Abstract
The effect of fiber tortuosity on fluid permeability in fibrous beds has been investigated. A particle model is employed in which a fiber is replaced by spherical particles and fiber tortuosity is represented by a bending angle. Assuming a low Reynolds number, the fluid permeability is calculated based on the Stokesian dynamics approach. The results show that the permeability of a tortuous fibrous bed is lower than that of a straight fibrous bed. To examine the permeability dependence on the fiber tortuosity in detail, the pore distribution and pore connectivity are evaluated quantitatively by defining the pore radius. It is found that the tortuous fibers prevent the formation of large pores and their connection in the flow direction, thereby decreasing the permeability.
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References
Al-Kharusi AS, Blunt MJ (2007) Network extraction from sandstone and carbonate pore space images. J Pet Sci Eng 56:219–231
Batchelor GK (2000) An introduction to fluid dynamics. Cambridge Mathematical Library, Cambridge
Beenakker CWJ (1986) Ewald sum of the Rotne–Prager tensor. J Chem Phys 85(3):1581–1582
Brady JF, Bossis G (1988) Stokesian dynamics. Ann Rev Fluid Mech 20:111–157
Brady JF, Phillips RJ, Lester JC, Bossis G (1988) Dynamic simulation of hydrodynamically interacting suspensions. J Fluid Mech 195:257–280
Brinkman HC (1947) On the permeability of media consisting of closely packed porous particles. Appl Sci Res A1:81–86
Bryant SL, King PR, Mellor DW (1993) Network model evaluation of permeability and spatial correlation in a real random sphere packing. Transp Porous Med 11:53–70
Carman PC (1937) Fluid flow through granular beds. Trans Inst Chem Eng 15:150–166
Clague DS, Phillips RJ (1997) A numerical calculation of the hydraulic permeability of three-dimensional disordered fibrous media. Phys Fluids 9(6):1562–1572
Davies CN (1952) The separation of airborne dust and particles. Proc. Inst Mech Eng Lond B1:185–213
Dong H, Blunt MJ (2009) Pore-network extraction from micro-computerized-tomography images. Phys Rev E 80:036307
Drummond JE, Tahir MI (1984) Laminar viscous flow through regular arrays of parallel solid cylinders. Int J Multiphase Flow 10(5):515–540
Durlofsky L, Brady JF, Bossis G (1987) Dynamic simulation of hydrodynamically interacting particles. J Fluid Mech 180:21–49
Gostick JT, Ioannidis MA, Fowler MW, Pritzker MD (2007) Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells. J Power Sour 173:277–290
Jackson GW, James DF (1986) The permeability of fibrous porous media. Can J Chem Eng 64:364–374
Jeffrey DJ, Onishi Y (1984) Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J Fluid Mech 139:261–290
Kim S, Karrila SJ (1991) Microhydrodynamics. Butterworth-Heinemann, Boston
Kirsch AA, Fuchs NA (1967) Studies on fibrous aerosol filters –II. Pressure drops in systems of parallel cylinders. Ann Occup Hyg 10:23–30
Nabovati A, Llewellin EW, Sousa ACM (2009) A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method. Compos A 40:860–869
Novák V, Štěpánek F, Kočí P, Marek M, Kubíček M (2010) Evaluation of local pore sizes and transport properties in porous catalysts. Chem Eng Sci 65(7):2352–2360
Odgaard A, Gundersen HJG (1993) Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone 14:173–182
Otomo R, Harada S (2011) End effect on permeability of particulate bed having different internal structures. Particul Sci Technol 29:2–13
Rotne J, Prager S (1969) Variational treatment of hydrodynamic interaction in polymers. J Chem Phys 50(11):4831–4837
Sangani AS, Acrivos A (1982) Slow flow past periodic arrays of cylinders with application to heat transfer. Int J Multiphase Flow 8(3):193–206
Shabro V, Torres-Verdín C, Javadpour F, Sepehrnoori K (2012) Finite-difference approximation for fluid-flow simulation and calculation of permeability in porous media. Transp Porous Med 94:775–793
Tahir MA, Tafreshi HV (2009) Influence of fiber orientation on the transverse permeability of fibrous media. Phys Fluid 21:083604
Tamayol A, Bahrami M (2009) Analytical determination of viscous permeability of fibrous porous media. Int J Heat Mass Transf 52:2407–2414
Tomadakis MM, Robertson TJ (2005) Viscous permeability of random fiber structures: comparison of electrical and diffusional estimates with experimental and analytical results. J Compos Mater 39(2):163–188
Vogel HJ (1997) Morphological determination of pore connectivity as a function of pore size using serial sections. Eur J Soil Sci 48:365–377
Vogel HJ, Roth K (2001) Quantitative morphology and network representation of soil pore structure. Adv Water Resour 24:233–242
White ML (1960) The permeability of an acrylamide polymer gel. J Phys Chem 64:1563–1565
Yazdchi K, Srivastava S, Luding S (2011) Microstructural effects on the permeability of periodic fibrous porous media. Int J Multiph Flow 37:956–966
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This study was partially supported by JSPS KAKENHI (Grant 17K14592).
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Otomo, R., Mori, K. Analysis of fluid permeability in tortuous fibrous bed based on pore radius distribution. J Vis 23, 71–80 (2020). https://doi.org/10.1007/s12650-019-00613-1
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DOI: https://doi.org/10.1007/s12650-019-00613-1