A diffuse interface-lattice Boltzmann model for surfactant transport on an interface

Abstract In this letter we propose a diffuse interface–lattice Boltzmann model for surfactant transport on an interface. A delta function formulation with a free parameter is given and proved to be equivalent to the interfacial convection–diffusion equation. By replacing the delta function by a discrete form, a diffuse interface formulation is obtained and further reformulated into the regularized form. We develop a multiple-relaxation-time lattice Boltzmann model to solve the regularized diffuse interface equation. A numerical test is performed to validate the present model. The numerical results indicate that appropriately increasing the diffusion coefficient in the normal direction will give more stable and accurate solution.