Modelagem multiescala do acoplamento eletro-químico em um meio poroso argiloso com dependência do PH / Multiscale modeling of eletro-chemical couplings in clays including PH dependence

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

In this work we develop a three-scale mathematical modeling to describe electro-chemical couplings in clays using the asymptotic homogenization procedure of periodic structures. We consider the porous medium composed of kaolinite particles saturated by an electrolyte solution of water-solvent and four ionic solutes monovalents Na+, H+, Cl-, OH-At the nanoscale we develop the model of the electrical double layer wherein the electric potential and local charge distribution are ruled by the Poisson- Boltzmann problem. In addition we incorporate the protonation/deprotonation chemical reaction between the fluid and the particle surface and consequently we quantify the dependence of the surface charge density of the particles with the pH of the electrolyte solution. At the microscale, or pore-scale, the movement of the aqueous solution is governed by the Stokes problem whereas ion transport by the Nernst-Planck equation. The pore-scale governing equations are supplemented by slip boundary condition in the tangential velocity of the fluid and adsorption interface conditions arising from the averaging of the nanoscale model. We then homogenize the microscopic model to the macroscale and derive effective equations with additional closure relations for the macroscopic coefficients. The macroscopic model is discretized by the finite volume method and numerical simulations of electrokinetical remediation of a contaminated soil are performed. The numerical results illustrate the strong dependence of the remediation efficiency on the pH of the aqueous solution.

ASSUNTO(S)

modelagem multiescala engenharia de materiais e metalurgica fenônemos eletroquímicos eletro-chemical couplings. multiscale modeling argilas.

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