Skip to main content
SpringerLink
Log in

Immiscible cellular-automaton fluids

  • Short Communications
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We introduce a new deterministic collision rule for lattice-gas (cellular-automaton) hydrodynamics that yields immiscible two-phase flow. The rule is based on a minimization principle and the conservation of mass, momentum, and particle type. A numerical example demonstrates the spontaneous separation of two phases in two dimensions. Numerical studies show that the surface tension coefficient obeys Laplace's formula.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. U. Frisch, B. Hasslacher, and Y. Pomeau,Phys. Rev. Lett. 56:1505 (1986).

    Google Scholar 

  2. S. Wolfram,Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).

    Google Scholar 

  3. U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet,Complex Systems 1:648 (1987).

    Google Scholar 

  4. S. Wolfram,J. Stat. Phys. 45:471 (1986).

    Google Scholar 

  5. L. Kadanoff, G. McNamara, and G. Zanetti. From automata to fluid flow: comparisons of simulation and theory, University of Chicago preprint (1987).

  6. D. d'Humières and P. Lallemand,Complex Systems 1:598 (1987).

    Google Scholar 

  7. D. d'Humières, P. Lallemand, and G. Searby,Complex Systems 1:632 (1987).

    Google Scholar 

  8. D. d'Humières, P. Lallemand, and U. Frisch,Europhys. Lett. 2:291 (1986); J.-P. Rivet,C. R. Acad. Sci. Paris II 305:751 (1987).

    Google Scholar 

  9. C. Burges and S. Zaleski,Complex Systems 1:31 (1987).

    Google Scholar 

  10. K. Balasubramanian, F. Hayot, and W. F. Saam,Phys. Rev. A 36:2248 (1987).

    Google Scholar 

  11. D. Rothman,Geophysics 53:509 (1988).

    Google Scholar 

  12. D. A. Drew,Annu. Rev. Fluid Mech. 15:261 (1983).

    Google Scholar 

  13. L. D. Landau and E. M. Lifshitz,Fluid Mechanics (Pergamon Press, New York, 1959), p. 230; G. K. Batchelor,An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1976), p. 68.

    Google Scholar 

  14. J. S. Rowlinson and B. Widom,Molecular Theory of Capillarity (Clarendon Press, Oxford, 1982).

    Google Scholar 

  15. J. M. Hyman,Physica 12D:396 (1984), and references therein; J. Glimm, O. McBryan, R. Menikoff, and D. H. Sharp,SIAM J. Sci Stat. Comput. 7:230 (1986); H. Aref, Finger, bubble, tendril, spike, University of California-San Diego preprint (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

    Daniel H. Rothman & Jeffrey M. Keller

Authors
  1. Daniel H. Rothman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeffrey M. Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rothman, D.H., Keller, J.M. Immiscible cellular-automaton fluids. J Stat Phys 52, 1119–1127 (1988). https://doi.org/10.1007/BF01019743

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01019743

Key words

Search

Navigation