Precursor simulations in spreading using a multi-mesh adaptive finite element method

Using the phase-field model for immiscible two-phase flows, we have numerically investigated the wetting dynamics. The long-range van der Waals forces towards the solid, which drive the spreading of the wetting phase into the nonwetting phase, have been explicitly taken into account in the governing equations. Our continuum model uses the generalized Navier boundary condition (GNBC) to account for the fluid slipping at the solid surface. The accurate description of the molecular-scale contact-line hydrodynamics makes the numerical simulations cost too much to abide. In this work, we propose an efficient multi-mesh adaptive finite element method which approximates different components of the solution (velocity, pressure and phase variable) on different h-adaptive meshes because of their strongly different local behaviors. That allows us to study the early stage of spreading, wherein the precursor is initiated and developed if the van der Waals forces are strong enough. We find that there is indeed a transition in the spreading behavior across a critical value of the Hamaker constant. In particular, this critical value is noted to be the one that separates the partial wetting from complete wetting.