Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions
RF - Rogaland Research, PO Box 2503, 4091 Stavanger, Norway
2 Department of Physics, Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
Revised: 19 November 1999
Published online: 15 May 2000
A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman , but differ somewhat from those of Halpern and Gaver  for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios.
PACS: 47.11.+j – Computational methods in fluid dynamics / 83.10.Lk – Multiphase flows / 66.20.+d – Viscosity of liquids; diffusive momentum transport
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000