Potential theory in the problems of interfraction at small gap widths. A solid sphere and a droplet

Abstract

A solid sphere approaches a spherical droplet at small gap widths. The radii of the particles are identical. Potential theory is applied and the problem of interaction brought to the solution of an integrodifferential equation for radial velocity at the droplet/ thin layer interface. Asymptotic formulae are reported for interface velocity and drag force for small and large viscosity ratios. The results are compared with the solutions for a solid sphere and flat tangentially mobile interface. Thus, two major effects may be distinguished: “opening of the gap” and “curving of the streamlines inside the droplets”. The latter is shown to cause a relative increase in the drag force.