Abstract
The current variety of filtration theories suggests that the porous medium and the fluid filling it form some continuous medium. That is, the elements of the porous medium-fluid system, though considered physically infinitesimal, however, are large enough compared to the size of pores and particles (grains, fibers) forming a porous medium. Averaged characteristics of the porous medium, which are introduced for mathematical description, may be sufficiently substantiated only for the volume with a large number of enclosed pores and particles. In terms of the elementary theory of filtration, the meaning of the solid skeleton of the porous medium is, above all, geometric—the skeleton limits the region of space in which the fluid moves. In more complex cases, we have seen strong interaction between the skeleton and the adjacent layers of the fluid. Therefore, the properties of the porous medium in the theory of filtration are usually described by a set of geometric averages. In this chapter, several cell models are considered for calculation of hydrodynamic permeability of porous media. It is assumed that porous media in general may consist of partially porous spherical or cylindrical particles. Different limiting cases are investigated and theoretical results are compared with experimental data.
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Happel J, Brenner H (1965) Low Reynolds number hydrodynamics with special applications to particulate media. Prentice-Hall, Englewood Cliffs (reprinted by Wolters-Nordhoff, 1973); paperback edition, (Martinus Nijhoff; Kluwer Academic Publishers, 1983)
Barenblatt GI, Entov VM, Ryzhik VM (1990) Theory of fluid flows through natural rocks. Kluwer Academic Publishers, Dordrecht
Whitaker S (1986) Transp Porous Med 1:3
Auriault J-L (2009) Transp Porous Med 79:215
Brinkman HC (1947) Appl Sci Res A1:27
Starov VM, Zhdanov VG (2008) Adv Colloid Interface Sci 137:2
McHale G, Newton MI, Shirtcliffe NJ (2010) Soft Matter 6:714
Qin Yu, Kaloni PN, Angew Z (1993) Math Mech 73:77
Greenkorn RA (1983) Flow phenomena in porous media: fundamentals and applications in petroleum, water, and food production. Marcel Dekker, New York
Zholkovskij EK, Masliyah JH, Shilov VN, Bhattacharjee S (2007) Adv Colloid Interface Sci 134–135:279
Kotov AA, Solomentsev YuE, Starov VM (1991) Prog Colloid Polym Sci 84:293
Kotov AA, Solomentsev YuE, Starov VM (1991) Colloid J 53(6):867
Kotov AA, Solomentsev YuE, Starov VM (1992) Int J Multiph Flow 18(5):739
Churaev N, Sergeeva I, Derjaguin B (1981) J Colloid Interface Sci 84:451
Churaev NV, Kotov AA, Solomentsev YuE, Starov VM (1991) Prog Colloid Polym Sci 84:290
Solomentsev YuE, Starov VM (1993) Colloid J 54(4):591
Starov VM, Solomentsev YuE (1993) J Colloid Interface Sci 158:159
Starov VM, Solomentsev YuE (1993) J Colloid Interface Sci 158:166
Varoqui R, Dejardin P (1977) J Chem Phys 66:4395
Hiller J, Hoffman H (1953) J Comp Physiol 42:203
Parsons D, Subjeck J (1972) Biochem Biophys Acta 55:440
Masliyah J, Neale G, Malysa K, van de Ven T (1987) Chem Eng Sci 42:245
Garvey M, Tadros Th, Vincent B (1975) J Colloid Interface Sci 55:440
Pefferkorn E, Dejardin P, Varoqui R (1975) J Colloid Interface Sci 63:353
Idol WK, Anderson JL (1986) J Membr Sci 28(3):269
Anderson JL, Kim J (1987) J Chem Phys 86:5163
Perepelkin PV, Starov VM, Filippov AN (1992) Colloid J 54(2):139
Vasin SI, Starov VM, Filippov AN (1996) Colloid J 58(3):291
Vasin SI, Filippov AN (2004) Colloid J 66(3):261
Vasin SI, Starov VM, Filippov AN (1996) Colloid J 58(3):282
Filippov AN, Vasin SI, Starov VM (2006) Colloids Surf A: Physicochem Eng Aspects 282–283:272
Vasin SI, Filippov AN, Starov VM (2008) Adv Colloid Interface Sci 139:83
Koplic J, Levine H, Zee A (1983) Phys Fluids 26(10):2864
Kuwabara S, Rhys J (1959) Soc Jpn 14:527
Kvashnin AG (1979) Izv Akad Nauk SSSR (Proceedings of the Academy of Sciences of the USSR), Mekh Zhidk Gaza (Mechanics of Liquid and Gas) 4, 154 (in Russian)
Mehta G, Morse T (1975) J Chem Phys 63(5):1877
Cunningham E (1910) Proc R Soc (London) A83:357
Vasin SI, Filippov AN (2009) Colloid J 71(1):31
Vasin SI, Filippov AN (2009) Colloid J 71(2):141
de Groot S, Mazur P (1962) Non-equilibrium thermodynamics. North-Holland, Amsterdam
Kirsh VA (2006) Colloid J 68(2):173
Sergeeva IP, Semenov DA, Sobolev VD, Churaev NV (2008) Colloid J 70(5):616
Churaev NV, Sobolev VD, Somov AN (1984) J Colloid Interface Sci 97:574
Filippov AN, Khanukaeva DYu, Vasin SI, Sobolev VD, Starov VM (2013) Colloid J 75(2):214
Kiseleva OA, Sobolev VD, Semenov DA, Ershov AP, Sergeeva IP, Churaev NV (2009) Colloid J 71(1):76
Yadav PK, Tiwari A, Deo S, Filippov A, Vasin S (2010) Acta Mech 215:193
Deo S, Filippov A, Tiwari A, Vasin S, Starov V (2011) Adv Colloid Interface Sci 164:21
Ivanov VI (2011) Vestnik Nizhegorodskogo universiteta imeni N.I.Lobachevskogo. Mehanika zhidkosti i gaza (Vestnik of Lobachevsky State University of Nizhny Novgorod, Mechanics of Liquid and Gas) 4(2), 438 (in Russian)
Brock TD (1983) Membrane filtration: a user’s guide and reference manual. Science Tech, Madison
Kemmer FN (ed) (1987) The NALCO water handbook, 2nd edn. McGraw-Hill, New York
Cohen RD, Probstein RF (1986) J Colloid Interface Sci 114:194
Schulz G, Ripperger S (1989) J Membrane Sci 40:173
Suki A, Fane AG, Fell CJD (1986) J Membrane Sci 27:181
Howell JA, Velicangil O, Lee MS, Herrera-Zeppelin AL (1981) Ann NY Acad Sci 369:355
Yasminov AA, Grekov AV, Gaidukova IP et al (1988) Vysokochist. Veshchestva (High-Purity Substances) 1, 110 (in Russian)
Persson KM, Nilsson JL (1991) Desalination 80(2–3):123
Hubble J (1989) Fouling and cleaning in food processing.In: Kessler HG, Lund DB (eds) Third international conference on fouling and cleaning in food processing, Prien, Bavaria, June 1989. p 239
Aimar P, Meireles M, Sanchez V (1990) J Membrane Sci 54(3):321
Meireles M, Aimar P, Sanchez V (1991) J Membrane Sci 56(1):13
Fan LT, Nassan R, Hwang SH, Chou ST (1985) AIChE J 1781
Fan LT, Hwang SH, Chou ST, Nassan R (1985) Chem Eng Commun 35:101
Polotskii AE, Cherkasov AN (1983) Colloid J 43:467
Cherkasov AN (1985) Colloid J 47:363
Cherkasov AN, Vlasova OL, Tsareva SV et al (1990) Colloid J 52:323
Kutepov AM, Sokolov MV (1986) Teor Osn Khim Tekhnol (Theoretical Foundations of Chemical Engineering) 19:123
Filippov AN, Starov VM, Gleizer SV, Yasminov AA (1990) Khim Tekhnol Vody (Water Chemistry and Technology) 12:483 (in Russian)
Torkunov AM, Filippov AN, Starov VM (1992) Colloid J 54:126
Filippov AN, Starov VM, Lloyd DR et al (1994) J Membr Sci 89:199
Starov V, Lloyd D, Filippov A, Glaser S (2001) Sep Purif Technol 26:51
Filippov AN, Iksanov RKh (2012) Petrol Chem 52(7):520
Brenner H (1961) Chem Eng Sci 16:242
Goldmann AJ, Cox RG, Brenner H (1967) Chem Eng Sci 22:637
Goldmann AJ, Cox RG, Brenner H (1967) Chem Eng Sci 22:653
Liu MK, Williams FA (1970) Int J Heat Mass Transfer 13:1441
Trettin DR, Doshi MK (1980) Ind Eng Chem Fundam 19:189
Blatt WF, Dravid A, Michaels AS, Nelsen L(1970) Membrane science and technology. In: Flinn JE (ed). Plenum, New York, p 47
Opong WS, Zydney AI (1991) AIChE J 37:1497
Starov VM, Churaev NV (1993) Adv Colloid Interface Sci 43:145
Kolmogorov AN (1941) Dokl Akad Nauk SSSR 31:99
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The support of Russian Science Foundation (RSF) is acknowledged (grant No 14-19-01045).
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Filippov, A.N. (2014). Mathematical Modeling of Filtration Processes in Porous Media. In: Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology. Engineering Materials and Processes. Springer, London. https://doi.org/10.1007/978-1-4471-6377-0_13
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DOI: https://doi.org/10.1007/978-1-4471-6377-0_13
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