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Analysis of the Brinkman equation as a model for flow in porous media

Durlofsky, L. and Brady, J. F. (1987) Analysis of the Brinkman equation as a model for flow in porous media. Physics of Fluids, 30 (11). pp. 3329-3341. ISSN 1070-6631. doi:10.1063/1.866465.

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The fundamental solution or Green's function for flow in porous media is determined using Stokesian dynamics, a molecular-dynamics-like simulation method capable of describing the motions and forces of hydrodynamically interacting particles in Stokes flow. By evaluating the velocity disturbance caused by a source particle on field particles located throughout a monodisperse porous medium at a given value of volume fraction of solids ø, and by considering many such realizations of the (random) porous medium, the fundamental solution is determined. Comparison of this fundamental solution with the Green's function of the Brinkman equation shows that the Brinkman equation accurately describes the flow in porous media for volume fractions below 0.05. For larger volume fractions significant differences between the two exist, indicating that the Brinkman equation has lost detailed predictive value, although it still describes qualitatively the behavior in moderately concentrated porous media. At low ø where the Brinkman equation is known to be valid, the agreement between the simulation results and the Brinkman equation demonstrates that the Stokesian dynamics method correctly captures the screening characteristic of porous media. The simulation results for ø ≥ 0.05 may be useful as a basis of comparison for future theoretical work.

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Brady, J. F.0000-0001-5817-9128
Additional Information:© 1987 American Institute of Physics. Received 21 May 1987; accepted 17 July 1987. We wish to thank J. Lester and R. Phillips for their assistance with some of the computer programming and G. Bossis for many useful discussions. Computer time was provided on the San Diego Supercomputer Center Cray X-MP through a National Science Foundation allocation. Partial support for this work was through National Science Foundation Grant No. CBT-8696067.
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Subject Keywords:porous materials; stokes law; brinkman−kramers approximation; green function; disturbances; velocity; viscous flow; disordered systems; randomness
Issue or Number:11
Classification Code:PACS: 47.56.+r
Record Number:CaltechAUTHORS:20120626-112949432
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Official Citation:Analysis of the Brinkman equation as a model for flow in porous media L. Durlofsky and J. F. Brady, Phys. Fluids 30, 3329 (1987), DOI:10.1063/1.866465
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32091
Deposited On:26 Jun 2012 19:42
Last Modified:09 Nov 2021 21:14

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