(455c) Cusp Formation and UFO Shapes for Capsules in Non-Linear Extensional Stokes Flows

Cusp formation has been observed in bubble and capsule steady-state
deformations in four-roll-mill experiments which may involve extensional
Stokes flows where the velocity is a non-linear function of position and
there is an increased pressure at the particle edges owing to the presence
of solid boundaries. Based on computational investigation, our study
shows that in this class of Stokes flows, an elastic capsule develops
steady-state shapes whose pointed edges suddenly become cusped when the
flow rate exceeds a critical value.  The critical flow rate decreases
with increasing the non-linearity strength, and thus the cusped capsules
are associated with an elongated slender or a less-deformed UFO shape at
low or high flow non-linearity.  The cusp formation is a feature of both
strain-hardening and strain-softening membranes, achieved via self-similar
finite-time singularities which for real capsules are expected to be
apparent, i.e. formation of very large (but finite) edge curvatures.