Four different types of a single drop dripping down a hole under gravity by lattice Boltzmann method

In this paper the dynamic of a droplet on a surface with a hole is investigated under gravitational effect by using lattice Boltzmann method. Incompressible two-phase flow with high density ratio proposed by Lee is considered. Cahn’s theory is used to observe the wettability of the surface in contact with liquid and gas phases. Several parameters such as contact angle, surface tension and gravitational acceleration are studied to demonstrate their effects on the deformation of the droplet. To evaluate the results, the benchmark problems for equilibrium contact angle, capillary rise and Laplace law are conducted and a satisfactory agreement with analytical results is shown. Based on this study, four typical deformations of a droplet dripping down a hole can be observed; equilibrium drop on the top of the surface, equilibrium drop under the bottom of the surface, splashing and dripping of the drop. It is seen that at low Ohnesorge numbers the droplet deforms slightly and tends to retain its state. Moreover any increase in the Archimedes number magnifies the tendency to pass through the hole. Also, the relationship between the volume of the remaining droplet on the surface and Archimedes and Ohnesorge numbers is investigated. It is found that by increasing the Archimedes number, the volume of the remaining droplet on the surface reaches a constant value that is dependent on geometric parameters.