A level-set method for two-phase flows with soluble surfactant

A level-set method is presented for solving two-phase flows with soluble surfactant. The Navier-Stokes equations are solved along with the bulk surfactant and the interfacial surfactant equations. In particular, the convection-diffusion equation for the bulk surfactant on the irregular moving domain is solved by using a level-set based diffusive-domain method. A conservation law for the total surfactant mass is derived, and a re-scaling procedure for the surfactant concentrations is proposed to compensate for the surfactant mass loss due to numerical diffusion. The whole numerical algorithm is easy for implementation. Several numerical simulations in 2D and 3D show the effects of surfactant solubility on drop dynamics under shear flow.