Maxwell-Stefan-theory-based lattice Boltzmann model for diffusion in multicomponent mixtures

Abstract

The phenomena of diffusion in multicomponent (more than two components) mixtures are very universal in both science and engineering, and from mathematical point of view, they are usually described by the Maxwell-Stefan (MS) based continuum equations. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures, and also perform a Chapman-Enskog analysis to show that the MS based continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS based continuum equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model, and find that the results are in good agreement with some available works. Besides, the reverse diffusion, osmotic diffusion and diffusion barrier phenomena are also captured. Finally, compared to the kinetic theory based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can be still implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

“…, N) represents the number of discrete velocities v σ iα , and the total number is N (= 16) in this work, see Eq. (20). The superscript σ stands for the chemical species in a fluid mixture.…”

“…In 2016, Liang et al employed an MRT multiphase LBM to investigate the three-dimensional (3-D) Rayleigh-Taylor instability in a long square duct [14]. In 2019, Chai et al presented an MRT LBM, as a solver of the Stefan-Maxwell continuum equations, for the mass diffusion in multicomponent mixtures [20]. Although the LBM has achieved great success in replacing traditional continuum governing equations, few of the lattice Boltzmann models could provide various significant thermodynamic nonequilibrium information beyond the continuum equations.…”

Consistent lattice Boltzmann model for multicomponent mixtures

“…To the best of our knowledge, the only LBM realization of the Stefan–Maxwell diffusion was reported recently by Chai et al. (2019) and Vienne, Marié & Grasso (2019); although the two-dimensional LBM models of Chai et al. (2019) and Vienne et al.…”

“…(2019) and Vienne, Marié & Grasso (2019); although the two-dimensional LBM models of Chai et al. (2019) and Vienne et al. (2019) differ from one another, they both are restricted by the isothermal and isobaric assumptions and can thus not provide a basis for the development of a compressible mixture LBM.…”

“…To the best of our knowledge, the only LBM realization of the Stefan-Maxwell diffusion was reported recently by Chai et al (2019) and Vienne, Marié & Grasso (2019); although the two-dimensional LBM models of Chai et al (2019) and Vienne et al (2019) differ from one another, they both are restricted by the isothermal and isobaric assumptions and can thus not provide a basis for the development of a compressible mixture LBM. The majority of existing LBM models for the multicomponent mixtures (Chiavazzo et al 2009;Hosseini, Darabiha & Thevenin 2018) are bound to use the Fick diffusion model rather than the Stefan-Maxwell model.…”