Recriprocal Theorem for Concentric Compound Drops in Arbitrary Stokes Flows

The Lorentz reciprocal theorem is generalized and applied to the study of the quasi-steady 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 Faxen'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.