Flow in a ring-sheared drop: Drop deformation

Abstract

The ring-sheared drop is a containerless system where shear is imparted by two contact rings, one rotating and the other stationary. In microgravity, aqueous drops can be studied in the air at the centimeter scale. Drops of this scale can also be studied experimentally on Earth, but the effects of gravity need to be mitigated by density matching the drop liquid and its surrounding fluid. The use of silicone oil drops surrounded by an aqueous solution allows density matching while retaining the viscosity ratio of the aqueous-air system in microgravity. The imposed shear drives a meridional flow in the drop which leads to a pear-shaped drop. A perturbation analysis with the capillary number as the small parameter is used to account for this mean drop deformation. The theory and time-averaged experiments agree, particularly at smaller ring rotation rates where the capillary number in the experiments is smaller. On top of the mean deformation, there is a smaller amplitude nonaxisymmetric deformation, which for slower ring rotation rates consists of a rotating wave with azimuthal wavenumber m = 1, that is, synchronous with the rotating ring. This is traced back to imperfections in the wetting and contact between the drop and the rotating ring in the experiment. At larger ring rotations, the experiments detect further unsteadiness with a broad frequency peak at about one third the ring rotation rate. Nonlinear simulations of the outer flow, assuming a nondeforming drop, find that at these ring rotations, the outer flow is unsteady with a similar frequency peak.