Flow in a ring-sheared drop with finite surface shear viscosity.

In the ring-sheared drop, a liquid drop is constrained by two contact rings, where the rings differentially rotate. This differential rotation generates a flow in the bulk primarily through surface shear viscosity. Numerical predictions of bulk flow and mixing within ring-sheared drops were recently reported. The previous work assumed that the surface shear viscosity, non-dimensionalized by the size of the drop, is large. However, in many cases, especially for large drops, which can be studied in microgravity, the dimensionless surface shear viscosity can be arbitrarily small but still able to affect the bulk flow. Computations reveal that an increasing Reynolds number correlates to an increase in sensitivity to the effects of changing surface shear viscosity. Furthermore, upon decreasing surface viscosity, the coupling between the surface and the bulk flows strengthens. The system is then driven towards solid-body rotation.