Modeling and simulation of dynamics of three-component flows on solid surface

In this paper, we propose a phase field model for the dynamics of three-component immiscible flows on solid surface. The model is an extension of the two-component phase field model consists of the Cahn–Hilliard Navier–Stokes equations with the generalized Navier boundary condition. The generalization of the approach to the three phase problem requires some extra consistency conditions for the system in the bulk and at the boundary in order for the model to give physically relevant results. We formulate the boundary conditions that enforce the consistency conditions using the Lagrangian multipliers. We then develop an efficient adaptive mesh refinement technique to solve the system. Several numerical results are given, including the buoyancy-driven droplet through a fluid–fluid interface, formation of four-phase contact line and dynamics of a compound droplet on solid surface under shear flow.