Investigation of Conditions for Droplet Capture in a Cavity with Stokes Flow

Channel geometries and fluid/particle properties have been studied for use in separation techniques. Neutral buoyancy is often assumed in these analyses. However, in this project, the balance of gravitational and viscous forces, represented by the Archimedes number, was investigated for Stokes flow by measuring the critical Archimedes number (Ar_c) required to achieve droplet entrapment. The system consisted of a cavity placed along the bottom of a rectangular channel. Aqueous glycerol drops of varied glycerol concentration were used in bulk castor oil. Ar_c was measured as a function of drop diameter, cavity geometry, and viscosity ratio. Ar_c was found to increase for larger drop diameters. The sensitivity to drop diameters was larger for viscosity ratios at or below 0.01 compared to viscosity ratios of 0.1 or larger. For increasing cavity size, the sensitivity to drop diameters for a given composition decreased, with Ar_c values varying inversely with well length (drops are easier to trap in longer cavities). Numerical simulations show good agreement with experimental observations. Investigation into the role of individual parameters on drop trapping is ongoing with numerical simulations.