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

Keywords: Multi-mesh Adaptive finite element Wetting and spreading Precursor film Diffuse-interface model a b s t r a c t 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. If a small liquid drop is deposited on a solid, three interfaces come into play, and three interfacial tensions are involved: c SV ; c SL , and c, which are solid–vapor, solid–liquid, and liquid–vapor interfacial tensions, respectively. The important quantity is the spreading coefficient S ¼ c SV À c SL À c. The case where S < 0, is referred to as partial wetting: the liquid remains as a drop on the solid and reaches an equilibrium shape. For S > 0, the drop spontaneously spreads and tends to cover the solid surface. Such a situation is called complete wetting. When a spreading liquid completely wets a substrate it forms a very thin film and the long-range character of the molecular interactions must be taken into account. Ahead of the macroscopic front, we have seen that van der Waals (VW) forces lead to the formation of a mesoscopic precursor film [4,8]. The precursor films play a crucial role in the dynamics of the wetting of a solid surface by a liquid. However, understanding the wetting dynamics involving precursor films has not been an easy task because several distinct length scales are simultaneously presented in this …