Thermodynamic consistency of the pseudopotential lattice Boltzmann model for simulating liquid-vapor flows

In this paper, the effects of the equation of state on the thermodynamic consistency and the interface thickness are examined in the pseudopotential lattice Boltzmann modeling of liquid-vapor flows. It is shown that, with the increase of the slope of the equation of state in the vapor-phase region (θV), the influence of the droplet size on the vapor density can be reduced. Numerically, it is found that, when the vapor-phase sound speed (θV) is of the same order of magnitude as the lattice sound speed (cs), the vapor density can be generally kept around its equilibrium value. Hence, to achieve thermodynamically consistent simulations, the vapor-phase sound speed should be comparable with the lattice sound speed. Furthermore, the interface thickness in the pseudopotential LB modeling is found to be related to the slope of the equation of state in the mechanically unstable region (θM). It is shown that |θM| should be decreased when the interface thickness needs to be widened to reduce the spurious currents.