Abstract
A new macroscopic model for swelling porous media is derived based on a rigorous upscaling of the microstructure. Considering that at the microscale the medium is composed of a charged solid phase (e.g. clay platelets, bio-macromolecules, colloidal or polymeric particles) saturated by a binary monovalent aqueous electrolyte solution composed of cations ‘+’ and anions ‘−’ of an entirely dissociated salt, the homogenization procedure is applied to scale up the pore-scale model. The microscopic system of governing equations consists of the local electro-hydrodynamics governing the movement of the electrolyte solution (Poisson–Boltzmann coupled with a modified Stokes problem including an additional body force of Coulombic interaction) together with modified convection–diffusion equations governing cations and anions transport. This system is coupled with the elasticity problem which describes the deformation of the solid phase. Novel forms of Terzaghi's effective principle and Darcy's law are derived including the effects of swelling pressure and osmotically induced flows, respectively. Micromechanical representations are provided for the macroscopic physico-chemical quantities.
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References
Anandarajah, A.: 1997, Influence of particle orientation on one-dimensional compression of montmorillonite, J. Colloid Interface Sci. 194, 44–52.
Auriault, J. L.: 1991, Heterogeneous media: is an equivalent homogeneous description always possible? Int. J. Engng Sci. 29, 785–795.
Auriault, J. L. and Adler, P. M.: 1995, Taylor dispersion in porous media: analysis by multiple scale expansions, Adv. Water Resour. 18(4), 217–226.
Auriault, J. L. and Sanchez-Palencia, E.: 1977, Etude du comportement macroscopique d'un milieu poreux saturé déformable, J. de Mécanique 16(4), 575–603.
Bennethum, L. S., Murad, M. A. and Cushman, J. H.: 2000, Macroscale thermodynamics and the chemical potential for swelling porous media, Transport in Porous Media 39, 187–225.
Bike, S. G. and Prieve, C.: 1992, Electrohydrodynamics of thin double layers: a model for the streaming potential profile, J. Colloid Interface Sci. 154(1), 87–96.
Callen, H.: 1985, Thermodynamics and an Introduction to Thermostatics, Wiley, New York.
Dahnert, K. and Huster, D.: 1999, Comparison of the Poisson-Boltzmann model and the Donnan equilibrium of a polyelectrolyte in salt solution, J. Colloid Interface Sci. 215, 131–139.
Derjaguin, B. V., Churaev, N. V. and Muller, V. M.: 1987, Surface Forces, Plenum Press, New York.
Donnan, F. G.: 1924, The theory of membrane equilibria, Chem. Rev. 1, 73–90.
Dormieux, L., Barboux, P., Coussy, O. and Dangla, P.: 1995, A macroscopic model of the swelling phenomenon of a saturated clay, Euro. J. Mech. /Solids 14(6), 981–1004.
Eringen, A. C. and Maugin, G. A.: 1989, Electrodynamics of Continua, Springer-Verlag.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1998, A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors, J. Biomech. Engng 120, 169–180.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1999, Transport of multi-electrolytes in charged hydrated biological soft tissues, Transport in Porous Media 34, 143–157.
Helfferich, F.: 1962, Ion Exchange, McGraw-Hill, USA.
Hunter, R. J.: 1994, Introduction to Modern Colloid Science, Oxford University Press.
Huyghe, J. M. and Janssen, J. D.: 1997, Quadriphasic mechanics of swelling incompressible porous media, Int. J. Engng Sci. 25(8), 793–802.
Israelachvili, J.: 1991, Intermolecular and Surfaces Forces, Academic Press, New York.
Ivanov, I. B. and Kralchevsky, P. A.: 1988, Mechanics and thermodynamics of curved thin films, In: I. B. Ivanov (ed.), Surfactant Science Series, Vol. 29, Dekker, pp. 49–129.
Kralchevsky, P. A. and Ivanov, I. B.: 1990, Micromechanical description of curved interfaces: II film surface tensions, disjoining pressure and interfacial stress balances, J. Colloid Interface Sci. 137(1), 235–252.
Lai, W. M., Hou, J. S. and Mow, V. C.: 1991, A triphasic theory for the swelling and deformation behaviors of articular cartilage, J. Biomech. Engng 113, 245–258.
Landau, L. D. and Lifshitz, E. M.: 1960, Electrodynamics of Continuous Media, Pergamon Press, Oxford.
Low, P. F.: 1987, Structural component of the swelling pressure of clays, Langmuir 3, 18–25.
Murad, M. A.: 1999, A thermomechanical model of hydration swelling in smectite clays, I. two-scale mixture-theory approach, Int. J. Numer. Analyt. Meth. Geomech. 23(7), 673–696.
Olphen, V.: 1977, An Introduction to Clay Colloid Chemistry: For Clay Technologists, Geologists, and Soil Scientists, Wiley, New York.
Rusanov, A.: 1978, On the thermodynamics of deformable solid surfaces, J. Colloid Interface Sci. 63(2), 330–345.
Samson, E., Marchand, J., Robert, J. and Bournazel, J.: 1999, Modeling ion diffusion mechanisms in porous media, Int. J. Numer. Meth. Engng 46, 2043–2060.
Sanchez-Palencia, E.: 1980, Non-Homogeneous Media and Vibration Theory, Lectures Notes in Physics, Springer Verlag.
Sasidhar, V. and Ruckestein, E.: 1981, Electrolyte osmosis through capillaries, J. Colloid Interface Sci. 82(2), 439–457.
Sasidhar, V. and Ruckestein, E.: 1982, Anomalous effects during electrolyte osmosis across charged porous membranes, J. Colloid Interface Sci. 85(2), 332–361.
Sridharan, A. and Rao, G. V.: 1973, Mechanisms controlling volume change of saturated clays and the role of the effective stress concept, Geotechnique 23(3), 359–382.
Terada, K., Ito, T. and N. Kikuchi, N.: 1998, Characterization of the mechanical behaviors of solid- fluid mixture by the homogenization method, Comput. Meth. Appl. Mech. Engng 153, 223–257.
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Moyne, C., Murad, M. Macroscopic Behavior of Swelling Porous Media Derived from Micromechanical Analysis. Transport in Porous Media 50, 127–151 (2003). https://doi.org/10.1023/A:1020665915480
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DOI: https://doi.org/10.1023/A:1020665915480