Lattice Boltzmann modeling of multicomponent diffusion in narrow channels

Lattice Boltzmann simulation of multicomponent noncontinuum diffusion in fractal porous structures

A lattice Boltzmann method (LBM) of multicomponent diffusion is developed to examine multicomponent, noncontinuum mass diffusion in porous media. An additional collision interaction is proposed to mimic the Knudsen diffusion caused by the collision interaction between gas molecules and solid pore walls. Using the improved LBM model, the ternary mixtures diffusion is simulated in fractal porous structures which are reconstructed by the random midpoint displacement algorithm. The effects of fractal characteristics and Knudsen diffusion resistance on the multicomponent diffusion in porous structures are investigated and discussed. The results indicate that the smaller fractal dimension enhances the diffusion rate of gas mixtures in fractal porous structures. When the dimensionless Knudsen diffusion coefficient is less than 20, the presence of Knudsen diffusion resistance reduces the rate of mass diffusion in porous structures obviously, especially for the species with larger molecular weight.

Thermal and second-law analysis of a micro- or nanocavity using direct-simulation Monte Carlo

In this study the direct-simulation Monte Carlo (DSMC) method is utilized to investigate thermal characteristics of micro- or nanocavity flow. The rarefied cavity flow shows unconventional behaviors which cannot be predicted by the Fourier law, the constitutive relation for the continuum heat transfer. Our analysis in this study confirms some recent observations and shows that the gaseous flow near the top-left corner of the cavity is in a strong nonequilibrium state even within the early slip regime, Kn=0.005. As we obtained slip velocity and temperature jump on the driven lid of the cavity, we reported meaningful discrepancies between the direct and macroscopic sampling of rarefied flow properties in the DSMC method due to existence of nonequilibrium effects in the corners of cavity. The existence of unconventional nonequilibrium heat transfer mechanisms in the middle of slip regime, Kn=0.05, results in the appearance of cold-to-hot heat transfer in the microcavity. In the current study we demonstrate that existence of such unconventional heat transfer is strongly dependent on the Reynolds number and it vanishes in the large values of the lid velocity. As we compared DSMC solution with the results of regularized 13 moments (R13) equations, we showed that the thermal characteristic of the microcavity obtained by the R13 method coincides with the DSMC prediction. Our investigation also includes the analysis of molecular entropy in the microcavity to explain the heat transfer mechanism with the aid of the second law of thermodynamics. To this aim, we obtained the two-dimensional velocity distribution functions to report the molecular-based entropy distribution, and show that the cold-to-hot heat transfer in the cavity is well in accordance with the second law of thermodynamics and takes place in the direction of increasing entropy. At the end we introduce the entropy density for the rarefied flow and show that it can accurately illustrate departure from the equilibrium state.

Higher-order Galilean-invariant lattice Boltzmann model for microflows: single-component gas

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.

Multicomponent lattice Boltzmann model from continuum kinetic theory

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

General solution of lattices for Cartesian lattice Bhatanagar-Gross-Krook models

We give the general solutions of lattices, i.e., velocity sets and weights, for the lattice Bhatanagar-Gross-Krook (LBGK) models on two- and three-dimensional Cartesian grids. The solutions define the necessary and sufficient conditions so that the resulting LBGK model can accurately capture the dynamics of the moments retained in the distribution function. In the parameter space of the weights, the general solutions form low-dimensional linear spaces from which minimal velocity sets are identified for the degrees of precision that are most relevant to the construction of high-order LBGK models. All well-known LBGK lattices are found to be special cases of the given general solutions.