Incompressible LBGK simulation of flow characteristics in a micro-channel with patterned superhydrophobic surfaces

Characteristics of flow in a micro-channel with patterned superhydrophobic surfaces were simulated by using an incompressible lattice Bhatnagar–Gross–Krook (LBGK) model. By the simulation, it can be seen that the depth-to-width ratio of the cavities between adjacent micro-ridges is an important effect parameter for the flow in the micro-channel. For the larger depth-to-width ratio, it is easy to keep the air in the cavities. Because of the influence of the air, there is no vortex phenomenon downstream of each micro-ridge. Such vortices are a common phenomenon in macro flows. The simulated results coincide with those of experiments. Moreover, keeping the air in the cavities, one can also find that the smaller the solid area fraction, the greater the slipping velocity at the air–water interface. With a decrease of the solid area fractions, the average exit velocity increases and the flow drag coefficient decreases.