Axisymmetric motion of capsules through cylindrical channels

Abstract

A boundary integral method is used to model the flow of capsules into pores. An axisymmetric configuration is considered where the capsule and the pore axis coincide. The channel is a cylinder with hyperbolic entrance and exit regions. The capsule has a discoidal unstressed shape, is filled with a Newtonian liquid and is enclosed by a very thin membrane with various elastic properties (neo-Hookean or area-incompressible). The motion of the internal capsule liquid and of the suspending fluid is governed by the Stokes equations whose solution is expressed as boundary integrals. Those are computed by a collocation technique, where points are distributed on the capsule interface, on the channel walls and on the entrance and exit sections of the flow domain. The capsule interface mechanics follow the theory of large deformations of elastic membranes. The numerical model uses a forward time-stepping method, where the position and the deformation of the capsule are computed at each time step.

The model allows the study of the effect of a number of parameters (capsule size and geometry, membrane elastic properties) on the flow. The entrance length in the pore, the steady additional pressure drop at equilibrium and the capsule deformed profiles are determined. It is found that the entrance of a capsule into a pore is not sensitive to downstream conditions; but the length of tube necessary to reach steady conditions depends strongly on capsule size and membrane behaviour. Bursting of capsules with a neo-Hookean membrane is predicted to occur through a phenomenon of continuous elongation. The flow of a capsule with a membrane that resists area dilatation depends strongly on particle size and shape.