Abstract
A lattice Boltzmann model for simulating fluids with multiple components and interparticle forces proposed by Shan and Chen is described in detail. Macroscopic equations governing the motion of each component are derived by using the Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirment by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity, so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confiremoed numerically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
U. Frisch, B. Hasslacher, and Y. Pomeau,Phys. Rev. Lett.56:1505 (1986).
G. D. Doolen,Lattice Gas Methods for Partial Differential Equations (Addison-Wesley, Redwood City, California, 1989).
G. R. McNamara and G. Zanetti,Phys. Rev. Lett. 61:2332 (1988).
F. J. Higuera and J. Jimenez,Europhys. Lett. 9:663 (1989).
H. Chen, S. Chen, and W. H. Matthaeus,Phys. Rev. A 45:R5339 (1992).
Y. H. Qian, D. d'Humieres, and P. Lallemand,Europhys. Lett. 17:479 (1992).
P. L. Bhatnagar, E. P. Gross, and M. Krook,Phys. Rev. 94:511 (1954).
D. O. Martinez, W. H. Matthaeus, S. Chen, and D. Montgomery,Phys. Fluid 6:1285 (1994).
D. O. Martinez, S. Chen and W. H. Matthaeus,Phys. Plasmas 1:1850 (1994).
J. S. Rowlinson and B. Widon,Molecular Theory of Capillarity (Clarendon Press, Oxford, 1982).
D. H. Rothman and J. M. Keller,J. Stat. Phys. 52:119 (1988).
A. K. Gunstensen, D. H. Rothmann, S. Zaleski, and G. Zanetti,Phys. Rev. A 43: 4320 (1991).
R. Holme and D. H. Rothman,J. Stat. Phys. 68:409 (1992).
C. Adler, D. d'Humières, and D. H. Rothmann,J. Phys. I France 4:29 (1994).
C. Appert and S. Zaleski,Phys. Rev. Lett. 64:1 (1990)
X. Shan and H. Chen,Phys. Rev. E 47:1815 (1993).
X. Shan and H. Chen,Phys. Rev. E 49:2941 (1994).
S. Chapman and T. G. Crowling,The Mathemaitcal Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge., 1970).
U. Frisch et al.,Complex Systems 1:649 (1987).
E. G. Flekkøy,Phys. Rev. E 47:4247 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shan, X., Doolen, G. Multicomponent lattice-Boltzmann model with interparticle interaction. J Stat Phys 81, 379–393 (1995). https://doi.org/10.1007/BF02179985
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02179985