Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 51, Issue 12, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3521555
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Funding
- GNR MOMAS CNRS(Modelisation Mathematique et Simulations numeriques liees aux problemes de gestion des dechets nucleaires)
- Chair Mathematical modeling and numerical simulation, F-EADS - Ecole Polytechnique - INRIA
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In this paper we undertake the rigorous homogenization of a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. The motion is governed by a small static electric field and a small hydrodynamic force, which allows us to use O'Brien's linearized equations as the starting model. We establish convergence of the homogenization procedure and discuss the homogenized equations. Even if the symmetry of the effective tensor is known from the literature [J. R. Looker and S. L. Carnie, Transp. Porous Media, 65, 107 (2006)], its positive definiteness does not seem to be known. Based on the rigorous study of the underlying equations, we prove that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. This result justifies the approach of many authors who use Onsager theory as starting point. (C) 2010 American Institute of Physics. [doi:10.1063/1.3521555]
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