Near-contact motion of surfactant-covered spherical drops: Ionic surfactant

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 F, the external force normalized by the maximum resistance force generated by Marangoni stresses. For F > 1 drops coalesce on a time scale commensurate with the coalescence time τ₀ for drops with clean interfaces. For F < 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 F < 1, drop coalescence does not occur without van der Waals attraction. Quantitative results depend only moderately on the surfactant equation of state.