Water droplet properties on periodically structured superhydrophobic surfaces: a lattice Boltzmann approach to multiphase flows with high water/air density ratio

Surface roughness affects the contact angle (CA) due to the increased area of solid-liquid interface and due to the effect of sharp edges of rough surfaces. Roughness may also lead to another non-wetting regime, by forming a composite solid-liquid-air interface between the water and the textured surface; this composite interface exhibits strong water repellency due to the various pockets of air entrapped between the surface textures. The contact between water and a hydrophobic textured surface leads to one of these two regimes depending on the thermodynamics stability of the regimes. In this study, the projection method of lattice Boltzmann method is used to analyze the large density difference at the air and water interface. The method is applied to simulate two-phase flows with the density ratio of up to 1,000. A numerical model is presented to provide a relationship between roughness and CA, which is used to develop optimized texture topography and create a biomimetic superhydrophobic surface. The numerical models encompass the effects of contact area, solid-liquid-gas composite interface and shape edges. The models are reused to analyze different possible roughness distributions and to calculate the effect of the cross-sectional area of pillars, including rectangular, triangular, cross, and pyramidal pillars. The energy barrier is investigated to predict the position of the transition between the Cassie and Wenzel regime observed for each roughness parameter as well as a theoretical free surface energy model.