A novel mass-conserving contact line boundary condition for 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 models 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 prescribe a contact angle model. In this presentation, we introduce a novel solution to this problem: a local mass conservation (no-flux) boundary condition on the phase-field equation in conjunction with the generalized Navier 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 (non-90 degree) equilibrium contact angles. We describe the formulation of the model as applied to a conservative second-order phase-field model and present numerical results of canonical contact line test cases.