Macroscopic surface tension in a lattice Bhatnagar-Gross-Krook model of two immiscible fluids

I. Halliday, S. P. Thompson, and C. M. Care
Phys. Rev. E 57, 514 – Published 1 January 1998
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Abstract

We present a method by which an interface generating algorithm, similar to that of earlier lattice Boltzmann models of immiscible fluids, may be extended to a two component, two-speed two-dimensional (D2), nine-link (Q9) lattice Bhatnagar-Gross-Krook fluid. For two-dimensional, microcurrent-free planar interfaces between the two immiscible fluids we derive expressions for static interfacial tensions and interfacial distributions of the two fluids. Extending our analysis to curved interfaces, we propose a scheme for incorporating the influence of interfacial microcurrents that is based upon general symmetry arguments and is correct to second order in lattice velocity. The analysis demonstrates that the interfacial microcurrents have only second-order influence upon the macroscopic behavior of the model. We find good agreement between our calculations and simulation results based on the microcurrent stream function and surface tension results from the pressure tensor or Laplace law.

  • Received 28 March 1997

DOI:https://doi.org/10.1103/PhysRevE.57.514

©1998 American Physical Society

Authors & Affiliations

I. Halliday1, S. P. Thompson2, and C. M. Care2

  • 1Division of Applied Physics, School of Science and Mathematics, Sheffield Hallam University, Pond Street, Sheffield, S1 1WB, United Kingdom
  • 2Materials Research Institute, Sheffield Hallam University, Pond Street, Sheffield, S1 1WB, United Kingdom

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Vol. 57, Iss. 1 — January 1998

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