Boundary conditions at the liquid-liquid interface in the presence of surfactants.

In this work, we studied the flow boundary conditions for the interface between two immiscible liquids under the condition of low shear rates in the presence or absence of surfactants. Our simulation results indicate that the boundary conditions are substantially changed by the presence of surfactants. Similar to the liquid-solid boundary, several boundary conditions at immiscible liquid-liquid interfaces, including slip, no-slip, and locking boundary conditions, are observed depending on the interfacial surfactant concentration. The slip boundary condition is achieved only at zero or lower surfactant concentration. The locking boundary condition is observed when the surfactant concentration is large enough to form a fully developed monolayer whereas the no-slip condition occurs for systems with intermediate values of surfactant concentration. The slip, no-slip, and locking boundary conditions yield the positive, zero, and negative slip lengths, respectively. We also investigated the dependence of boundary slip on shear rate at different interfacial surfactant concentrations. Compared to the systems without surfactants, the increase in slip with shear rate slows down because of the presence of surfactants, and consequently, the linear dependence of slip length changes to a nonlinear dependence. Simulation results also indicate that the shear rate also affects the surfactant distribution. In particular, when the surfactant concentration is high enough to form a fully developed monolayer, the higher shear rate would make the monolayer rupture.