The effect of hydrodynamic coupling on the steady drainage of a thin film between a solid sphere approaching a fluid—liquid interface

Abstract

The steady, axisymmetric drainage of a thin film trapped between a rigid sphere approaching a fluid—liquid interface has been analyzed theoretically and the results compared with experiment. The velocity profiles in the draining film and its adjacent phase depend upon the distant motion in the latter, the pressure gradient in the former, the physical properties of both (through the dynamic viscosity ratio η), and the curvature. Asymptotic forms of the solutions for very large and very small values of η have been derived, as have results for the special case η = 1. Perturbation formulae for small values of the curvature are also presented. A film-thinning equation has been derived from the general microflow solution, as have corresponding special, asymptotic, and perturbation formulae. Numerical computations for the evolution of the film thickness have been made for various ranges of the initial thickness, the applied force, the distant motion, the dynamic viscosity ratio, and the curvature. The experimental film-thinning curves available in the literature have been predicted satisfactorily.