Effect of Slip on Circulation Inside a Droplet

Abstract

Internal recirculation in a moving droplet, enforced by the presence of fluid–fluid interfaces, plays an important role in several droplet-based microfluidic devices as it could enhance mixing, heat transfer, and chemical reaction. The effect of slip on droplet circulation is studied for two canonical steady-state problems: two-phase Couette, boundary-driven, and Poiseuille, pressure/body force-driven, flows. A simple model is established to estimate the circulation in a droplet and capture the effect of slip and aspect ratio on the droplet circulation. The circulation in a droplet is shown to decrease with increasing slip length in the case of a boundary-driven flow, while for a body force-driven flow it is independent of slip length. Scaling parameters for circulation and slip length are identified from the circulation model. The model is validated using continuum and molecular dynamics (MD) simulations. The effect of slip at the fluid–fluid interface on circulation is also briefly discussed. The results suggest that active manipulation of velocity slip, e.g., through actuation of hydrophobicity, could be employed to control droplet circulation and consequently its mixing rate.