Three-dimensional lattice Boltzmann simulations of high density ratio two-phase flows in porous media

A three-dimensional multiphase lattice Boltzmann model is implemented to study the spontaneous phase transport in complex porous media. The model is validated against the analytical solution of Young's and Laplace's laws. Afterward, three-dimensional porous layers are randomly generated to investigate droplet penetration into a substrate, liquid transport in a porous channel as well as extraction of a droplet from a porous medium. Effects of several geometrical and flow parameters such as porosity, density ratio, Reynolds number, Weber number, Froude number and contact angle are considered. A parametric study of the influence of main non-dimensional parameters upon the impact of liquid drops on permeable surface is performed. Results show that while increasing Froude number causes spreading of the droplet on the surface, increasing Reynolds number, Weber number, porosity and liquid-air density ratio will enhance the penetration rate into the surface. Furthermore, increasing the contact angle decreases both the spreading and the penetration rate at the same time. In the same way, for the liquid transport in a porous channel, it is found that increasing the porosity and Reynolds number will result in increasing penetration rate in the channel. For the extraction of a droplet from a porous medium, it is shown that by increasing the gravitational force and/or porosity the droplet extracts faster from the substrate.