Fluid-fluid interactions in pseudopotential lattice Boltzmann models: Effects of model schemes and fluid properties

This article demonstrates the characteristics of interparticle forces and forcing schemes in pseudopotential lattice Boltzmann simulations. The Yuan-Schaefer (YS), multipseudopotential interaction (MPI), and piecewise linear methods are examined as techniques of equation of state (EOS) inclusion in pseudopotential models. It is suggested here that it is important to have an understanding of the interparticle forces generated by the models in order to obtain good quality results. Poor choice of parameters can lead to generation of unphysical interactions. The piecewise linear method is found to perform well and to decouple parameters. It decouples the density ratio from the surface tension and from the collision operator relaxation rates. It is proposed that the decoupling occurs due to generation of lower values of high-order error terms in the interfacial region by the piecewise linear EOS. In general, the multiple-relaxation-time (MRT) collision operator should be combined with the Huang-Wu forcing scheme for simulating high values of surface tension and with the Li-Luo method for simulating low values of surface tension. It is found that reducing kinematic viscosity is more detrimental to the stability of the simulations than increasing the density ratio. Introducing a kinematic viscosity ratio between the phases practically eliminates the influence of density ratio on spurious velocities. The factors affecting stability of dynamic simulations are examined. It is found that they have the following hierarchy from the greatest impact to the least: kinematic viscosity ratio between the phases, bulk viscosity, method of EOS inclusion, and reduced temperature/density ratio.