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 a1 within the suspension equals U10 [1 - (3/2)c1 + O(c1^2)], where c1 is the volume fraction of the bubbles and U10 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 = k a1, in which case U1 = U10 [1 - (3/2 )c1 - S(k) c2 + ...], where c1 and c2 are the corresponding volume fractions of the two sets of bubbles. Values for S(k) are presented for some typical size ratio, and asymptotic expressions for S(k) are derived for k tending to zero and infinity.
|Autori:||WANG Y; MAURI R; ACRIVOS A|
|Titolo:||Thermocapillary Migration of a Bidisperse Suspension of Bubbles|
|Anno del prodotto:||1994|
|Digital Object Identifier (DOI):||10.1017/S002211209400025X|
|Appare nelle tipologie:||1.1 Articolo in rivista|