Permeability Tensor for Heterogeneous Porous Medium of Fibre Type

Transport in Porous Media

Volumn 32, Issue 1, 1998, Pages 1-19

  Kołodziej, Jan A ^a   Dziȩcielak, Ryszard ^a   Kończak, Zenon ^a  

^a POZNAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Anisotropic porous media; Bundle of parallel fibres; Cell model; Darcy's law; Permeability tensor

Indexed keywords

ANISOTROPY; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; POROUS MATERIALS; TENSORS; VOLUME FRACTION;

DARCY'S LAW;

FIBERS;

FIBER; POROUS MEDIUM;

FIBER; PERMEABILITY; THEORETICAL ANALYSIS;

EID: 0032125396     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006548025449     Document Type: Article

References (44)

1. Baumstart, J.: 1959, Upper atmospheric monitoring program, Atomic Energy Commision, Report AECU-4280.
2. Billing, C. E.: 1966, Effect of particle accumulation in aerosol filtration, PhD Dissertation, California Institute of Technology.
3. Bruschke, M. V. and Advani, S. G.: 1993, Flow of generalized Newtonian fluids across a periodic array of cylinders, J. Rheol. 37, 479-497.
4. Carter, E. J., Fell, A. W., Griffin, P. R. and Summerscales, J.: 1996, Data validation procedures for the automated determination of the two-dimensional permeability tensor of a fabric reinforcement, Composites: Part A 27, 255-261.
5. Drummond, J. E. and Tahir, M. I.: 1984, Laminar viscous flow through regular arrays of parallel solid cylinders, Int. J. Multiphase Flow 10, 515-539.
6. Gebart, B. R.: 1990, SICOMP Technical Report 90-006, August.
7. Gebart, B. R.: 1992, Permeability of unidirectional reinforcements for RTM, J. Composite Materials 26, 1100-1133.
8. Greenspan, D.: 1974, Discrete Numerical Methods for Engineers, Academic Press, New York.
9. Guj, G. and Guido, de M.: 1987, Fully developed flow in periodic multi-connected domains: numerical and experimental study, Meccanica 22, 185-192.
10. Gulowski, T. G., Cai, Z., Bauer, S., Boucher, D., Kingery, J. and Wineman, S.: 1987, Consolidation experiments for laminate composites, J. Composite Materials 21, 650-669.
11. Happel, J.: 1959, Viscous flow relative to arrays of cylinders, AIChE J. 5, 174-177.
12. Higdon, J. J. L. and Ford, G. D.: 1996, Permeability of three-dimensional models of fibrous porous media, J. Fluid Mech. 308, 341-361.
13. Holman, J. P. and Gajda, W. J. Jr.: 1978, Experimental Methods for Engineers, McGraw-Hill, New York.
14. Itoh, S.: 1984. The permeability of a random array of parallel infinite cylindrical rods. J. Phys. Soc. Japan 53, 1718-1727.
15. Jackson, G. W. and James, D. F.: 1986. The permeability of fibrous porous media. Can. J. Chem. Eng. 64, 364-374.
16. Kalita, W. and Kowalewski, T: 1976, Experimental determination of filtration coefficients along a fibrous bundle, IFR Report 28/1976, (in Polish).
17. Kirsch, A. A. and Fuchs, N. A.: 1967, The fluid flow in a system of parallel cylinders perpendicular to the flow direction at small Reynolds numbers, J. Phys. Soc. Japan 22, 527-532.
18. Kołodziej, J. A.: 1980. Filtration resistance of a system of parallel cylinders at longitudinal laminar flow, Archiwum Budowy Maszyn 27, 487-502, (in Polish).
19. Kołodziej, J. A.: 1986, Filtration resistance of a system of parallel cylinders at transverse creeping flow. J. Theo. Appl. Mech. 24, 537-549.
20. Kuwabara, S.: 1959, The force experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow al small Reynolds numbers, J. Phys. Soc. Japan 14, 527-532.
21. Luce, T. L., Advani, S. G., Howard, J. G. and Parnas, R. S.: 1995, Permeability Characterization. Part 2: Flow behaviour in multiple-layer performs. Polym. Compo. 16, 446-458.
22. Lundstrom, T. S. and Gebart, B. R.: 1995, Effect of perturbation of fibre architecture on permeability inside fibre tows, 1995, J. Composite Materials 29, 424-443.
23. Meegoda, N. J., King, I. P. and Arulanandan, K.: 1989. An expression for the permeability of anisotropic granular media, Int. J. Num. Anal. Meth. Geomech. 13, 575-598.
24. Mottaghian, R. and Wolf, L.: 1974, A two-dimensional analysis of laminar flow in rod bundles of arbitrary arrangement, Int. J. Heat Mass Transfer 17, 1121-1134.
25. Nagelhout, D., Bhat, M. S., Heinrich, J. C. and Poirier, D. R.: 1995, Permeability for flow normal to a sparse array of fibres, Materials Sci. Engng. A191, 203-208.
26. Neale, G.: 1977, Degrees of anisotropy for fluid flow and diffusion (electrical conduction) through anisotropic porous media, AIChE J. 23, 56-61.
27. Neale, G. and Anaka, H. and Hampel, D.: 1975, Transport phenomena in non-homogeneous porous media, Can. J. Chem. Eng. 53, 691-694.
28. Neuman, S. P: 1977. Theoretical derivation of Darcy's law, Acta Mech. 25, 153-165.
29. Parnas, R. S. and Salem, A. J.: 1993, A comparison of the unidirectional and radial in-plane flow of fluids through woven composite reinforcements, Polymer Composites 14, 383-394.
30. Parnas, R. S., Howard, J. G., Luce, T. L. and Advani, S. G.: 1995, Permeability characterization. Part 1: A proposed standard reference fabric for permeability, Polymer Composites 16, 429-445.
31. Phelan, F. R. Jr. and Geoff, W.: 1996, Analysis of transverse flow in aligned fibrous porous media, Report AECU-4280, Composites Part A 27, 25-34.
32. Pillai, K. M. and Advani, S. G.: 1995, Numerical and analytical study to estimate the effect of two length scales upon the permeability ofa fibrous porous medium, Transport in Porous Media 21, 1-17.
33. Poreh, M. and Elata, C.: 1966, An analytical derivation of Darcy's law, Israel J. Technol. 25, 214-230.
34. Sadiq, T. A. K., Advani, S. G. and Parnas, R. S.: 1995, Experimental investigation of transverse flow through aligned cylinders, Int. J. Multiphase Flow 21, 755-774.
35. Rahli, O., Tadrist, L. and Miscevic, M.: 1996, Experimental analysis of fibrous porous media permeability, AIChE J. 42, 3547-3549.
36. Sangani, A. S. and Guobiao, Mo.: 1994, Inclusion of lubrication forces in dynamic simulations, Phys. Fluids 6, 1653-1662.
37. Sangani, A. S. and Yao, C.: 1988, Transport processes in random arrays of cylinders. II. Viscous flow, Phys. Fluids 31, 2435-2444.
38. Sparrow, E. M. and Loeffler, A. M.: 1959, Longitudinal laminar flow between cylinders arranged in regular array, AIChE J. 5, 325-330.
39. Spielman, L. and Goren, S. L.: 1968, Model for predicting pressure drop and filtration efficiency in fibrous media, Environ. Sci. Technol. 2, 279-287.
40. Sullivan, R. R.: 1942, Specific surface measurements on compact bundles of parallel fibres, J. Appl. Phys. 13, 725-730.
41. Westhuizen, J. V. and Prieur Du Plessis, J.: 1994, Quantification of unidirectional fibre bed permeability, J. Composite Materials 28, 619-637.
42. Westhuizen, J. V. and Prieur Du Plessis, J.: 1996, An attempt to quantify fibre bed permeability utilizing the phase average Navier-Stokes equation, Composites: Pari A, 21, 263-269.
43. Woerdeman, D. L., Phelan, F. R., Jr. and Parnas, R. S.: 1995, Interpretation of 3-D permeability Measurements for RTM Modeling, Polymer Composites 16, 470-480.
44. Young, W.-B., Wu, S. F.: 1995, Permeability measurement of bidirectional woven glass fibres, J. Reinforced Plastics and Composites 21, 755-774.