HYDRODYNAMIC INTERACTION OF A SMALL FLUID PARTICLE AND A SPHERICAL DROP IN LOW-REYNOLDS NUMBER FLOW

Abstract

The present study is concerned with estimating the hydrodynamic interactions between a small droplet and a much larger fluid drop when both drops are translating through an otherwise quiescent fluid. The method of solution is a matched asymptotic expansion involving resolution of the local undisturbed flow produced by the motion of the large drop into component flows that provide the far-field boundary conditions for calculating the disturbance flows produced by the small droplet. In the limit of very small size ratio, the surface of the large drop appears as locally planar. The theory yields a complete trajectory equation including a proper description of the effect of hydrodynamic interactions between the two neighboring drops. The trajectory of the small droplet on approaching the large drop does not deviate significantly from the streamlines of the undisturbed flow until it comes within range of the hydrodynamic repulsion from the surface of the large drop. The magnitude of hydrodynamic repulsion becomes weaker as the viscosity of the droplet is reduced, and this effect is a strong function of the separation distance from the surface of the large drop.