Numerical study of gravity-driven droplet displacement on a surface using the pseudopotential multiphase lattice Boltzmann model with high density ratio

Gravity-driven displacement of a droplet on a grooved surface is studied using the Shan and Chen's pseudopotential multiphase lattice Boltzmann (LB) model allowing a high density ratio between the gas and liquid phases. To verify and validate the multiphase LB model, we find good agreement of the LB simulations with the pressure difference over a droplet described by Laplace's law, as well as with the dynamic capillary intrusion process obtained by Washburn's law. The equilibrium contact angle of a droplet on a smooth horizontal surface is studied as a function of the wettability, finding good agreement with an empirical scheme obtained with Young's equation. The dynamic behavior of a droplet moving down a vertical surface under different gravitational forces is studied. On a vertical wall, the liquid droplet reaches a terminal velocity, which value depends on the wettability of the surface and strength of the gravitational force. When a hydrophilic groove is introduced along the surface, the droplet shows a complex behavior and, depending on the height of the groove, different patterns and mechanisms of the liquid filling the groove are observed. For small groove heights, the droplet totally fills in the groove. At certain groove height, a liquid bridge is formed between top and bottom surfaces dragging most liquid onto the bottom surface. At increasing height, this liquid bridge is broken, and liquid can be dragged into the groove by adhesion force. At high groove heights, the droplet breaks up in smaller droplets dripping from the top surface onto the bottom surface, and only a small amount of liquid remains in the groove. When the wettability of the groove or surface is changed, the liquid filling behavior changes notably. For a hydrophobic surface, but hydrophilic groove, the groove is filled partly by the liquid, while, for the opposite condition, a hydrophobic groove in a hydrophilic wall, the droplet runs into the groove, but the liquid is again dragged out and no filling of the groove occurs.