A thermodynamically consistent model and its conservative numerical approximation for moving contact lines with soluble surfactants

We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in thermodynamically consistent framework. The consists of the isothermal two-phase incompressible Navier-Stokes equations fluid dynamic and bulk\slash surface convection-diffusion surfactant transportation. interface condition, slip boundary angle adsorption\slash desorption condition are derived based on principle total free energy dissipation. In particular, we recover classical adsorption isotherms from different forms energy. is then numerically solved two spatial dimensions. present an Eulerian weak formulation together arbitrary Lagrangian-Eulerian transport equations. Finite element approximations proposed to discretize formulations mesh. resulting numerical method shown conserve mass exactly. By using its method, investigate droplet spreading migration presence study their dependencies various dimensionless parameters.