Mesoscopic hydrodynamics of diphasic Lattice Bhatnagar Gross Krook fluid interfaces

Abstract

We consider the most appropriate way to assess the interfacial tension locally, on a meso-scale, in one particular class of diphasic lattice Bhatnagar Gross Krook fluid, in which the interface is supported by a simple segregation algorithm. Our investigative methodology and observations will support similar analysis of other lattice Boltzmann models containing discrete interfaces. By assessing the performance of a lattice fluid/fluid interface against the most general hydrodynamic boundary conditions, we measure an orientational dependence in the model's surface tension. In attempting to assess this anisotropy, which must obstruct the performance of the model and others similarly conceived, we devise a simple correction to the segregation algorithm. The useful result provides a platform for future work.

References

1. M. R. Swift, W. R. Osborn and J. M. Yeomans, Phys. Rev. Lett., 1995, 75, 830.
2. I. Halliday, C. M. Care and S. P. Thompson, Phys. Rev. E, 1998, 57(1), 514.
3. A. K. Gunstensen, D. H. Rothman, S. Zaleski and G. Zanetti, Phys. Rev. A, 1991, 43(8), 4320.
4. U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau and J. P. Rivet, Complex Syst., 1987, 1, 649 and references therein.
5. R. Benzi, S. Succi and M. Vergassola, Phys. Rep., 1992, 22(3), 145.
6. Y. H. Qian, S. Succi and S. A. Orszag, Annu. Rev. Comput. Phys., 1995, 3, 195.
7. H. Chen, S. Chen and W. H. Matthaeus, Phys. Rev. A, 1992, 45(8), R5339.
8. D. d'Humieres, P. Lallemand and U. Frisch, Europhys. Lett., 1986, 56, 1505.
9. F. Higuera and J. Jimenez, Europhys. Lett., 1989, 9, 7, 663.
10. F. Higuera, S. Succi and R. Benzi, Europhys. Lett., 1989, 9(4), 345.
11. Y. H. Qian, D. d'Humieres and P. Lallemand, Europhys. Lett., 1992, 17(6), 479.
12. X. W. Shan and H. D. Chen, Phys. Rev. E, 1994, 49(4), 2941.
13. I. Halliday, C. M. Care, S. Thompson and D. White, Phys. Rev. E, 1996, 54(3), 2573.
14. A. J. Wagner and J. M. Yeomans, J. Mod. Phys. C, 1997, 8(4), 773.
15. E. Orlandini, M. R. Swift and J. M. Yeomans, Europhys. Lett., 1995, 32, 463.
16. E. Orlandini, G. Gonnella and J. M. Yeomans, Physica A, 1997, 240(1–2), 277.
17. D. H. Rothman and S. Zaleski, Rev. Mod. Phys., 1994, 52, 1417.
18. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford, UK, 1966.
19. G. K. BatchelorAn Introduction to Fluid Mechanics, Cambridge University Press, Cambridge, UK, 1973.
20. J. S. Rawlinson and B. Widom, Molecular Theory of Capilarity, Oxford University Press, London, UK, 1989.
21. D. H. Rothman and J. M. Keller, J. Stat. Phys., 1988, 52(3-4), 1119.
22. I. Halliday and C. M. Care, Phys. Rev. E, 1995, 53(3), 1602.
23. M. R. Speigel, Vector analysis and an introduction to Tensor analysis, Schaum's Outline Series, McGraw–Hill, New York, USA, 1959.
24. S. Chen, G. D. Doolen, K. Eggert, D. Grunau and Y. E. Loh, Phys. Rev. A, 1994, 43(12), 7053.
25. S. Hou, X. Shan, Q. Zou, G. D. Doolen and W. E. Soll, J. Comput. Phys., 1997, 138(2), 695.