On the motion of a non-rigid sphere in a perfect fluid

Abstract

The problem of the general motion (i.e. translation and rotation) of a deformable body moving in an ambient non-uniform potential flow field, has a number of important applications in various areas of fluid mechanics such as bubble dynamics ([1,2]), naval hydrodynamics ([3]) and fluid flow chaotisation ([4]). The consideration of deformable bodies allows us to account for the phenomena of the body’s self-propulsion, i.e. the controlled motion of a body due to small surface deformations in a prescribed ambient flow field. Pointed out firstly by Saffman ([5]), the effect of self-propulsion in a quiescent (otherwise being at rest) flow field has been re-examined recently by Benjamin and Ellis ([1]) for spherical shapes moving rectilinearly and by Miloh and Galper ([6]) for arbitrary shapes in general motion. Nevertheless, it must be noted that in many engineering applications the ambient flow field is generally nonuniform. Indeed, phenomena such as bubble dynamics in a cloud, coalescence and bouncing of bubbles, motion in waves and motion in confined domains, are just several examples which involve the effect of flow non-uniformity.