We study the shear-induced self-diffusion of both liquid tracer and a tagged spherical particle along the directions perpendicular to the ambient flow in a dilute suspension of neutrally buoyant spheres undergoing a simple shearing motion in the absence of inertia and Brownian motion effects. The calculation of the liquid diffusivity requires the velocity of a fluid point under the influence of two spheres, which was determined via Lamb's series expansion; conversely, the calculation of the particle diffusivity involves the trajectoruees of three spheres, which was determined using far-field and near-field asymptotic expressions. The displacements of the liquid tracer and of the tagged sphere were then computed analytically when the spheres and the tracer are all far apart, and numerically for close encounters. After summing over all possible encounters, the leading terms of the lateral lipuid diffusion coefficients, both within and normal to the plane of shear, were thereby found to be 0.12 gamma a^2 c^2 and 0.004 gamma a^2 c^2, respectively, where gamma is the applied shear rate, a the radius of the spheres and c their volume fraction. The analogous coefficients of the lateral particle diffusivity were found to be 0.11 gamma a^2 c^2 and 0.005 gamma a^2 c^2, respectively. Also, liquid and particle diffusivities in a monolayer, with the liquid tracer and all the particle centres lying on the same plane of shear, were found to be 0.067 gamma a^2 c^2 and 0.032 gamma a^2 c^2, respectively, with c denoting the areal fraction occupied by the spheres on the plane.

The Transverse Shear-Induced Liquid and Particle Tracer Diffusivities of a Dilute Suspension of Spheres Undergoing a Simple Shear Flow

MAURI, ROBERTO;
1996

Abstract

We study the shear-induced self-diffusion of both liquid tracer and a tagged spherical particle along the directions perpendicular to the ambient flow in a dilute suspension of neutrally buoyant spheres undergoing a simple shearing motion in the absence of inertia and Brownian motion effects. The calculation of the liquid diffusivity requires the velocity of a fluid point under the influence of two spheres, which was determined via Lamb's series expansion; conversely, the calculation of the particle diffusivity involves the trajectoruees of three spheres, which was determined using far-field and near-field asymptotic expressions. The displacements of the liquid tracer and of the tagged sphere were then computed analytically when the spheres and the tracer are all far apart, and numerically for close encounters. After summing over all possible encounters, the leading terms of the lateral lipuid diffusion coefficients, both within and normal to the plane of shear, were thereby found to be 0.12 gamma a^2 c^2 and 0.004 gamma a^2 c^2, respectively, where gamma is the applied shear rate, a the radius of the spheres and c their volume fraction. The analogous coefficients of the lateral particle diffusivity were found to be 0.11 gamma a^2 c^2 and 0.005 gamma a^2 c^2, respectively. Also, liquid and particle diffusivities in a monolayer, with the liquid tracer and all the particle centres lying on the same plane of shear, were found to be 0.067 gamma a^2 c^2 and 0.032 gamma a^2 c^2, respectively, with c denoting the areal fraction occupied by the spheres on the plane.
Wang, Y; Mauri, Roberto; Acrivos, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/44375
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