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Wetting Boundary Conditions in Phase-Field-Based Simulation of Binary Fluids: Some Comparative Studies and New Development

We studied several wetting boundary conditions (WBCs) in the simulation of binary fluids based on phase-field theory. Five WBCs, three belonging to the surface energy (SE) formulation using the linear, cubic and sine functions (denoted as LinSE, CubSE and SinSE), the fourth using a geometric formulation (Geom), and the fifth using a characteristic interpolation (CI), were compared with each other through the study of several problems: (1) the static contact angle of a drop; (2) a Poiseuille flow-driven liquid column; (3) a wettability gradient (WG)-driven liquid column; (4) drop dewetting. It was found that while all WBCs can predict the static contact angle fairly accurately, they may affect the simulation outcomes of dynamic problems differently, depending on the driving mechanism. For the flow-driven problem, to use different WBCs had almost no effect on the flow characteristics over a large scale. But for other capillarity-driven problems, the WBC had some noticeable effects. For the WG-driven liquid column, Geom gave the most consistent prediction between the drop velocity and dynamic contact angles, and LinSE delivered the poorest prediction in this aspect. Except for Geom, the dynamic contact angle differed from the prescribed (static) one when other WBCs were used. For drop dewetting, Geom led to the most violent drop motion whereas CubSE caused the weakest motion; the initial contact line velocity was also found to be dependent on the WBC. For several problems, CubSE and SinSE gave almost the same results, and those by Geom and CI were close as well, possibly due to similar consideration in their design. Besides various comparisons, 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.