The stability of drop shapes for translation at zero Reynolds number through a quiescent fluid

Abstract

Boundary-integral calculations are used to investigate the evolution of the shape of an initially nonspherical drop that translates at zero Reynolds through a quiescent, unbounded fluid. For finite capillary numbers, it is shown that the drop reverts to a sphere, provided the initial deformation is not too large. However, drops that are initially deformed to a greater extent are shown to deform continuously, forming an elongated shape with a tail when initially prolate, and a flattened shape with a cavity at the rear when initially oblate. The critical degree of deformation decreases as the capillary number increases and appears to be consistent with the results of Kojima et al. [Phys. Fluids 27, 19 (1984)], who showed that the spherical drop is unstable to infinitesimal disturbances in the limit Ca=∞.