Lattice Boltzmann model for the simulation of multicomponent mixtures

A lattice Boltzmann (LB) model for the simulation of realistic multicomponent mixtures is constructed. In the hydrodynamic limit, the LB model recovers the equations of continuum mechanics within the mixture-averaged diffusion approximation. The present implementation can be used to simulate realistic mixtures with arbitrary Schmidt numbers and molecular masses of the species. The model is applied to the mixing of two opposed jets of different concentrations and the results are in excellent agreement with a continuum model. An application to the simulation of mixtures in microflows is also presented. Results compare well with existing kinetic theory predictions of the slip coefficient for mixtures in a Couette flow.

Figure 1

Discrete velocity vectors of various species. The velocities $c_{1i}$ of the lighter component of mass $m_1$ are on the lattice. The corresponding magnitudes are $c_{1\{1,2,3,4\}}=c_1$ and $c_{1\{5,6,7,8\}}=c_1\sqrt{2}$. The generic off-lattice velocity vectors $c_{ji}$ corresponding to species with the molecular mass $m_j>m_1$ are also represented.

Figure 2

LB simulation of the mixing in an opposed-jet configuration: Velocity vector plot superimposed on the $H_2$ mole fraction isocontours.

Figure 3

Opposed-jet mixing: Comparison of the velocity and the concentrations along the plane of symmetry $(y=0)$ between the LB mixture model (symbols) and the 1D continuum code OPPDIF predictions (continuous lines).

Figure 4

Slip coefficient versus helium molar fraction $X_{\mathrm{He}}$. (a) Helium-argon mixture. (b) Helium-xenon mixture. Squares: linearized kinetic theory results from Ref. 53. Triangles: DSMC results [52]. Circles: present work.