The shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method

An extended Benzi-Dellar lattice Boltzmann equation scheme (R. Benzi, S. Succi and M. Vergassola, Europhys. Lett. 13, 727 (1990), R. Benzi, S. Succi and M. Vergassola, Phys. Rep. 222, 145 (1992), P. M. Dellar, Phys Rev. E 65 036309 (2002)) is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c, the variation of effective shear viscosity, Data obtained with our enhanced multi-component lattice Boltzmann method, using average shear stress and hydrodynamic dissipation agree well, once appropriate corrections to Landau's volume average shear stress (L. Landau and E. M. Lifshitz, Fluid Mechanics, Sixth Edition, Pergamon Press ) are applied. Simulation results also confirm the expected form for f(_i; _2) and provide a reasonable estimate of its parameters. Most significantly, perhaps the generality of our data support the validity of Taylor's disputed simplification (G. I. Taylor. Proc. R. Soc. Lond. A 1932 138 133-146) to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.