Effects of finite surface shear viscosity in ring-sheared drops.

Bulk flow and mixing within ring-sheared drops was reported recently. In the ring-sheared drop, the drop is constrained by two contact rings, where typically one of the rings rotates steadily while the other is stationary. Rotation of the ring generates a strong flow in the bulk through surface shear viscosity. The previous work assumed that the size of the drop is small and the surface shear viscosity is large, so that interfacial stress dominates over the viscous stress in the bulk. Here, this restriction is relaxed so that we can model flow in large drops, such as those that can be grown in microgravity, and drops with arbitrarily small surface shear viscosity. The computations reveal that even small surface shear viscosity can produce a significant secondary flow at moderate Reynolds numbers Re = 100. At very low Re, surface viscosity makes very little difference. At very high Re, secondary flow becomes very weak if surface viscosity is small and the flow tends toward solid-body rotation. Finally, for finite surface shear viscosity, the flow field in the ring-sheared drop was found to be stronger than the flow field in its cylindrical analog, namely a knife-edge surface viscometer.