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

HALLIDAY, Ian, XU, Xu and BURGIN, Kallum (2017). The shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method. Physical Review E (PRE), 95 (2-1).

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Official URL: https://journals.aps.org/pre/abstract/10.1103/Phys...
Link to published version:: 10.1103/PhysRevE.95.023301

Abstract

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.

Item Type: Article
Uncontrolled Keywords: lattice Boltzmann, multiple-relaxation-time, body force
Research Institute, Centre or Group: Materials and Engineering Research Institute > Polymers Nanocomposites and Modelling Research Centre > Materials and Fluid Flow Modelling Group
Identification Number: 10.1103/PhysRevE.95.023301
Depositing User: Jill Hazard
Date Deposited: 20 Dec 2016 12:12
Last Modified: 19 Aug 2017 19:15
URI: http://shura.shu.ac.uk/id/eprint/14337

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