Abstract
In this work we develop the volume averaged form of the frequency-dependent governing equations for electrohydrodynamics in a saturated porous medium. The concept of local electrical equilibrium is identified, and when this condition is valid we obtain a one-equation model describing the coupled transport of momentum and electric charge. When local electrical equilibrium is not valid, separate forms of Maxwell's equations must be developed for both the fluid and solid phases.
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Allan, R. S. and Mason, S. G.: 1962, Particle behavior in shear and electric fields I: Deformation and burst of fluid drops, Proc. Roy. Soc. A267, 45-61.
Auriault, J. L. and Strzelecki, T.: 1981, On the electro-osmotic flow in a saturated porous media, Int. J. Engng Sci. 19, 915-928.
Anderson, T. B. and Jackson, R.: 1967, A fluid mechanical description of fluidized beds, Ind. Engng Chem. Fundam. 6, 527-538.
Azizi, S., Moyne, C. and Degiovanni, A.: 1988, Approche exp érimentale et théorique de la conductivité thermique des milieux poreux humides I: Expérimentation, Int. J. Heat Mass Trans. 31, 2305-2317.
Barrère, J., Gipouloux, O. and Whitaker, S.: 1992, On the closure problem for Darcy's law, Transport in Porous Media 7, 209.
Bensoussan, A., Lions, J. L. and Papanicolaou, G.: 1978, Asymptotic Analysis for Periodic Structures, North-Holland Publishing Company, Amsterdam, The Netherlands.
Brenner, H.: 1980, Dispersion resulting from flow through spatially periodic porous media, Trans. Roy. Soc. (London) 297, 81-133.
Carbonell R. G. and Whitaker, S.: 1984, Heat and mass transfer in porous media, In: J. Bear and M.Y. Carapcioglu (eds.), Fundamentals of Transport Phenomena in Porous Media, Martinus Nijhoff, Dordrecht, The Netherlands, pp. 123-198.
Castellanos, A.: 1998, Electrohydrodynamics, Springer, New York.
Chang, J.-S.: 1998, EHD Gas-liquid two-phase flow, In: A. Castellanos (ed.) Electrohydrodynamics, Chap. 20, Springer, New York.
Cwirko, E. H. and Carbonell R. G.: 1989, Transport of electrolytes in charged pores: analysis using the method of spatial averaging, J. Colloid Interface Sci. 129, 513-531.
Edwards, D. A.: 1995, Charge transport through a spatially periodic porous medium: Electrokinetic and convective dispersion phenomena, Phil. Trans. Roy. Soc. Lond. A353, 205-242.
Eringen, A. C. and Maugin, G. A.: 1990, Electrodynamics of Continua I: Foundations and Solid Media, Springer-Verlag, New York.
Eringen, A. C. and Maugin, G. A.: 1990, Electrodynamics of Continua II: Fluid and Complex Media, Springer-Verlag, New York.
Eringen, A. C. and Maugin, G. A.: 1990, Electrodynamics of Continua II: Fluid and Complex Media, Chap. 11, Springer-Verlag, New York.
Gray, W. G.: 1975, A derivation of the equation for multiphase transport, Chem. Engng Sci. 30, 229-233.
de Groot and Mazur, P.: 1984, Thermodynamics of Irreversible Process. Dover New York.
Howes, F. A. and Whitaker, S.: 1985, The spatial averaging theorem revisited, Chem. Engng Sci. 40, 1387-1392.
Jackson, R.: 1997, Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid, Chem. Engng Sci. 52, 2457-2469.
Léonetti, M. and Dubois-Violette, E.: 1997, Pattern formation by electro-osmotic self-organization in flat biomembranes, Phys. Rev. E 56, 4521-4525.
López de Haro, M., del Río, J. A. and Whitaker, S.: 1996, Flow of Maxwell fluids in porous media, Transport in Porous Media 25, 167-192.
Marle, C. M.: 1967, Écoulements monophasique en milieu poreux, Rev. Inst. Français du Pétrole 22(10), 1471-1509.
Melcher, J. R.: 1981, Continuum Electromechanics, The MIT Press Cambridge, Massachusetts.
Mochan, W. L. and Barrera, R. G.: 1994, Electrical Transport and Optical Properties of Inhomogeneous Media, Proc. 3rd Int. Conf. North-Holland, Amsterdam.
Moyne, C., Batsale, J.-C. and Degiovanni, A.: 1988, Approche expérimentale et théorique de la conductivité thermique des milieux poreux humides II: Théorie, Int. J. Heat Mass Trans. 31, 2319-2330.
O'Konski, C. T. and Thacher, H. C., Jr.: 1953, The distortion of aerosol droplets by an electric field, J. Phys. Chem. 57, 955-958.
Ochoa-Tapia, J. A., del Río, J. A. and Whitaker, S.: 1993, Bulk and surface diffusion in porous media: An application of the surface averaging theorem, Chem. Engng Sci. 48, 2061-2082.
Quintard, M. and Whitaker, S.: 1995, Local thermal equilibrium for transient heat conduction: Theory and comparison with numerical experiments, Int. J. Heat Mass Trans. 38, 2779-2796.
Quintard, M. and Whitaker, S.: 1994, Transport in ordered and disordered porous media I: The cellular average and the use of weighting functions, Transport in Porous Media 14, 163-177: Transport in ordered and disordered porous media II: Generalized volume averaging, Transport in Porous Media 14 (1994), 179-206.
del Río, J. A. and Whitaker, S.: 2000a, Maxwell's equations in two-phase systems I: Local electrodynamic equilibrium, Transport in Porous Media 39, 159-186.
del Río, J. A. and Whitaker, S.: 2000b, Maxwell's equations in two-phase systems II: Two-equation model, Transport in Porous Media 39, 259-287.
Sanchez-Palencia, E.: 1980, Non-homogeneous media and vibration theory, In: Lecture Notes in Physics, Vol. 127, Springer-Verlag, New York.
Sauer, S. G., Locke, B. R. and Arce, P.: 1995, Effects of axial and orthogonal applied electric fields on solute transport in poiseuille flows. An area averaging approach, Ind. Eng. Chem. Res. 34, 886-894.
Saville, D. A.: 1997, Electrohydrodynamics: the Taylor-Melcher leaky dielectric model, Annual Review of Fluid Mechanics 29, 27-64, Annual Reviews, Palo Alto, California.
Slattery, J. C.: 1967, Flow of viscoelastic fluids through porous media, AIChE J. 13, 1066-1071.
Taylor, G. I.: 1966, Electrically driven jets, Proc. Roy. Soc. A313, 453-475.
Whitaker, S.: 1967, Diffusion and dispersion in porous media, AIChE J. 13, 420-427.
Whitaker, S.: 1991, Improved constraints for the principle of local thermal equilibrium, Ind. Eng. Chem. Res. 30, 983-997.
Whitaker, S.: 1986, Theoretical derivation of Darcy's Law, Transport in Porous Media 1, 3-25.
Whitaker, S.: 1999, The Method of Volume Averaging, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Whitaker, S.: 1998, Coupled transport in multiphase systems: A theory of drying, In: Advances in Heat Transfer, Chap. 1, Vol. 31, Academic Press, New York.
Zhang, D. Z. and Prosperetti, A.: 1994, Averaged equations for inviscid dispersed two-phase flow, J. Fluid Mech. 267, 185-219.
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del Río, J.A., Whitaker, S. Electrohydrodynamics in Porous Media. Transport in Porous Media 44, 385–405 (2001). https://doi.org/10.1023/A:1010762226382
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DOI: https://doi.org/10.1023/A:1010762226382