Phase-field-based lattice Boltzmann method for the transport of insoluble surfactant in two-phase flows

In this work, we present a general second-order phase-field model for the transport of insoluble surfactant in incompressible two-phase flows. In this model, a second-order local Allen-Cahn equation is applied for interface capturing, a general form of the simple scalar transport equation [S. S. Jain, J. Comput. Phys. 515, 113277 (2024)0021-999110.1016/j.jcp.2024.113277] is adopted for interface-confined surfactant, and the consistent and conservative Navier-Stokes equations with the surface tension and Marangoni force are used for fluid flows. To solve this model, we further developed a mesoscopic lattice Boltzmann (LB) method, in which the LB model for a surfactant transport equation is proposed under the general LB framework for the convection-diffusion type equation and it can correctly recover the governing equation for surfactant transport. The accuracy of the present LB method is tested by several benchmark problems and the numerical results show that it has a good performance for the transport of the insoluble surfactant in two-phase flows.