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Microscopic flow near the surface of two-dimensional porous media. Part 1. Axial flow

Published online by Cambridge University Press:  21 April 2006

R. E. Larson  and
J. J. L. Higdon
R. E. Larson
Affiliation:
Department of Chemical Engineering, University of Illinois, 1209 W California St, Urbana, Illinois 61801
J. J. L. Higdon
Affiliation:
Department of Chemical Engineering, University of Illinois, 1209 W California St, Urbana, Illinois 61801
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Abstract

A model problem is analysed to study the microscopic flow near the surface of two-dimensional porous media. In the idealized problem we consider axial flow through infinite and semi-infinite lattices of cylindrical inclusions. The effect of lattice geometry and inclusion shape on the permeability and surface flow are examined. Calculations show that the definition of a slip coefficient for a porous medium is meaningful only for extremely dilute systems. Brinkman's equation gives reasonable predictions for the rate of decay of the mean velocity for certain simple geometries, but fails for to predict the correct behaviour for media anisotropic in the plane normal to the flow direction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 166 , May 1986 , pp. 449 - 472
Copyright
© 1986 Cambridge University Press

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References

Beavers, G. S. & Joseph, D. D. 1967 Boundary condition at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Beavers, G. S., Sparrow, E. M. & Masha, B. A. 1974 Boundary condition at a porous surface which bounds a fluid flow. AIChE J. 20, 596–597.Google Scholar
Brebbia, C. A. (ed.) 1983 Boundary Element Techniques in Computer-Aided Engineering. Martinus Nijhoff.
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. App. Sci. Res. A1, 27.Google Scholar
Darcy, H. P. G. 1856 Les Fontaines Publiques de la Ville de Dijon. Paris: Victor Dalmont.
Howells, I. D. 1974 Drag due to the motion of a Newtonian fluid through a sparse random array of small rigid fixed objects. J. Fluid Mech. 64, 449–475.Google Scholar
Matsumoto, K. & Suganuma, A. 1977 Settling velocity of a permeable model floc. Chem. Engng Sci. 32, 445–447.Google Scholar
Richardson, S. 1971 A model for the boundary condition of a porous material. Part 2. J. Fluid Mech. 49, 327–336.Google Scholar
Saffman, P. G. 1971 On the boundary condition at the surface of a porous medium. Stud. Appl. Maths 50, 93–101.Google Scholar
Sangani, A. S. & Acrivos, A. 1982a Slow flow past periodic arrays of cylinders with application to heat transfer. Intl J. Multiphase Flow 8, 193–206.Google Scholar
Sangani, A. S. & Acrivos, A. 1982b Slow flow through a periodic array of spheres. Intl J. Multiphase Flow 8, 343–360.Google Scholar
Sneddon, I. N. 1957 Elements of Partial Differential Equations. McGraw-Hill.
Sparrow, E. M. & Loeffler, A. L. 1959 Longitudinal laminar flow between cylinders arranged in a regular array. AIChE J. 5, 325–330.Google Scholar
Taylor, G. I. 1971 A model for the boundary condition of a porous material. Part 1. J. Fluid Mech. 49, 319–326.Google Scholar
Zick, A. A. & Homsy, G. M. 1982 Stokes flow through periodic arrays of spheres. J. Fluid Mech. 115, 13–26.Google Scholar