Multicomponent interparticle-potential lattice Boltzmann model for fluids with large viscosity ratios

Abstract

This work focuses on an improved multicomponent interparticle-potential lattice Boltzmann model. The model results in viscosity-independent equilibrium densities and is capable of simulating kinematic viscosity ratios greater than 1000. External forces are incorporated into the discrete Boltzmann equation, rather than through an equilibrium velocity shift as in the original Shan and Chen (hereafter, SC) model. The model also requires the derivation of a momentum conserving effective velocity, which is substituted into the equilibrium distribution function and applies to both the single- and multiple-relaxation-time formulations. Additionally, higher-order isotropy is used in the calculation of the fluid-fluid interaction forces to reduce the magnitude of spurious currents (i.e., numerical errors) in the vicinity of interfaces. First, we compare the model to the SC model for static bubble simulations. We demonstrate that the model results in viscosity-independent equilibrium bubble densities for a wide range of kinematic viscosities, which is not the case for the SC model. Furthermore, we show that the model is capable of simulating stable bubbles for kinematic viscosity ratios greater than 1000 (when higher-order isotropy is used), whereas the SC model is known to be limited to kinematic viscosity ratios on the order of 10. Next we verify the model for surface tension via Laplace's law and show that the model results in the same surface tension values for a range of kinematic viscosities and kinematic viscosity ratios of 10, 100, and 1000. The model is also verified for layered cocurrent flow though parallel plates. We show that the simulated velocity profiles preserve continuity at the interface for kinematic viscosity ratios ranging from 0.001 to 1000 and that the model accurately predicts nonwetting and wetting phase relative permeability for kinematic viscosity ratios of 0.01 to 100.