On the capillary motion of arbitrary clusters of spherical bubbles. Part 1. General theory

International audienceA new and systematic approach is proposed to determine the migration of torque-free spherical bubbles immersed in a steady and non-uniform unbounded Stokes flow and subject to arbitrary capillary effects. The advocated procedure appeals to only a very few quantities on the surface of each bubble and is therefore suitable for a future numerical treatment of arbitrary clusters of bubbles. For a single bubble, the theory allows a straightforward analytical implementation and the predicted results agree well with Hetsroni and Haber (1970), Hetsroni et al. (1971) and Subramanian (1985). The thermocapillary motion of non-conducting spherical bubbles freely suspended in a quiescent liquid in the presence of an arbitrary ambient temperature T8, is considered and it is shown that it is futile to determine the disturbed temperature field, whatever T8, once bubbles are equivalent (i.e. experience the same velocity in a given uniform temperature gradient ?T8, as obtained by Acrivos et al. 1990 and Wang et al. 1994 . © 2004 Cambridge University Press