Multiple-relaxation-time lattice Boltzmann model for binary mixtures of nonideal fluids based on the Enskog kinetic theory

Abstract

In this paper, a lattice Boltzmann equation (LBE) model with multiple-relaxation-time (MRT) collision operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time (SRT) LBE model (Guo and Zhao in Phys Rev E 68:035302, 2003). The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt number and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen (SC) model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of numerical simulations, including the static droplet and layered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.