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Pressure-driven flow of suspensions: simulation and theory

Published online by Cambridge University Press:  26 April 2006

Prabhu R. Nott  and
John F. Brady
Prabhu R. Nott
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Current address: India Institute of Science, Bangalore, India.
John F. Brady
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

Dynamic simulations of the pressure-driven flow in a channel of a non-Brownian suspension at zero Reynolds number were conducted using Stokesian Dynamics. The simulations are for a monolayer of identical particles as a function of the dimensionless channel width and the bulk particle concentration. Starting from a homogeneous dispersion, the particles gradually migrate towards the centre of the channel, resulting in an homogeneous concentration profile and a blunting of the particle velocity profile. The time for achieving steady state scales as (H/a)3a/〈u〉, where H is the channel width, a the radii of the particles, and 〈u〉 the average suspension velocity in the channel. The concentration and velocity profiles determined from the simulations are in qualitative agreement with experiment.

A model for suspension flow has been proposed in which macroscopic mass, momentum and energy balances are constructed and solved simultaneously. It is shown that the requirement that the suspension pressure be constant in directions perpendicular to the mean motion leads to particle migration and concentration variations in inhomogeneous flow. The concept of the suspension ‘temperature’ – a measure of the particle velocity fluctuations – is introduced in order to provide a nonlocal description of suspension behaviour. The results of this model for channel flow are in good agreement with the simulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 275 , 25 September 1994 , pp. 157 - 199
Copyright
© 1994 Cambridge University Press

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