A unified interaction model for multiphase flows with the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been increasingly adopted for modelling multiphase fluid simulations in engineering problems. Although relatively easy to implement, the ubiquitous Shan-Chen pseudopotential model suffers from limitations such as thermodynamic consistency and the formation of spurious currents. In the literature, the Zhang-Chen, Kupershtokh et al., the beta-scheme, and the Yang-He alternative models seek to mitigate these effects. Here, through analytical manipulations, we call attention to a unified model from which these multiphase interaction forces can be recovered. Isothermal phase-transition simulations of single-component in stationary and oscillating droplet conditions, as well as spinodal decomposition calculations, validate the model numerically and reinforce that the multiphase forces are essentially equivalent. Parameters are selected based on the vapour densities at low temperatures in the Maxwell coexistence curve, where there is a narrow range of optimal values. We find that expressing the model parameters as functions of the reduced temperature further enhances the thermodynamic consistency without losing stability or increasing spurious velocities.