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Physics of Fluids : An analysis of the far-field response to external forcing of a suspension in the Stokes flow in a parallel-wall channel

By J. B›awzdziewicz and E. Wajnryb

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Book Id: WPLBN0002169593
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 19 September 2008

Title: Physics of Fluids : An analysis of the far-field response to external forcing of a suspension in the Stokes flow in a parallel-wall channel  
Author: J. B›awzdziewicz and E. Wajnryb
Volume: Issue : September 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Physics of Fluids Collection
Historic
Publication Date:
Publisher: American Institute of Physics

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And E. Wajnry, J. B. (n.d.). Physics of Fluids : An analysis of the far-field response to external forcing of a suspension in the Stokes flow in a parallel-wall channel. Retrieved from http://kindle.worldlibrary.net/


Description
Description: The leading-order far-field scattered flow produced by a particle in a parallel-wall channel under creeping-flow conditions has a form of the parabolic velocity field driven by a two-dimensional dipolar pressure distribution. We show that in a system of hydrodynamically interacting particles, the pressure dipoles contribute to the macroscopic suspension flow in a similar way as the induced electric dipoles contribute to the electrostatic displacement field. Using this result we derive macroscopic equations governing suspension transport under the action of a lateral force, a lateral torque, or a macroscopic pressure gradient in the channel. The matrix of linear transport coefficients in the constitutive relations linking the external forcing to the particle and fluid fluxes satisfies the Onsager reciprocal relation. The transport coefficients are evaluated for square and hexagonal periodic arrays of fixed and freely suspended particles, and a simple approximation in a Clausius–Mossotti form is proposed for the channel permeability coefficient. We also find explicit expressions for evaluating the periodic Green’s functions for the Stokes flow between two parallel walls.

 

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