Flow of Stokesian fluid through a cellular medium and thermal effects

• Autorzy: Wojnar R.

Identyfikatory

DOI

10.2478/bpasts-2014-0031

• Języki publikacji: EN

Abstrakty

EN

The thermal effects of a stationary Stokesian flow through an elastic micro-porous medium are compared with the entropy produced by Darcy’s flow. A micro-cellular elastic medium is considered as an approximation of the elastic porous medium. It is shown that after asymptotic two-scale analysis these two approaches, one analytical, starting from Stoke’s equation and the second phenomenological, starting from Darcy’s law give the same result. The incompressible and linearly compressible fluids are considered, and it is shown that in micro-porous systems the seepage of both types of fluids is described by the same equations.

Słowa kluczowe

EN

porous media; Onsager’s principle; entropy; heat production

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2014
• Tom: Vol. 62, nr 2
• Strony: 321--329
• Opis fizyczny: Bibliogr. 35 poz., rys.

Twórcy

autor

Wojnar R.

• Institute of Fundamental Technological Research of the Polish Academy of Sciences, 5B Pawinskiego St., 02-106 Warsaw, Poland

Bibliografia

• [1] K. Terzahgi, Theoretical Soil Mechanics, Wiley, New York, 1943.
• [2] M.A. Biot, “Theory of elasticity and consolidation for a porous anisotropic solid”, J. Applied Physics 26 (2), 182–185 (1955).
• [3] A.E. Scheidegger, The Physics of Flow Through Porous Media, 3rd ed., University of Toronto Press, Toronto, 1974.
• [4] G.I. Barenblatt, V.M. Entov, and V.M. Ryzhik, Theory of Fluid Flows Through Natural Rocks, Kluwer Academic, London, 1990.
• [5] M. Cieszko and J. Kubik, “Derivation of matching conditions at the contact surface between fluid-saturated porous solid and bulk fluid”, Transport in Porous Media 34 (1–3), 319–336 (1999).
• [6] J. Kubik, M. Kaczmarek, and I. Murdoch, Modelling Coupled Phenomena in Saturated Porous Materials: Advanced Course, Lecture notes 20, AMAS Centre of Excellence for Advanced Materials and Structures, Warsaw, 2004.
• [7] R. Drelich, M. Pakula, and M. Kaczmarek, “Identification of drag parameters of flow in high permeability materials by U-tube method”, Transport in Porous Media 101 (1), 69–79 (2014).
• [8] G. Szefer and M. Mikołajek, “Consolidation of a porous multilayered subsoil undergoing large deformation”, J. Theoretical and Applied Mechanics 36 (3), 759–773 (1998).
• [9] G. Hetsroni, “Boiling in micro-channels”, Bull. Pol. Ac.: Tech. 58 (1), 155–163 (2010).
• [10] J. Ignaczak, “Tensorial equations of motion for a fluid saturated porous elastic solid”, Bull. Pol. Ac.: Tech. 26 (8–9) 371 [705]–375 [709] (1978).
• [11] W. Derski, “Equations of thermoconsolidation in case of temperature difference between components of medium”, Bull. Pol. Ac.: Tech. 26 (12), 529 [1035]–540 [1046] (1978).
• [12] A. Szekeres, “Cross-coupled heat and moisture transport: Part 1 – Theory”, J. Thermal Stresses 35 (1–3), 248–268 (2012).
• [13] L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford 1959.
• [14] Lars Onsager, “Reciprocal relations in irreversible processes”, Physical Review 37 (4), 405–426 (1931).
• [15] E. Sanchez-Palencia, Non-homogeneous Media and Vibration Theory, Springer, Berlin, 1980.
• [16] G. Allaire, “Homogenization of the Stokes flow in connected porous medium”, Asymptotic Analysis 2 (3), 203–222 (1989).
• [17] Kenneth Walters, “Relation between Coleman-Noll, Rivlin-Ericksen, Green-Rivlin and Oldroyd fluids”, Zeitschrift fur Angewandte Mathematik und Physik ZAMP 21 (4), 592–600 (1970).
• [18] H. Attouch, Variational Convergence for Functions and Operators, Pitman, Boston, 1984.
• [19] J.-L. Auriault and E. Sanchez-Palencia, “´Etude du comportement macroscopique d’un milieu poreux satur´e deformable”, J. M´ecanique 16 (4), 575–603 (1977).
• [20] J.-L. Auriault, “Dynamic behaviour of a porous medium saturated by a Newtonian fluid”, Int. J. Engineering Science 18 (6), 775–785 (1980).
• [21] W. Bielski, J.J. Telega, and R. Wojnar, “Nonstationary flow of a viscous fluid through a porous elastic medium: asymptotic analysis and two-scale convergence”, Mechanics Research Communications 26 (5), 619–628 (1999).
• [22] W. Bielski, J.J. Telega, and R. Wojnar, “Nonstationary twophase flow through porous medium, Archives of Mechanics 53 (4–5), 333–366 (2001).
• [23] J.J. Telega and R. Wojnar, “Flow of electrolyte through porous piezoelectric medium: macroscopic equations”, Comptes Rendus de l’Acad´emie des Sciences, Series Mechanics IIB 328 (3), 225–230 (2000).
• [24] J.J. Telega and R. Wojnar, “Electrokinetics in random piezoelectric porous media”, Bull. Pol. Ac.: Tech. 55 (1), 125–128 (2007).
• [25] P.A. Domenico and M.D. Mifflin, “Water from low permeability sediments and land subsidence”, Water Resources Research 1 (4), 563–576 (1965).
• [26] Rana A. Fine and F.J. Millero, “Compressibility of water as a function of temperature and pressure”, J. Chemical Physics 59 (10), 5529–5536 (1973).
• [27] B. Moore, T. Jaglinski, D.S. Stone, and R.S. Lakes, “Negative incremental bulk modulus in foams”, Philosophical Magazine Letters 86 (10), 651–659 (2006).
• [28] Rod Lakes and K.W. Wojciechowski, “Negative compressibility, negative Poisson’s ratio, and stability”, Physica Status Solidi (b) 245 (3), 545–551 (2008).
• [29] J. Koplik, H. Levine, and A. Zee, “Viscosity renormalization in the Brinkman equation”, Physics of Fluids 26 (10), 2864–2870 (1983).
• [30] O. Penrose and P.C. Fife, “Nonlinear Phenomena”, Physica D 43 (1), 44–62 (1990).
• [31] S. Claesson, Nobel Prize in Chemistry 1968 Presentation Speech: Lars Onsager, http://www.nobelprize.org/nobelprizes/chemistry/laureates/1968/press.html (1968).
• [32] A.C. Eringen, Microcontinuum Field Theories, Fluent Media, vol. 2, Springer-Verlag, New York, 2001.
• [33] T.K.V. Iyengar and T.S.L. Radhika, “Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell”, Bull. Pol. Ac: Tech. 59 (1), 63–74 (2011).
• [34] R. Zwanzig and R.D. Mountain, “High-frequency elastic moduli of simple fluids”, J. Chemical Physics 43 (12), 4464–4471 (1965).
• [35] W. Bielski and R. Wojnar, “Homogenisation of flow through double scale porous medium”, in: Analytic Methods of Analysis and Differential Equations, pp. 27–44, eds. A.A. Kilbas and S.V. Rogosin, Cambridge Scientific Publishers, Cambridge, 2008.