Nott, Prabhu R. and Brady, John F. (1994) Pressure-driven flow of suspensions: simulation and theory. Journal of Fluid Mechanics, 275 . pp. 157-199. ISSN 0022-1120 http://resolver.caltech.edu/CaltechAUTHORS:NOTjfm94
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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/[left angle bracket]u[right angle bracket], where H is the channel width, a the radii of the particles, and [left angle bracket]u[right angle bracket] 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.
|Additional Information:||Copyright © 1994 Cambridge University Press. Reprinted with permission. (Received 27 December 1992 and in revised form 3 April 1994) This work was supported by the Office of Naval Research under Grant No. N00014-90-5-1945. The authors also wish to acknowledge the San Diego Supercomputer Center for providing computational facilities. Discussions with Mr J.F. Morris regarding the origin of velocity fluctuations in low-Reynolds-numbers flows were especially helpful.|
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