Thermodynamic properties of pseudopotential lattice Boltzmann model for simple multiphase interfaces

The thermodynamic properties of the pseudopotential lattice Boltzmann model are typically assessed using the mechanical stability condition. However, this condition is derived based on simple multiphase interfaces, limiting its applicability to circular interfaces such as droplets and bubbles. To address this limitation, this paper introduces a generalized mechanical stability condition that allows for the investigation of thermodynamic properties for multiphase interfaces. The equilibrium densities of the liquid and gas phases under the equilibrium pressure for simple multiphase interfaces $p_0$ are determined. The results indicate that thermodynamic consistency is achieved when the index of the pressure tensor ϵ is appropriately set. For the Carnahan-Starling equation of state, the optimal ϵ is 1.87. For the Peng-Robinson equation of state, the optimal ϵ is 1.73. The equilibrium gas pressure for circular interfaces, $p_{g,c}$, is derived. It is found that $p_{g,c}$ deviates from the Kelvin equation significantly, with $ln\left(p_{g,c}/p_0\right)$ being eight times larger than the expected value. To rectify this, a modified pseudopotential model is proposed. This model achieves thermodynamic consistency without the need for tuning ϵ, and allows for tunable $p_{g,c}$ by adjusting the effective mass. Comparison with the current pseudopotential model reveals that the proposed model is closer to the Kelvin equation, with $ln\left(p_{g,c}/p_0\right)$ being four times larger than the expected value. Nevertheless, it is noted that the Kelvin equation cannot be strictly guaranteed, as the interface collapses or deforms due to insufficient surface tension. These findings suggest that an overestimated gas pressure is essential in the pseudopotential model to maintain the liquid-gas interface, albeit with a deviation from thermodynamic laws.