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

Abstract

A 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 & 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 $T_{\infty}$ is considered and it is shown that it is futile to determine the disturbed temperature field, whatever $T_{\infty},$ once bubbles are equivalent (i.e. experience the same velocity in a given uniform temperature gradient ${\bm \nabla}T_{\infty},$ as obtained by Acrivos et al. 1990 and Wang et al. 1994).