A NOTE ON MEMORY-INTEGRAL CONTRIBUTIONS TO THE FORCE ON AN ACCELERATING SPHERICAL DROP AT LOW REYNOLDS-NUMBER

Abstract

The hydrodynamic force on a spherical drop that undergoes a translational acceleration in an unbounded fluid at low Reynolds number is considered. The force involves a memory-integral contribution that is not of the familiar form for a solid sphere. This result, in conjunction with the prior results of Lawrence and Weinbaum [J. Fluid Mech. 171, 208 (1986)] for a nonspherical particle, suggest that the form of the force law for a solid sphere is a very special case that is invalidated if there are any departures in either rigidity or shape from a solid sphere. In this Brief Communication the force on a spherical drop is evaluated for a number of limiting cases, after transforming the result from the Fourier-transform domain in which it is derived to the time domain.