Modelos computacionais multiescala de meios porosos expansivos derivados a partir da mecânica estatística

• Autor(a) principal: Rocha, Aline Cristina da
• Data de Publicação: 2013
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/142
• topic: Materiais porosos; Mecânica estatística; Porous materials; Statistical mechanics; CNPQ::ENGENHARIAS::ENGENHARIA DE MATERIAIS E METALURGICA

A new two-scale computational model is constructed for swelling porous media. The model, based on the homogenization technique is applied to the nanoscopic governing equations of the electro-chemo-mechanical coupling that arises when the charged solid matrix is saturated by an electrolyte solutions containing cations and anions. The non-local pore-scale model is constructed within the framework of Statistical Mechanics and leads to a Fredholm integral equation of second type for the ion-particle correlation function coupled with Poisson problem for the electric potential. When combined with the fluid equilibrium condition such problem gives rise to a constitutive law for the fluid stress tensor in terms of the disjoining pressure which dictates the swelling of the porous medium. The homogenization procedure, based on formal asymptotic expansions, is applied to up-scale the model to the macroscale leading to a two-scale constitutive law for the swelling pressure appearing in the modified effective stress principle. Within the framework of Statistical Mechanics the two-scale model is capable of capturing the deviations from the classical Gouy-Chapman Poisson-Boltzmann-based theory (which treat the ions as point charges) induced by the finite size short-range ion-ion correlations effects due to the treatment of the ions as charged hard spheres with charge located at their center. Numerical solutions of the integro-differential problem posed in a periodic cell are constructed making use of a sequential algorithm which consists of delaying the terms independent of the electric potential in the Poisson equation. Application of this technique give rise to two problems, the first being a non-linear Poisson problem, discretized by Galerkin's method and the second consisting of integral equations for the correlation functions. These in turn are discretized by the Collocation method taking as basis functions the eigenfunctions related to their respective kernels. With this choice of basic functions, each integral equation reduces to an algebraic equation. In this context we are faced with two new problems. The first consists of the integral eigenvalue problems concerning the kernels, discretized by Galerkin's method and the second a system of nonlinear equations for the coefficients of expansions of the unknowns. Numerical results for the correlation functions and electric potential are obtained for two-dimension and stratified arrangements of the macromolecules. Continuing in the stratified arrangements results for the swelling pressure are obtained showing that the effects of ion-ion correlation forces give rise to anomalous attraction patterns between the particles for divalent ions. Such class of attractive adverse phenomena lead to new reactive transport regimes of contaminants in swelling media due to the anomalous adsorption/desorption of the ionic species coupled with clay swelling.