A lattice Boltzmann model for wall-bounded two-phase flows with insoluble surfactant

Within the phase-field framework, we present a unified lattice Boltzmann (LB) model for simulating wall-bounded two-phase flows with insoluble surfactant. This model utilizes three particle distribution functions, two of which are used to solve two conservative Allen-Cahn-like equations for capturing surfactant and order parameter fields, and the rest is used to solve the incompressible Navier-Stokes equations with Marangoni stress for deriving the hydrodynamic field. Also, to account for the surfactant effect on wall surface wettability, a dynamic contact angle formulation is incorporated into the present model. The most striking advantage of this model lies in that it does not involve the delta function with a sharp jump or discontinuity inherited in the previous LB models, greatly simplifying the computation. Besides, the proposed LB model is capable of handling high-density-ratio two-phase dynamics involving both the moving contact line and insoluble surfactant, which is unavailable in all the existing LB models. Further, the complex contact angle hysteresis phenomenon is also examined in this model. Some numerical examples, including the static surfactant-laden droplet, the Spinodal decomposition with insoluble surfactant, the surfactant-laden droplet spreading on a solid substrate, the shearing dynamics of a surfactant-laden droplet on a wetting substrate, are conducted to validate the proposed LB model. The numerical results are found to be good agreement with the analytical solutions and some available results.