A bottom-up approach to non-ideal fluids in the lattice Boltzmann method

The Shan-Chen (SC) pseudopotential lattice Boltzmann model for multiphase fluids has been revised to incorporate the particle exclusion-volume effect. Previous attempts to simulate a non-ideal fluid with the SC model tailored the interparticle potential to obtain the desired equation of state. Such an approach lumped the contributions from the particle exclusion-volume effect and the interparticle interactions together, and undermined the excellent physical basis of the SC model. In this letter, the equilibrium distributions are modified to include the particle exclusion-volume effect, and the clear physical meaning of interparticle potential in the original SC model has been reserved. Without losing the simple mathematical formulation and unique physical representation, the revised model can easily model non-ideal fluids with various equations of state. A van der Waals fluid has also been simulated as an example to demonstrate the significance of this improvement.