Stokes flow inside a sphere in an inviscid extensional flow

Abstract

We derive the streamfunction solution for flow in and around a viscous sphere suspended in an inviscid extensional flow with matched stress boundary conditions, which is a model for estimating the stresses on a tiny suspended organism by a nearby expanding and collapsing bubble. The boundary conditions are enforced in an easily resolvable form by expressing the surface stresses as sums of Legendre and Gegenbauer functions. The flow inside the sphere reflects a balance of exterior inertia with internal viscous forces, which together are shown to constitute the relevant flow Reynolds number. The solution is evaluated to examine the flow field inside this sphere as a potential source of damage to the organism.