(221e) Spindles, Cusps and Bifurcation for Capsules in Strong Extensional Flows

Interfacial dynamics of membrane-enclosed fluid volumes (e.g. artificial capsules and red blood cells) in viscous flows is complicated due to the coupling of the fluid dynamics with the membrane properties. This is clearly reflected in the fact that the existing analytical and computational studies are unable to predict (and thus provide physical insight on) the spindled and cusped capsule's shapes observed in experiments.

Based on computational investigation via our interfacial spectral boundary element algorithm, our study shows that a Skalak-type capsule in a planar extensional Stokes flow develops equilibrium 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 equilibrium 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 to reach equilibrium. The linear increase of the maximum equilibrium tension with the flow rate can be used to predict membrane rupture.

We emphasize again that the transition from spindled to cusped shapes is possible via the appearance of compressive tensions near the capsule edges at high flow rates. It is of interest to note that compressive tensions at low flow rates result in interfacial wrinkling around the capsule equator. The importance of compressive tensions has been well recognized either as a result of mechanical deformation (e.g. due to an external flow as in the present work) or owing to a physico-chemical process (as in the case of a fluid vesicle undergoing lipid uptake). At large deformations, the analytical prediction of the formation of compressive tensions for nonlinear elastic laws is practically unattainable; thus, computational investigation is an attractive alternative.