Phase field simulations of dynamic wetting by the Volume of Fluids method.

Practical simulation of real dynamic wetting flows are still challenging. In the Volume-of-Fluid method a contact line is moved using empirical information, and a slip Navier Slip condition is used for velocity. In the phase-field (PF) method the Cahn-Hilliard equations are formulated from the thermodynamics of an immiscible two-component mixture and a phase function is used to represent the moving interface. While the PF method has the advantage of needing less empirical fitting, it is considerably more expensive.

We show how VoF simulations can produce results essentially equivalent to those from the more expensive PF method. We introduce a computational boundary at a specified short distance from the wall in the VoF simulation. There we apply a Navier condition for tangential velocity, and an apparent contact angle that accounts for the interface curvature at the wall. The basis for the model is a theoretical relation between total diffusive mass transport across the interface and curvature at the wall for the PF model.

We compare full PF simulations with VoF simulations using these boundary conditions. The input parameters for these VoF simulations are the same as for the full PF solution and the VoF solutions reproduce the PF solutions, at a much lower cost.