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.