Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations

Lattice Boltzmann method for miscible gases: A forcing-term approach

A lattice Boltzmann method for miscible gases is presented. In this model, the standard lattice Boltzmann method is employed for each species composing the mixture. Diffusion interaction among species is taken into account by means of a force derived from kinetic theory of gases. Transport coefficients expressions are recovered from the kinetic theory. Species with dissimilar molar masses are simulated by also introducing a force. Finally, mixing dynamics is recovered as shown in different applications: an equimolar counterdiffusion case, Loschmidt's tube experiment, and an opposed jets flow simulation. Since collision is not altered, the present method can easily be introduced in any other lattice Boltzmann algorithms.

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

The phenomena of diffusion in multicomponent (more than two components) mixtures are universal in both science and engineering, and from the mathematical point of view, they are usually described by the Maxwell-Stefan (MS)-theory-based diffusion equations where the molar average velocity is assumed to be zero. 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 continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS-theory-based diffusion 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 the previous work. 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 still be implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.

Thermal multicomponent lattice Boltzmann model for catalytic reactive flows

Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013)] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008)] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model.

Lattice Boltzmann scheme for electrolytes by an extended Maxwell-Stefan approach

This paper presents an extended multicomponent lattice Boltzmann model for the simulation of electrolytes. It is derived by means of a finite discrete velocity model and its discretization. The model recovers momentum and mass transport according to the incompressible Navier-Stokes equation and Maxwell-Stefan formulation, respectively. It includes external driving forces (e.g., electric field) on diffusive and viscous scales, concentration-dependent Maxwell-Stefan diffusivities, and thermodynamic factors. The latter take into account nonideal diffusion behavior, which is essential as electrolytes involve charged species and therefore nonideal long and short-range interactions among the molecules of the species. Furthermore, we couple our scheme to a finite element method to include electrostatic interactions on the macroscopic level. Numerical experiments show the validity of the presented model.

Lattice-Boltzmann method for the simulation of multiphase mass transfer and reaction of dilute species

Despite the popularity of the lattice-Boltzmann method (LBM) in simulating multiphase flows, a general approach for modeling dilute species in multiphase systems is still missing. In this report we propose to modify the collision operator of the solute by introducing a modified redistribution scheme. This operator is based on local fluid variables and keeps the parallelism inherent to LBM. After deriving macroscopic transport equations, an analytical equation of state of the solute is exhibited and the method is proven constituting a unified framework to simulate arbitrary solute distribution between phases, including single-phase soluble compounds, amphiphilic species with a partition coefficient, and surface-adsorbed compounds.

Lattice Boltzmann model for thermal binary-mixture gas flows

A lattice Boltzmann model for thermal gas mixtures is derived. The kinetic model is designed in a way that combines properties of two previous literature models, namely, (a) a single-component thermal model and (b) a multicomponent isothermal model. A comprehensive platform for the study of various practical systems involving multicomponent mixture flows with large temperature differences is constructed. The governing thermohydrodynamic equations include the mass, momentum, energy conservation equations, and the multicomponent diffusion equation. The present model is able to simulate mixtures with adjustable Prandtl and Schmidt numbers. Validation in several flow configurations with temperature and species concentration ratios up to nine is presented.