Permeability calculations in three-dimensional isotropic and oriented fiber networks

Physics of Fluids

Volumn 20, Issue 12, 2008, Pages

  Stylianopoulos, Triantafyllos ^a   Yeckel, Andrew ^a   Derby, Jeffrey J ^a   Luo, Xiao Juan ^b   Shephard, Mark S ^b   Sander, Edward A ^a   Barocas, Victor H ^a  

^a University of Minnesota   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DRAG; DRAG COEFFICIENT; FINITE ELEMENT METHOD; PARALLEL FLOW; PERIODIC STRUCTURES; VOLUME FRACTION;

COMPUTATIONAL POWER; DIRECT CALCULATION; FIBER VOLUME FRACTIONS; HIGH PERFORMANCE COMPUTERS; HYDRAULIC PERMEABILITY; STRUCTURED NETWORKS; VOLUME AVERAGING METHOD; VOLUME AVERAGING THEORY;

FIBERS;

EID: 58249084802     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3021477     Document Type: Article

References (60)

1. J. Ghassemzadeh and M. Sahimi, "Pore network simulation of fluid imbibition into paper during coating: II. Characterization of paper's morphology and computation of its effective permeability tensor," Chem. Eng. Sci. CESCAC0009-250910.1016/j.ces.2004.01.057 59, 2265 (2004).
2. A. Koponen, D. Kandhai, E. Hellen, M. Alava, A. Hoekstra, M. Kataja, K. Niskanen, P. Sloot, and J. Timonen, "Permeability of three-dimensional random fiber webs," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.80.716 80, 716 (1998).
3. J. Hyvaluoma, P. Raiskinmaki, A. Jasberg, A. Koponen, M. Kataja, and J. Tomonen, "Simulation of liquid penetration in paper," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.73.036705 73, 036705 (2006).
4. E. Schweers and F. Loffler, "Realistic modeling of the behaviour of fibrous filters through consideration of filter structure," Powder Technol. POTEBX0032-591010.1016/0032-5910(94)02850-8 80, 191 (1994).
5. L. Skartsis, J. L. Kardos, and B. Khomami, "Resin flow through fiber beds during composite manufacturing processes. Part I: Review of Newtonian flow through fiber beds," Polym. Eng. Sci. PYESAZ0032-388810.1002/pen.760320402 32, 221 (1992).
6. J. R. Levick, "Review article: Flow through interstitium and other fibrous matrices," Q. J. Exp. Physiol. QJEPD30144-8757 72, 409 (1987).
7. S. Ramanujan, A. Pluen, T. D. McKee, E. B. Brown, Y. Boucher, and R. K. Jain, "Diffusion and convection in collagen gels: Implications for transport in the tumor interstitium," Biophys. J. BIOJAU0006-3495 83, 1650 (2002).
8. J. A. White and W. M. Deen, "Agarose-dextran gels as synthetic analogs of glomerular basement membrane: Water permeability," Biophys. J. BIOJAU0006-3495 82, 2081 (2002).
9. E. A. Sander, D. A. Shimko, K. C. Dee, and E. A. Nauman, "Examination of continuum and micro-structural properties of human vertebral cancellous bone using combined cellular solid models," Biomech. Model. Mechanobiol. BMMICD1617-7959 2, 97 (2003).
10. S. He, H. Cao, A. Antovic, and M. Blomback, "Modifications of flow measurement to determine fibrin gel permeability and the preliminary use in research and clinical materials," Blood Coagul Fibrinolysis ZZZZZZ0957-5235 16, 61 (2005).
11. S. Whitaker, "Flow in porous media I: A theoretical derivation of Darcy's law," Transp. Porous Media TPMEEI0169-391310.1007/ BF01036523 1, 3 (1986).
12. J. J. L. Higdon and G. D. Ford, "Permeability of three-dimensional models of fibrous porous media," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096001504 308, 341 (1996).
13. H. Hasimoto, "On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres," J. Fluid Mech. JFLSA70022-112010.1017/S0022112059000222 5, 317 (1959).
14. J. E. Drummond and M. I. Tahir, "Laminar viscous flow through regular arrays of parallel solid cylinders," Int. J. Multiphase FlowI JMFBP0301-932210.1016/0301-9322(84)90079-X 10, 515 (1984).
15. A. S. Sangani and A. Acrivos, "Slow flow past periodic arrays of cylinders with application to heat transfer," Int. J. Multiphase FlowI JMFBP0301-932210.1016/0301-9322(82)90029-5 8, 193 (1982).
16. E. M. Sparrow and J. R. Loeffler, "Longitudinal laminar flow between cylinders arranged in regular array," AIChE J. AICEAC0001-154110.1002/aic.690050315 5, 325 (1959).
17. S. Kuwabara, "The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers," J. Phys. Soc. Jpn. JUPSAU0031-901510.1143/ JPSJ.14.527 14, 527 (1959).
18. J. Happel, "Viscous flow relative to arrays of cylinders," AIChE J. AICEAC0001-154110.1002/aic.690050211 5, 174 (1959).
19. G. W. Jackson and D. F. James, "The permeability of fibrous porous media," Can. J. Chem. Eng. CJCEA70008-4034 64, 364 (1986).
20. A. S. Sangani and C. Yao, "Transport processes in random arrays of cylinders. II. Viscous flow," Phys. Fluids PFLDAS0031-917110.1063/ 1.866596 31, 2435 (1988).
21. A. S. Sangani and G. Mo, "Inclusion of lubrication forces in dynamic simulations," Phys. Fluids PHFLE61070-663110.1063/1.868228 6, 1653 (1994).
22. G. Bechtold and L. Ye, "Influence of fibre distribution of fibre distribution on the transverse flow permeability in fibre bundles," Compos. Sci. Technol. CSTCEH0266-353810.1016/S0266-3538(03)00112-X 63, 2069 (2003).
23. D. L. Koch and A. J. C. Ladd, "Moderate Reynolds number flows through periodic and random arrays of aligned cylinders," J. Fluid Mech. JFLSA70022-1120 349, 33 (1997).
24. J. R. Quispe, R. E. Rozas, and P. G. Toledo, "Permeability-porosity relationship from a geometrical model of shrinking and lattice Boltzmann and Monte Carlo simulations of flow in two-dimensional pore networks," Chem. Eng. J. CMEJAJ0300-946710.1016/j.cej.2005.02.003 111, 225 (2005).
25. G. Liu and K. E. Thompson, "A domain decomposition method for modeling Stokes flow in porous media," Int. J. Numer. Methods FluidsI JNFDW0271-209110.1002/fld.249 38, 1009 (2002).
26. K. E. Thompson, "Pore-scale modeling of fluid transport in disordered fibrous materials," AIChE J. AICEAC0001-154110.1002/ aic.690480703 48, 1369 (2002).
27. S. Amico and C. Lekakou, "Flow through a two-scale porosity, oriented fibre porous medium," Transp. Porous Media TPMEEI0169-391310.1023/A:1025799404038 54, 35 (2004).
28. R. Ethier, "Flow through mixed fibrous porous materials," AIChE J. AICEAC0001-154110.1002/aic.690370812 37, 1227 (1991).
29. Y. Huang, D. Rumschitzki, S. Chien, and S. Weinbaum, "A fiber matrix model for the growth of macromolecular leakage spots in the arterial intima," J. Biomech. Eng. JBENDY0148-073110.1115/1.2895794 116, 430 (1994).
30. R. Y. Tsay and S. Weinbaum, "Viscous flow in a channel with periodic cross-bringing fibres: Exact solutions and Brinkman approximation," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112091002318 226, 125 (1991).
31. M. Palassini and A. Remuzzi, "Numerical analysis of viscous flow through fibrous media: A model for glomerular basement membrane permeability," Am. J. Physiol. AJPHAP0002-9513 274, F223 (1998).
32. N. D. Ngo and K. K. Tamma, "Microscale permeability predictions of porous fibrous media," Int. J. Heat Mass TransferI JHMAK0017-931010.1016/S0017-9310(00)00335-5 44, 3135 (2001).
33. N. D. Ngo and K. K. Tamma, "Complex three-dimensional microstructural permeability prediction of porous fibrous media with and without compaction," Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/nme.1020 60, 1741 (2004).
34. B. Markicevic and N. Djilali, "Two-scale modeling in porous media: Relative permeability predictions," Phys. Fluids PHFLE61070-663110.1063/1.2174877 18, 033101 (2006).
35. W. H. Zhong, I. G. Currie, and D. F. James, "Creeping flow through a model fibrous porous medium," Exp. Fluids EXFLDU0723-486410.1007/ s00348-005-0053-1 40, 119 (2006).
36. D. S. Clague and R. J. Phillips, "A numerical calculation of the hydraulic permeability of three-dimensional disordered fibrous media," Phys. Fluids PHFLE61070-663110.1063/1.869278 9, 1562 (1997).
37. D. S. Clague, B. D. Kandhai, R. Zhang, and P. M. Sloot, "Hydraulic permeability of (un)bounded fibrous media using the lattice Boltzmann method," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.61.616 61, 616 (2000).
38. J. Wang, X. Zhang, A. G. Bengough, and J. W. Crawford, "Domain-decomposition method for parallel lattice Boltzmann simulation of incompressible flow in porous media," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.72.016706 72, 016706 (2005).
39. A. L. Chernyakov, "Fluid flow through three-dimensional fibrous porous media," J. Exp. Theor. Phys. JTPHES1063-776110.1134/1.558586 86, 1156 (1998).
40. S. Jaganathan, H. Vahedi Tafreshi, and B. Pourdeyhimi, "A realistic approach for modeling permeability of fibrous media: 3-D imaging coupled with CFD simulation," Chem. Eng. Sci. CESCAC0009-250910.1016/ j.ces.2007.09.020 63, 244 (2008).
41. A. Pluen, P. A. Netti, R. K. Jain, and D. A. Berk, "Diffusion of macromolecules in agarose gels: Comparison of linear and globular configurations," Biophys. J. BIOJAU0006-3495 77, 542 (1999).
42. R. G. Cox, "The motion of long slender bodies in a viscous fluid. Part 1. General theory," J. Fluid Mech. JFLSA70022-112010.1017/ S002211207000215X 44, 791 (1970).
43. T. Stylianopoulos and V. H. Barocas, "Volume-averaging theory for the study of the mechanics of collagen networks," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/j.cma.2006.06.019 196, 2981 (2007).
44. T. Stylianopoulos and V. H. Barocas, "Multiscale, structure-based modeling for the elastic mechanical behavior of arterial walls," J. Biomech. Eng. JBENDY0148-073110.1115/1.2746387 129, 611 (2007).
45. F. H. Bertrand, M. R. Gadbois, and P. A. Tanguy, "Tetrahedral elements for fluid flow," Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/nme.1620330610 33, 1251 (1992).
46. M. Crouzeix and P. A. Raviart, "Conforming and non-conforming finite element methods for solving the stationary Stokes equation," RAIRO: Anal. Numer. RFANDS0399-0516 7, 33 (1973).
47. P. Keast, "Moderate-degree tetrahedral quadrature formulas," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/ 0045-7825(86)90059-9 55, 339 (1986).
48. A. G. Salinger, Q. Xiao, Y. Zhou, and J. J. Derby, "Massively parallel finite element computations of three-dimensional, time-dependent, incompressible flows in materials processing systems," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/ 0045-7825(94)00081-6 119, 139 (1994).
49. A. Yeckel and J. J. Derby, "Parallel computation of incompressible flows in materials processing: Numerical experiments in diagonal preconditioning," J. Cryst. Growth JCRGAE0022-0248 23, 1379 (1997).
50. H. Zhou and J. J. Derby, "An assessment of a parallel, finite element method for three-dimensional, moving-boundary flows driven by capillarity for simulation of viscous sintering," Int. J. Numer. Methods FluidsI JNFDW0271-209110.1002/fld.159 36, 841 (2001).
51. V. H. Barocas and R. T. Tranquillo, "An anisotropic biphasic theory of tissue-equivalent mechanics: The interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance," J. Biomech. Eng. JBENDY0148-073110.1115/1.2796072 119, 137 (1997).
52. See EPAPS Document No. E-PHFLE6-20-017811 for supplementary tables. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
53. K. J. Mattern and W. M. Deen, "'Mixing rules' for estimating the hydraulic permeability of fiber mixtures," AIChE J. AICEAC0001-154110.1002/aic.11350 54, 32 (2008).
54. P. L. Chandran, T. Stylianopoulos, and V. H. Barocas, "Microstructure based, multiscale modeling for the mechanical behavior of hydrated fiber networks," Multiscale Model. Simul. MMSUBT1540-345910.1137/070689504 7, 22 (2008).
55. W. Y. Gu, H. Yao, C. Y. Huang, and H. S. Cheung, "New insight into deformation-dependent hydraulic permeability of gels and cartilage, and dynamic behavior of agarose gels in confined compression," J. Biomech. JBMCB50021-929010.1016/S0021-9290(02)00437-2 36, 593 (2003).
56. M. H. Holmes and V. C. Mow, "The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration," J. Biomech. JBMCB50021-929010.1016/0021-9290(90)90007-P 23, 1145 (1990).
57. Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, 1993).
58. E. D. Grassl, T. R. Oegema, and R. T. Tranquillo, "A fibrin-based arterial media equivalent," J. Biomed. Mater. Res. JBMRBG0021-9304 66, 550 (2003).
59. T. Stylianopoulos, C. A. Bashur, A. S. Goldstein, S. A. Guelcher, and V. H. Barocas, "Computational predictions of the tensile properties of electrospun fibre meshes: Effect of fibre diameter and fibre orientation," J. Mech. Behav. Biomed. Mater.ZZZZZZ1751-6161 1, 326 (2008).
60. E. A. Sander, T. Stylianopoulos, R. T. Tranquillo, and V. H. Barocas, "Image-based biomechanics of collagen-based tissue equivalents: Multiscale models compared to fiber alignment predicted by polarimetric imaging," IEEE Eng. Med. Biol. Mag. IEMBDE0739-5175 (to be published).