On the force scheme influence on pseudopotential method coexistence curve

Abstract

Pseudopotential method has been drawing attention in simulating multiphase flows by adding an interparticle force to lattice Boltzmann method (LBM). However, implementing a known force field effect into evolution of particle distribution function is still an active field of interest, specially when higher order terms play significant role in resulting macroscopic equations. A considerable number of forcing schemes has already been proposed, and although many have shown their differences up to second order analysis, there is still some debate about high order terms. In this work, a study taking into account third order forcing terms is carried out, in order to better identify the reasons for existing distinct coexistence curves when the same interparticle force is employed through distinct forcing schemes. Third order terms related to spatial interparticle force gradients are taken into account, and a theoretical analysis is carried out in order to study gas–liquid coexistence curves. It is shown that this curve can be characterized by a single parameter, Γ, dependent on employed relaxation time and forcing scheme, which allows the current analysis to be used for other schemes as well. Flat interface simulations are carried out in order to study the behavior of gas–liquid coexistence curve. A good agreement between the numerical and theoretical results validates the presented approach. Static droplet simulations were carried out, where surface tension behavior also respect the expected trend of higher values for lower Γ. Maximum spurious velocities of renowned forcing schemes from literature were also studied, without a clear correlation with Γ parameter.