Comparison and evaluation of Shan–Chen model and most commonly used equations of state in multiphase lattice Boltzmann method

Abstract

A method to couple the Equation of State (EoS) with the Shan–Chen model (SC) is proposed in this paper. The difference between previously proposed approaches and the one developed here is in the manner of determining parameters of the EoS, which are a function of the critical properties of a substance. The modified relationships of the parameter that controls the strength of the inter-particle force as a function of temperature are developed for each EoS. These modified relationships eliminate the difference between pressures calculated by the SC model and each EoS. A comparison between the SC model and different popular EoSs is presented based on the proposed approach. Four models—the SC model, van der Waals EoS, Redlich–Kwong EoS, and Carnahan and Starling' EoS—are evaluated and compared, and the sign of the strength-controlling parameter (G) is discussed. The effects of the range of coexistence density, an arbitrary constant (ρo), temperature, and G on surface tension are discussed. The results of simulations show that the SC model sometimes yields negative values of surface tension when ρo is set below 1.5. Therefore, ρo should be set to 1 or ≥ 1.5.