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Permeability of three-dimensional models of fibrous porous media

Published online by Cambridge University Press:  26 April 2006

J. J. L. Higdon  and
G. D. Ford
J. J. L. Higdon
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana, IL 61801-3791, USA
G. D. Ford
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana, IL 61801-3791, USA
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Abstract

Viscous flow through three-dimensional models of fibrous porous media is analysed. The periodic models are based on ordered networks of cylindrical fibres on regular cubic lattices. Numerical solutions are obtained using the spectral boundary element method introduced by Muldowney & Higdon (1995). Results are presented for solid volume fractions ranging from extreme dilution to near the maximum volume fraction for permeable media. Theoretical estimates are derived using slender-body theory and lubrication approximations in the appropriate asymptotic regimes. Comparisons are made with model predictions based on properties of two-dimensional media (Jackson & James 1986), and with results for disordered dispersions of prolate spheroids (Claeys & Brady 1993b).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 308 , 10 February 1996 , pp. 341 - 361
Copyright
© 1996 Cambridge University Press

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References

Chapman, A. M. & Higdon, J. J. L. 1992 Oscillatory Stokes flow in periodic porous media. Phys. Fluids A 4, 2099–2116.Google Scholar
Chapman, A. M. & Higdon, J. J. L. 1994 Effective elastic properties for a periodic bicontinuous porous medium. J. Mech. Phys. Solids 42, 283–305.Google Scholar
Claeys, I. L. & Brady, J. F. 1993a Suspensions of prolate spheroids in Stokes flow. Part 1. Dynamics of a finite number of particles in a unbounded fluid. J. Fluid Mech. 251, 441–442.Google Scholar
Claeys, I. L. & Brady, J. F. 1993b Suspensions of prolate spheroids in Stokes flow. Part 2. Statistically homogeneous dispersions. J. Fluid Mech. 251, 443–477.Google Scholar
Claeys, I. L. & Brady, J. F. 1993c Suspensions of prolate spheroids in Stokes flow. Part 3. Hydrodynamic transport properties of crystalline dispersions. J. Fluid Mech. 251, 411–442.Google Scholar
Drummon, J. E. & Tahir, M. I. 1984 Laminar viscous flow through regular arrays of parallel solid cylinders. Intl J. Multiphase Flow 10, 515–540.Google Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 174–177.Google Scholar
Howells, I. D. 1974 Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects. J. Fluid Mech. 64, 449–475.Google Scholar
Jackson, G. W. & James, D. F. 1982 The hydrodynamic resistance of hyaluronic acid and its contribution to tissue permeability. Biorheology 19, 317–330.Google Scholar
Jackson, G. W. & James, D. F. 1986 The permeability of fibrous porous media. Can. J. Chem. Engng 64, 364–374.Google Scholar
Johnson, R. E. 1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411–431.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications Butterworth-Heinemann.
Larson, R. E. & Higdon, J. J. L. 1986 Microscopic flow near the surface of two-dimensional porous media. Part 1. Axial flow. J. Fluid Mech. 166, 449–472.Google Scholar
Larson, R. E. & Higdon, J. J. L. 1987 Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow. J. Fluid Mech. 178, 119–136.Google Scholar
Larson, R. E. & Higdon, J. J. L. 1989 A periodic grain consolidation model of porous media. Phys. Fluids A 1, 38–46.Google Scholar
Muldowney, G. P. & Higdon, J. J. L. 1995 A spectral boundary element approach to three dimensional Stokes flow. J. Fluid Mech. 298, 167–192.Google Scholar
Pozrikidis, C. 1992 Boundary and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
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
Sangani, A. S. & Yao, C. 1988a Transport processes in random arrays of cylinders. I. Thermal conduction. Phys. Fluids 31, 2426–2434.Google Scholar
Sangani, A. S. & Yao, C. 1988b Transport processes in random arrays of cylinders. II. Viscous flow. Phys. Fluids 31, 2426–2434.Google Scholar
Sparrow, E. M. & Loeffler, A. L. 1959 Longitudinal laminar flow between cylinders arranged in a regular array. AIChE J. 5, 325–330.Google Scholar
Spielman, L. & Goren, S. L. 1968 Model for predicting pressure drop and filtration efficiency in fibrous media. Environ. Sci. Technol. 2, 279–287.Google Scholar
Dyke, M. Van 1974 Analysis and improvement of perturbation series. Q. J. Mech. Appl. Maths 27, 423–450.Google Scholar
Zick, A. A. & Homsy, G. M. 1982 Stokes flow through periodic arrays of spheres. J. Fluid Mech. 115, 13–26.Google Scholar