Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties

The paper shows that it is possible to combine the free energy lattice Boltzmann approach to multi-phase modelling of fluids involving both liquid and vapour with the partial bounce back lattice Boltzmann approach to modelling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce back approach, an effective media parameter or bounce back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (grey nodes) and solids (black nodes). The use of the wetting potential combined with the bounce back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid / material systems. Results for phase separation, permeability, contact angle and wicking in grey media are shown. Sorption is explored in small sections of model multi-scale porous systems to demonstrate two-step desorption, sorption hysteresis and the ink-bottle effect