The role of interfacial viscosity and Marangoni stresses on droplet coalescence

We perform boundary-integral simulations to explore the role of surface viscosity on the coalescence of two equal-sized droplets. We assume an insoluble surfactant monolayer, and numerically solve the droplet shape and surfactant surface coverage during a head-on collision by solving the Stokes equations inside and outside the droplet and a convection-diffusion equation at the drop surface. The surfactant obeys a Langmuir adsorption isotherm, and exhibits a 2D surface viscosity obeying the Boussinesq-Scriven constitutive relationship. We observe that the surface viscosity significantly delays coalescence and that the film drainage time depends only on the sum of the surface dilatational viscosity and surface shear viscosity. We provide explanations to these effects using lubrication theory, and provide scaling analyses for the drainage time versus capillary number. Lastly, we find that the mechanism of coalescence stabilization is very different for Marangoni effects compared to surface viscous effects. Whereas Marangoni effects delay drainage by increasing the dimpling of the thin film, surface viscosity delays drainage by widening the film and flattening it. We show thin film profiles for different combinations of Marangoni and surface viscous effects and discuss its consequences for different classes of surfactants.