Numerical Simulation of a Contaminated Water Drop Sinking in a Oil by a Front-tracking Method

In this study, a front-tracking (FT) method combined with a solver for the interfacial transport of surfactant is proposed to analyze interfacial flows affected by contamination. Because the interfaces are expressed explicitly in the FT method, the advection-diffusion equation on the interface can be treated easily and can be solved with high accuracy. In this study, a scheme that completely conserves the total amount of surfactant was constructed. Numerical simulations of a water drop sinking in silicone oil were performed, taking into account the Marangoni effect caused by concentrations. The effects of three parameters—a damping coefficient of interfacial tension, a diffusion coefficient, and the total amount of surfactant—were evaluated. Calculated results were compared with experimental results and were in very good agreement with variables including the stagnant cap size, the flow separation point, and the peak of shear stress. We can therefore expect that our simulations can estimate the conditions of surfactant at the interfaces.