title: Shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method.
abstract: An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990)EULEEJ0295-507510.1209/0295-5075/13/8/010; R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992)PRPLCM0370-157310.1016/0370-1573(92)90090-M; P. J. Dellar, Phys. Rev. E 65, 036309 (2002)1063-651X10.1103/PhysRevE.65.036309] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c, the variation of effective shear viscosity, η_{eff}=η_{1}[1+f(η_{1},η_{2})c], with respect to c for a sheared, two-dimensional, initially crystalline emulsion [here η_{1} (η_{2}) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent 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, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for f(η_{i},η_{2}), and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932)1364-502110.1098/rspa.1932.0175] 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.
authors.affiliation: Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom.
authors.forename: I
authors.initials: I
authors.lastname: Halliday
authors.affiliation: Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom.|Department of Engineering and Mathematics, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom.
authors.forename: X
authors.initials: X
authors.lastname: Xu
authors.affiliation: Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom.
authors.forename: K
authors.initials: K
authors.lastname: Burgin