A continuum model of interfacial surfactant transport for particle methods

Employing the moving particle semi-implicit (MPS) method, this study proposes a numerical framework of Lagrangian particle method to solve the Navier–Stokes equations for multiphase flows coupled with soluble surfactant transport equations. Each particle carries interfacial and bulk surfactant concentrations, as well as momentum. With a diffuse-interface approximation, the discontinuous of the interfacial surfactant across the interface is replaced by a smooth continuous distribution. The interfacial surfactant transport equation is redefined and solved at all particles in a fluid domain. The discrete form of surfactant dynamics is derived in conservative form, and thus, global mass of surfactant is conserved exactly. An artificial normal diffusion is introduced to prevent interfacial mass from leaking from a fuzzy interface. The suitable normal diffusivity depends on the rate of surface contraction and the size of grid. A criterion to determine the size of grid at a given characteristic speed and length scale is discussed.