Brady, John F. and Durlofsky, Louis J. (1988) The sedimentation rate of disordered suspensions. Physics of Fluids, 31 (4). pp. 717-727. ISSN 0031-9171. http://resolver.caltech.edu/CaltechAUTHORS:BRApof88
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An explicit expression for the sedimentation velocity at low particle Reynolds number in a concentrated suspension is derived and evaluated for two different approximations to the hydrodynamic interactions: a strict pairwise additive approximation and a far-field, or Rotne–Prager, approximation. It is shown that the simple Rotne–Prager approximation gives a very accurate prediction for the sedimentation velocity of random suspensions from the dilute limit all the way up to close packing. The pairwise additive approximation, however, fails completely, predicting an aphysical negative sedimentation velocity above a volume fraction φ ≈ 0.23. The explanation for these different behaviors is shown to be linked to the "effective medium" behavior of the suspensions. It is shown analytically and by Stokesian dynamics simulation that a suspension of neutrally buoyant particles may be modeled as a homogeneous fluid with an effective viscosity, but a sedimenting suspension cannot. As a result, the Rotne–Prager approximation actually captures the correct features of the many-body interactions in sedimentation. An analytical expression for the sedimentation rate, which is in good agreement with experiment, is obtained using the Percus–Yevick hard-sphere distribution function.
|Additional Information:||Copyright © 1988 American Institute of Physics. Received 2 November 1987; accepted 22 December 1987. We wish to thank J. Lester for her assistance with several aspects of the computations. Partial support for this work was through National Science Foundation Grant No. CBT-8696067. Computer time was supplied by the San Diego Supercomputer Center.|
|Subject Keywords:||SUSPENSIONS, SEDIMENTATION, COMPUTERS, DISORDERED SYSTEMS, VELOCITY, EQUATIONS, REYNOLDS NUMBER, CORRELATIONS|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||26 Nov 2008 19:52|
|Last Modified:||26 Dec 2012 10:32|
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