A level-set continuum method for two-phase flows with insoluble surfactant

A level-set continuum surface force method is presented to compute two-phase flows with insoluble surfactant. Our method recasts the Navier–Stokes equations for a two-phase flow with insoluble surfactant as “one-fluid” formulation. Interfacial transport and interfacial jump conditions are treated using the level-set method and the discrete Dirac function. Based on the density-weighted projection method, a stable semi-implicit scheme is used to decouple the velocity components in solving the regularized Navier–Stokes equations. It allows numerical simulations for a wide range of viscosity ratios and density ratios.Numerical simulations on single drop deformation in a 2D shear flow are presented. Simulations on two drop interaction shows that surfactants can play a critical role in preventing drop coalescence. A fully 3D simulation demonstrating the physical interactions of multiple surfactant-laden drops is presented.