Inertial Effects on Particle Interactions in Viscous Flows (fluid-Solid, Low Reynolds Number)

Adamides, Adamos

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Permalink

https://hdl.handle.net/2142/69765

Description

Title

Inertial Effects on Particle Interactions in Viscous Flows (fluid-Solid, Low Reynolds Number)

Author(s)

Adamides, Adamos

Issue Date

1986

Department of Study

Chemical Engineering

Discipline

Chemical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Engineering, Chemical

Abstract

The interactions between two equal spheres fixed in a viscous uniform flow are investigated. Using matched asymptotic expansions, assuming that both particles are within each other's inner domain and applying Stokes flow techniques the first inertial correction to the Stokes velocity and pressure fields and the corresponding force for each particle are evaluated to O(R(epsilon)('2)), where R is the particle Reynolds number and (epsilon) is the ratio of the radius to the distance between the spheres. For an arbitrary configuration and difference between the forces on each sphere has a component parallel to the uniform flow (DELTA)F(,1) = 221/24 (pi)R(epsilon)('3)(3(epsilon)('2)y(,1)('3)-y(,1)) and a component normal to the flow (DELTA)F(,2) = 1/600 (pi)R(epsilon)('3)(16575(epsilon)('2)y(,1)('2)-3713)(gamma)(,2) where the origin is at the center of the one sphere and (gamma) denotes the position vector of the second sphere made non-dimensional with the radius.

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