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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 12: Homogenization in fluid mechanics and porous media (a tribute to the memory of Andro Mikelic)
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Articles

Non-linear boundary condition for non-ideal electrokinetic equations in porous media

Grégoire Allairea CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, FranceCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-8213-1092View further author information
ORCID Icon,
Robert Brizzia CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, FranceView further author information
,
Christophe Labbezb ICB UMR 6303 CNRS, Université de Bourgogne Franche-Comté, Dijon, FranceORCID Iconhttps://orcid.org/0000-0001-6652-6329View further author information
ORCID Icon &
Andro Mikelićc CNRS UMR, 5208, Université Claude Bernard Lyon 1, Institut Camille Jordan F-69622, Villeurbanne cedex, FranceORCID Iconhttps://orcid.org/0000-0002-4752-8705View further author information
ORCID Icon
Pages 4203-4234 | Received 22 Nov 2021, Accepted 13 May 2022, Published online: 26 May 2022

References

  • Karniadakis G, Beskok A, Aluru N. Microflows and nanoflows: fundamentals and simulation. New York: Springer; 2005. (Interdisciplinary Applied Mathematics; 25).
  • Blum L, Hoye JS. Mean spherical model for asymmetric electrolytes. 2. Thermodynamic properties and the pair correlation. J Phys Chem. 1977;81:1311–1316.
  • Hansen J-P, McDonald IR. Theory of simple liquids, 2nd ed. London: Academic Press: 1986.
  • Bernard O, Kunz W, Turq P, et al. Conductance in electrolyte solutions using the mean spherical approximation. J Phys Chem. 1992;96:3833–3840.
  • Dufrêche J-F, Bernard O, Durand-Vidal S, et al. Analytical theories of transport in concentrated electrolyte solutions from the MSA. J Phys Chem B. 2005;109:9873–9884.
  • Allaire G, Brizzi R, Dufrêche J-F, et al. Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Phys D. 2014;282:39–60.
  • Borkovec M. Origin of 1-pK and 2-pK models for ionizable water-solid interfaces. Langmuir. 1997;13(10):2608–2613.
  • Davis JA, James RO, Leckie JO. Surface ionization and complexation at the oxide/water interface: I. Computation of electrical double layer properties in simple electrolytes. J Colloid Interface Sci. 1978;63(3):480–499.
  • Hiemstra T, Van Riemsdijk WH. A surface structural approach to ion adsorption: the charge distribution (CD) model. J Colloid Interface Sci. 1996;179(2):488–508.
  • Yates DE, Levine S, Healy TW. Site-binding model of the electrical double layer at the oxide/water interface. J Chem Soc, Faraday Trans. 1974;70:1807–1818.
  • Allaire G, Brizzi R, Dufrêche J-F, et al. Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Comp Geosci. 2013;17(3):479–495.
  • Ray N, Muntean A, Knabner P. Rigorous homogenization of a Stokes–Nernst–Planck–Poisson system. J Math Anal Appl. 2012;390(1):374–393.
  • Schmuck M, Bazant MZ. Homogenization of the Poisson–Nernst–Planck equations for ion transport in charged porous media. SIAM J Appl Math. 2015;75(3):1369–1401.
  • Friedman A, Tintarev K. Boundary asymptotics for solutions of the Poisson–Boltzmann equation. J Differ Equ. 1987;69:15–38.
  • Looker JR. Semilinear elliptic Neumann problems and rapid growth in the nonlinearity. Bull Austral Math Soc. 2006;74(2):161–175.
  • Park J-H, Jerome JW. Qualitative properties of steady-state Poisson-Nernst-Planck systems: mathematical study. SIAM J Appl Math. 1997;57(3):609–630.
  • Evans LC. Partial differential equations. 2nd ed. Providence: AMS; 2010. (Graduate Studies in Mathematics).
  • Pao CV. Nonlinear parabolic and elliptic equations. New York: Plenum Press; 1992.
  • Hecht F. New development in FreeFem++. J Numer Math. 2012;20(3–4):251–265.

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