Wetting boundary conditions in numerical simulation of binary fluids by using phase-field method: some comparative studies and new development

We studied several wetting boundary conditions (WBCs) in the numerical simulation of binary fluids by using phase-field method. Five WBCs, three using the linear, cubic, and sine form surface energy (LinSE, CubSE, and SinSE), the other two using the geometric formulation (Geom) and the characteristic interpolation (CI), were compared through the study of several problems: (1) the static contact angle (CA) of a drop; (2) a Poiseuille flow-driven liquid column; (3) a wettability gradient (WG)-driven liquid column; and (4) drop dewetting. It was found that while all WBCs can predict the static CA fairly accurately, they may affect the simulation outcomes of dynamic problems differently, depending on the CA. For the flow-driven problem with a CA near 90 degrees, using different WBCs had almost no effect on the flow characteristics over a large scale. For the WG-driven problem, to use different WBCs may lead to different steady drop velocities, and all WBCs except LinSE can give reasonably consistent prediction between the drop velocity and dynamic CAs. For drop dewetting, Geom led to the most violent drop motion, whereas CubSE caused the weakest motion. For several problems, CubSE and SinSE gave almost the same results, and those by Geom and CI were also close, possibly due to similar consideration in their design. Besides, a new implementation that may be used for all WBCs was proposed to mimic the wall energy relaxation and control the degree of slip. This new procedure made it possible to allow the simulations to match experimental measurements well. Copyright (C) 2014 John Wiley & Sons, Ltd.