Van der Waals equation of state for phase separation; Pseudopotential (Shan-Chen) lattice Boltzmann

Pseudopotential (Shan-Chen) lattice Boltzmann (LB) model is used to simulate phase separation. A halfway density between saturated liquid and vapour is selected and with a slight noise is set as the initial condition. The domain size is 200x200 lattices, the collision term is BGK with relaxation time of 1.0 and Van der Waals equation of state is adopted. The forcing term, pseudopotentials and related parameters are set based on the paper of Yuan, P. and L. Schaefer (2006). “Equations of state in a lattice Boltzmann model.“ Physics of Fluids 18(4): 042101. As a result, the liquid separates itself from vapour phase and they end up an equilibrium state