(179h) Near-Contact Motion of Deformable Surfactant-Covered Drops

We present an analysis of the near-contact motion of surfactant-covered drops under low-elasticity conditions where the lubrication flow between the drops can redistribute surfactant. Our results reveal several distinct regimes, depending on the surfactant elasticity, and film drainage which can be non-monotonic in time. At short-times, drop deformation is unimportant; surfactant redistributes quickly and Marangoni stresses are established on a time scale which is proportional to the drop-phase viscosity. If the surfactant elasticity exceeds a critical value, the Marangoni stresses balance the external force that drives the near-contact motion but do not immobilize the drop interfaces. For large values of the drop-phase viscosity, excessive Marangoni stresses can develop during the initial evolution that produce a short-time transient behavior during which the separation between the drops rebounds. For super-critical values of the surfactant elasticity, the surfactant distribution attains a self-similar form which is independent of the initial distribution of surfactant and the drop-phase viscosity; the film thickness decays exponentially as for rigid spherical particles except that the time scale is slower. At long times, drop deformation becomes important, slowing the evolution and fixing the radial length scale; Marangoni stresses immobilize the drop interfaces.

For sub-critical values of the surfactant elasticity, surfactant is swept completely out of the near-contact region during the initial short-time evolution. The system evolves as for drops with clean interfaces, on a time scale proportional to the drop-phase viscosity. Later, after deformation slows the near-contact motion, the surfactant distribution attains a self-similar form which contracts by Marangoni stresses on a slow time scale set by the surfactant elasticity. This is followed by a slow transient regime during which the film thickness between the drops increases as the surfactant distribution contracts into the deformed thin-film region. At long times, Marangoni stresses immobilize the drop interfaces and the system evolves as for the case of super-critical surfactant elasticity.