Thermodynamic consistency assessment of the multiphase pseudopotential lattice-Boltzmann for liquid spray dynamics

A comprehensive thermodynamic consistency assessment of the pseudopotential lattice-Boltzmann (PP-LB) method, using both the Carnahan-Starling (CS) and the Peng-Robinson (PR) equation of state (EOS) was carried out. For PR EOS, the acentric factor was varied from -0.22 to 0.56. The multi-relaxation times (MRT) collision operator was implemented, while the forcing term was computed using the β-scheme with an 8th-order isotropic Shan & Chen interaction force. The thermodynamic consistency of the PP-LB method was assessed following the behavior of the thermodynamic pressure, the equilibrium densities, and the surface tension. The PP-LB model accurately predicts the equilibrium vapor-liquid densities and satisfactorily captures the theoretical coexistence curve given by the analytical solution of the EOS. The maximum average error for the liquid and vapor branches and density ratio did not exceed 4 % in any of the cases tested for both PR and CS. However, it was found that the predicted thermodynamic pressure deviates from the theoretical, and it is sensitive to the spatial resolution used. The surface tension was retrieved using the Laplace-Young relation. The surface tension was retrieved using the Laplace-Young relation. The predicted surface tension exhibited a consistent behavior with temperature and satisfied the linear relation between the natural logarithm of the surface tension and the liquid-vapor density difference given by the Parachor model. Finally, the applicability of the PP-LB for actual fluids, including alkanes with a different number of carbons, methanol, ammonia, and hydrogen, was evaluated.