Thermodynamic consistency of liquid-gas lattice Boltzmann methods: Interfacial property issues

Abstract

In the present study we examine the thermodynamic consistency of lattice Boltzmann equation (LBE) models that are based on the forcing method by comparing different numerical treatments of the LBE for van der Waals fluids. The different models are applied for the calculation of bulk and interfacial thermodynamic properties at various temperatures. The effect of the interface density gradient parameter, kappa , that controls surface tension, is related explicitly with the fluid characteristics, including temperature, molecular diameter, and lattice spacing, through the employment of a proper intermolecular interaction potential. A comprehensive analysis of the interfacial properties reveals some important shortcomings of the LBE methods when central finite difference schemes are employed in the directional derivative calculations and proposes a proper treatment that ensures thermodynamically consistent interfacial properties in accord with the van der Waals theory. The results are found to be in excellent quantitative agreement with exact results of the van der Waals theory preserving all the major features of the interfacial characteristics of vapor-liquid systems of different shapes and sizes.

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

“…It can be seen that both of them are in good agreement with the solution given by the Maxwell construction. Here it should also be pointed out that, for circular interfaces, the coexistence liquid and vapor densities will vary with the droplet size according to Laplace's law [45]. To reduce the influence of droplet size, an alternative choice may be a piecewise equation of state, which can offer a separate control of ∂p/∂ρ in every single phase region and the mixed region [46].…”

Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method

“…However, there are variations of the pressure across the interface, which indicates that the mechanical stability condition is not satisfied around the interface. This issue happens in the lattice Boltzmann methods by using a force to introduce the nonideal EOS (for more details see [59][60][61][62]). The temperature distributions at different times are also shown in Fig.…”

Investigating the effects of shear rate on the collapse time in a gas–liquid system by lattice Boltzmann

“…In the past two decades, many researchers showed that lattice Boltzmann method is very suitable for simulation of two-phase systems [11,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”