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Chapitre D'ouvrage Année : 2017

An introduction to the homogenization modeling of non-Newtonian and electrokinetic flows in porous media

Résumé

The flow of complex fluids through porous media is common to many engineering applications. The upscaling is a powerful tool for modeling nonhomo-geneous media and we consider homogenization of quasi-Newtonian and electroki-netic flows through porous media. For the quasi-Newtonian polymeric fluids, the incompressible Navier-Stokes equations with the invariants dependent viscosity is supposed to hold the pore scale level. The 2-scale asymptotic expansions and the two-scale convergence of the monotone operators are applied to derive the reservoir level filtration law, given as a monotone relation between the filtration velocity and the pressure gradient. The second problem, we consider, is the quasi-static transport of an electrolyte through an electrically charged medium. The physical chemistry modeling is presented and used to get a dimensionless form of the problem. Next the equilibrium solutions are constructed through solving the Poisson-Boltzmann equation. For the solutions being close to the equilibrium, the two-scale convergence is applied to obtain the Onsager relations linking gradients of the pressure and of the chemical potentials to the filtration velocity and the ionic fluxes.
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Dates et versions

hal-01488276 , version 1 (13-03-2017)

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  • HAL Id : hal-01488276 , version 1

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Andro Mikelic. An introduction to the homogenization modeling of non-Newtonian and electrokinetic flows in porous media. Springer. New trends in non-newtonian fluid mechanics and complex flow, 2212, Springer, pp.171-227, 2017, Lecture Notes Centro Internazionale Matematico Estivo (C.I.M.E.) Series, Lecture Notes in Mathematics, Springer. ⟨hal-01488276⟩
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