Spindles, Cusps, and Bifurcation for Capsules in Stokes Flow

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Abstract
Interfacial dynamics of membrane-enclosed fluid volumes in viscous flows is complicated due to the coupling of the fluid dynamics with the membrane properties. Based on computational investigation via our interfacial spectral boundary element algorithm, our study shows that a (strain-hardening) Skalak-type capsule in a planar extensional Stokes flow develops steady-state shapes whose edges from spindled become cusped with increasing flow rate owing to a transition of the edge tensions from tensile to compressive. A bifurcation in the steady-state shapes is also found (i.e., existence of both spindled and cusped edges for a range of high flow rates) by implementing different transient processes, owing to the different evolution of the membrane tensions.

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