Retardation of Droplet Motion by Surfactant. Part 1. Theoretical Development and Asymptotic Solutions

The equations describing the retardation by surfactant of an essentially spherical droplet in creeping flow through an unbounded Newtonian liquid are developed in a general way. The concentration distribution is determined by convection and the coupled mass transfer processes of liquid-phase diffusion, adsorption kinetics, and surface diffusion. Assuming that mass transfer occurs rapidly, an asymptotic solution is obtained showing uniform retardation, treating both phases and all mass transfer mechanisms simultaneously. For slow mass transfer, an asymptotic solution is obtained for stagnant cap behavior.