The dynamics of a deformable drop suspended in an unbounded Stokes flow

Abstract

The velocity fields in and around a deformed drop suspended in an arbitrary (albeit Stokesian) unbounded flow field are solved. The usefulness of the solution is demonstrated by solving the drag force and lateral migration of a drop suspended in an unbounded Poiseuillian field. It is demonstrated that, due to the deformation of the drop, there exists a radial component of the settling velocity. The direction of the radial migration depends primarily on the product U HR (the Hadamard-Rybczynski terminal settling velocity) by U 0 (the maximum Poiseuillian velocity). A positive product results in a lateral migration away from the location of maximum velocity; the converse also holds.