The lattice Boltzmann method for mass transfer of miscible multicomponent mixtures: A review

Abstract

Based on kinetic theory, the lattice Boltzmann method (LBM) is a versatile computational tool extensively applied to simulate diverse problems. It has particularly advanced in addressing general fluid flow, multiphase scenarios, and heat transfer. However, there is a notable gap in research concerning miscible fluids and an urgent need for thorough discussions on mass transfer via LBM in literature, emphasizing alternative modeling over traditional force and passive scalar models. Critical for applications, the understanding of mass transfer in miscible mixtures extends from scientific inquiry to engineering contexts. Hence, this review paper explores the dynamic interplay between mass transfer and fluid dynamics, focusing on the simulation of advection–diffusion problems for miscible non-reactive multicomponent mixtures through LBM. The paper categorizes two broad LBM strategies, the single-fluid and multifluid approaches, sheds light on their distinctive collision modeling techniques, and connects their mesoscale concepts to macroscopic properties and equations, such as viscosity, diffusion coefficient, and the Maxwell–Stefan and Fick equations. In the single-fluid strategy, we discuss the progress of the passive scalar models in mass transfer and the relevance of force models, such as the pseudopotential modeling, for simulation purposes. For multifluids, we detail the single collision technique and the alternative split collision scheme, in which, in this last one, we suggest classifying the models into explicit velocity-difference (Sirovich-based), equilibrium-adapted (Hamel-based), and quasi-equilibrium collision models. By providing a comprehensive overview, this text consolidates information regarding LBM mass transfer modeling, highlights directions for future research, and contributes to establishing a systematic approach for miscible mixtures.