The interaction of surfactant-contaminated drops in Stokes flow

Abstract

Exact solutions for any number of surfactant-contaminated bubbles rising steadily in Stokes flow are obtained using the method of reflections. The solutions take the form of infinite dimensional matrix equations, which are truncated to obtain the solution to any required accuracy. The dimension required increases rapidly as the bubbles' separation decreases. Typically dimensions of about, 80 are required for bubbles whose separation to radius ratio is about 2.1. In the second part of this thesis solutions are obtained for two equal drops, with internal circulation, rising steadily with equal velocities in Stokes flow. This solution is obtained by using bispherical coordinates and is shown to give faster convergence than that obtained in part 1, by about a factor of 4. The size of the matmees needed to obtain results to 5 significant figures is 20x20 for the range S 72.1. The difference in the sizes of the surfactant caps on the bubbles, which is needed to keep the forces on both bubbles equal is calculated using iteration.