The Stokes force on a droplet in an unbounded fluid medium due to capillary effects

Abstract

The Stokes force on a fluid droplet is obtained when the droplet is placed in an unbounded fluid medium and motion ensues due to an arbitrary interfacial-tension gradient on the droplet surface. The force, derived here for a spherical droplet, is proportional to the integral of the interfacial-tension gradient over the droplet surface. It may be calculated without solving the complete governing equations from a knowledge of this integral and the ratio of the viscosity of the droplet phase to that of the continuous phase, as shown in the principal result displayed in (29).When the interfacial-tension gradients are caused by temperature or concentration variations, the result for the force may be further specialized when convective transport effects are negligible. In this case, it is possible to express the force in terms of the gradient of the undisturbed temperature (or concentration) field evaluated at the location of the droplet centre in a form analogous to Faxén's force law.