Near-Contact Motion of Surfactant-Covered Spherical Drops: Ionic Surfactant

Abstract

A lubrication analysis is presented for near-contact axisymmetric motion of spherical drops covered with an insoluble nondiffusing surfactant. The surfactant equation of state is arbitrary; detailed results are presented for ionic surfactants. The qualitative behavior of the system is determined by the dimensionless force parameter F̂, the external force normalized by the maximum resistance force generated by Marangoni stresses. For F̂ > 1 drops coalesce on a time scale commensurate with the coalescence time τ0 for drops with clean interfaces. For F̂ < 1, the system evolves on the time scale τ0 until Marangoni stresses approximately balance the external force; thereafter a slow evolution occurs on the Stokes time scale. In the long-time regime a self-similar surfactant concentration profile is attained that scales with the extent of the near-contact region. The gap width decreases exponentially with time but slower than for rigid particles because of surfactant backflow. For F̂ < 1, drop coalescence does not occur without van der Waals attraction. Quantitative results depend only moderately on the surfactant equation of state.