(448f) Theoretical Analysis for the Dynamics of Artificial and Physiological Capsules in Non-Small Deformations

The study of the dynamics of artificial or physiological capsules
(i.e. membrane-enclosed fluid volumes) in viscous flows has seen an
increased interest during the last few decades due to their numerous
engineering and biomedical applications.  We emphasize that the
interfacial dynamics of membrane-enclosed fluid volumes in viscous
flows is complicated owing to the coupling of the deforming hydrodynamic
forces with the restoring interfacial forces of the capsule membrane. The
latter forces are a non-linear function of the local stretches of the
deformed capsule with respect to its undeformed shape.  The non-linear
development of membrane tensions restricts the analytical solutions to
small deformations around a spherical shape, and thus the investigation
of non-small capsule deformations relies on an  array of diverse
computational methodologies, developed especially during the last decade.

In this talk we show that moderate and large capsule deformations can
be described very accurately via a scaling analysis appropriate for
membrane interfaces. First, we will present our scaling analysis for
capsules in planar extensional Stokes flows, which reveals that the
two distinct capsule conformations we found via our computations, i.e.
slender spindle and lamellar capsules, represent two different types
of steady-state capsule extensional dynamics. Then, we will present our
scaling analysis for elongated erythrocytes which is used to justify the
great variation of erythrocyte shear modulus as determined via a diverse
array of methodologies. In addition, we will discuss the development
of a scaling analysis for capsules under confinements which provides
useful physical insight for their non-linear dynamics.