title: A Two-Scale Computational Model ofpH-Sensitive Expansive Porous Media.
abstract: We propose a new two-scale model to compute the swelling pressure in colloidal systems with microstructure sensitive topHchanges from an outer bulk fluid in thermodynamic equilibrium with the electrolyte solution in the nanopores. The model is based on establishing the microscopic pore scale governing equations for a biphasic porous medium composed of surface charged macromolecules saturated by the aqueous electrolyte solution containing four monovalent ions [Formula: see text]. Ion exchange reactions occur at the surface of the particles leading to apH-dependent surface charge density, giving rise to a nonlinear Neumann condition for the Poisson-Boltzmann problem for the electric double layer potential. The homogenization procedure, based on formal matched asymptotic expansions, is applied to up-scale the pore-scale model to the macroscale. Modified forms of Terzaghi's effective stress principle and mass balance of the solid phase, including a disjoining stress tensor and electrochemical compressibility, are rigorously derived from the upscaling procedure. New constitutive laws are constructed for these quantities incorporating thepH-dependency. The two-scale model is discretized by the finite element method and applied to numerically simulate a free swelling experiment induced by chemical stimulation of the external bulk solution.
authors.affiliation: Pontifícia Universidade Católica do Rio de Janeiro PUC/RJ , Department of Mechanical Engineering, R. Marques de Sao Vicente 225 , Gavea, 22453-900 , Rio de Janeiro, RJ , Brazil e-mail:  poncerv@puc-rio.br.
authors.forename: Ranena V
authors.initials: RV
authors.lastname: Ponce F
authors.affiliation: Laboratório Nacional de Computacao Científica LNCC/MCT , Av Getúlio Vargas 333 , 25651-070 Petrópolis, RJ , Brazil e-mail:  murad@lncc.br.
authors.forename: Márcio A
authors.initials: MA
authors.lastname: Murad
authors.affiliation: Universidade Federal do Rio Grande do Norte UFRN , Av Salgado Filho , s/n 59078-970 Natal, RN , Brazil e-mail:  sidarta@ccet.ufrn.br.
authors.forename: Sidarta A
authors.initials: SA
authors.lastname: Lima
keywords: Poisson–Boltzmann; disjoining pressure; effective stress principle; finite element method; homogenizaton; ion exchange reactions; nonlinear surface charge; pH; swelling porous media