Recriprocal theorem for concentric compound drops in arbitrary Stokes flows

Abstract

The Lorentz reciprocal theorem is generalized and applied to the study of the quasisteady motion of a concentric spherical (CS) compound drop at zero Reynolds number. Using this result, the migration velocities of a force-free CS compound drop placed in a general ambient Stokes flow, as well as the forces on each drop when subjected to specified migration velocities, are calculated. The latter constitutes a generalization of Faxén's law to the case of a CS compound drop. Also some earlier results on the thermocapillary migration of such drops (Borhan et al. 1992) are rederived more simply and in greater generality.