The deformation of a viscous particle surrounded by an elastic shell in a general time-dependent linear flow field

Abstract

The dynamics of a viscous particle surrounded by an elastic shell of arbitrary thickness freely suspended in a general linear flow field is investigated. Assuming the unstressed shell to be spherical, an analysis is presented for the case in which the flow-induced deformation leads to small departures from sphericity. The general time-dependent evolution of shape is derived and various special cases (purely elastic sphere, rigid and gaseous interior, elastic membranes) are discussed in detail. It is found that for steady-state flows the equilibrium deformations are absolutely stable and depend only upon the shell thickness, although the rates at which they are attained show the effect of the inside viscosity, too.