THERMOCAPILLARY MIGRATION OF A BIDISPERSE SUSPENSION OF BUBBLES

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 U1 of a test bubble of radius a, within the suspension equals U1(0)[1-3/2c1 + O(c1(2))], where c1 is the volume fraction of the bubbles and U1(0) is the thermocapillary velocity of a 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 = lambdaa1 in which case U1 = U1(0)[1 - 3/2c1 - S(lambda)c2 +...], where c1 and c2 are the corresponding volume fractions of the two sets of bubbles. Values for S(lambda) are presented for some typical size ratios lambda, and asymptotic expressions for S(lambda) are derived for lambda --> 0 and for lambda --> infinity.