 and a2 ≡ λa1 in which case $\bar{U}_1 = U^{(0)}_1[1-\frac{3}{2}c_1 - S(\lambda)c_2+\ldots]$, where c1 and c2 are the corresponding volume fractions of the two sets of bubbles. Values for S(Λ) are presented for some typical size ratios Λ, and asymptotic expressions for S(Λ) are derived for Λ → 0 and for Λ → ∞.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 261 , 25 February 1994 , pp. 47 - 64
Copyright
© 1994 Cambridge University Press

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