A novel mass-conserving contact line boundary condition for conservative second-order phase-field models

The phase-field method is a widely adopted technique for simulating multiphase flows. One popular class consists of models based on second-order phase-field equations, which offer advantages over higher-order equations in certain aspects, including better bound preservation and milder timestep restrictions. However, an ongoing challenge with such models is the treatment of contact lines. Because a second-order phase-field equation admits only one constraint on the phase-field variable at each boundary, it is unclear how to simultaneously conserve mass and model contact line physics. In this presentation, we describe a novel solution to this problem: a local mass conservation (no-flux) boundary condition on the phase-field equation in conjunction with a slip velocity boundary condition on the momentum equation. The result is a second-order phase-field model that conserves mass while also accurately modeling contact lines in systems with arbitrary equilibrium contact angles. We describe the formulation of the model as applied to the Conservative Diffuse Interface (CDI) model and present numerical results of canonical contact line test cases.