Steady state hydrodynamics of a lattice Boltzmann immiscible lattice gas

We report results from a simulation that assesses steady state hydrodynamics of two-phase lattice gas fluids by considering isolated fluid drops that are suspended in an immiscible fluid of identical viscosity. Gunstensen's method of incorporating phase segregation between different species of colored densities [(A.K. Gunstensen et al., Phys. Rev. A 43, 4320 (1991)] is combined with Kingdon's recent nonlinear, nonlocal lattice Boltzmann equation [R. Kingdon, J. Phys. A 25, 3559 (1992)], which facilitates meaningful observations of lattice gas interfacial hydrodynamics. After the approach to a steady flow state has been assessed, the deformation of a suspended fluid drop, its angle of orientation to the shear flow, and the relationship between these quantities are extracted from simulations over a range of shear rates and interfacial tensions. Qualitative and quantitative comparison of these results with hydrodynamic theory shows further work to be necessary but worthwhile. Gunstensen's automaton phase segregation rule is also found to be responsible for inducing steady microscopic currents or microcurrents close to the inferface in a static flow. The influences of these microcurrents are briefly considered after Gunstensen [Ph.D. thesis, Massachusetts Institute of Technology, 1992 (unpublished)].