TY - JOUR

T1 - On the effective viscosity of a nondilute emulsion of two Stokes fluids with small capillary number

AU - Miloh, T.

AU - Benveniste, Y.

PY - 1989

Y1 - 1989

N2 - A rigorous analytical framework is presented for the computation of the effective viscosity of a neutrally buoyant nondilute emulsion of two immiscible Newtonian Stokes fluids. The capillary number, which is a relative measure of viscous forces that tend to distort the drop and of the interfacial tension that favors sphericity, is assumed to be small. Thus drop distortion is ignored to first order and sphericity is preserved under small shear rates. The so-called "direct method," which does not involve any energy concepts, is used and also is shown to be equivalent to the traditional approach based on the dissipation function. The micromechanics model is based on the "generalized self-consistent model" commonly used in composite media. At low concentrations the present theoretical prediction reduces to Taylor's formula [Proc. R. Soc. London Ser. A 138, 41 (1932)] and is also compared against other approximate theories and experimental data for the nondilute case. The agreement is in general surprisingly good. The present model is also shown to fall between some existing bounds, which result from the application of various variational principles. A critical comparison between these bounds is also given.

AB - A rigorous analytical framework is presented for the computation of the effective viscosity of a neutrally buoyant nondilute emulsion of two immiscible Newtonian Stokes fluids. The capillary number, which is a relative measure of viscous forces that tend to distort the drop and of the interfacial tension that favors sphericity, is assumed to be small. Thus drop distortion is ignored to first order and sphericity is preserved under small shear rates. The so-called "direct method," which does not involve any energy concepts, is used and also is shown to be equivalent to the traditional approach based on the dissipation function. The micromechanics model is based on the "generalized self-consistent model" commonly used in composite media. At low concentrations the present theoretical prediction reduces to Taylor's formula [Proc. R. Soc. London Ser. A 138, 41 (1932)] and is also compared against other approximate theories and experimental data for the nondilute case. The agreement is in general surprisingly good. The present model is also shown to fall between some existing bounds, which result from the application of various variational principles. A critical comparison between these bounds is also given.

UR - http://www.scopus.com/inward/record.url?scp=0024532085&partnerID=8YFLogxK

U2 - 10.1063/1.857517

DO - 10.1063/1.857517

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AN - SCOPUS:0024532085

SN - 0899-8213

VL - 1

SP - 1915

EP - 1925

JO - Physics of fluids. A, Fluid dynamics

JF - Physics of fluids. A, Fluid dynamics

IS - 12

ER -