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Research Articles

A Two-Scale Computational Model of pH-Sensitive Expansive Porous Media

[+] Author and Article Information
Ranena V. Ponce F.

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

Márcio A. Murad

Laboratório Nacional de Computacao Científica LNCC/MCT,
Av Getúlio Vargas 333,
25651–070 Petrópolis, RJ, Brazil
e-mail: murad@lncc.br

Sidarta A. Lima

Universidade Federal do Rio Grande do Norte UFRN,
Av Salgado Filho,
s/n 59078–970 Natal, RN, Brazil
e-mail: sidarta@ccet.ufrn.br

Manuscript received July 27, 2011; final manuscript received March 20, 2012; accepted manuscript posted November 19, 2012; published online February 4, 2013. Assoc. Editor: Younane Abousleiman.

J. Appl. Mech 80(2), 020903 (Feb 04, 2013) (14 pages) Paper No: JAM-11-1259; doi: 10.1115/1.4023011 History: Received July 27, 2011; Revised March 20, 2012; Accepted November 19, 2012

We propose a new two-scale model to compute the swelling pressure in colloidal systems with microstructure sensitive to pH changes 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 (Na+,Cl-,H+,OH-). Ion exchange reactions occur at the surface of the particles leading to a pH-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 the pH-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.

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Figures

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Fig. 1

Sketch of the microscopic domains of the model

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Fig. 2

Stratified microstructure of parallel particles

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Fig. 3

Portrait of dry and saturated swollen Purolite C104E cation exchange resin

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Fig. 4

Batch titration curve of the C104E resin for three NaCl concentrations

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Fig. 5

Electric potential and electric field distributions (E*=H∇yΨ*) for NaCl concentration 0.001 M and pH = 3

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Fig. 6

Electric potential and electric field distributions (E*=H∇yΨ*) for NaCl concentration 0.001 M and pH = 11

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Fig. 7

Charge density as a function of pH for H = 1 nm and two salinities

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Fig. 8

Charge density as a function of pH for NaCl concentration 0.1 M and two thicknesses

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Fig. 10

Zeta potential as a function of pH for NaCl concentration 0.1 M and two thicknesses

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Fig. 9

Zeta potential as a function of pH for H = 1 nm and two salinities

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Fig. 11

Swelling pressure as a function of pH for H = 1 nm and two salinities

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Fig. 12

Swelling pressure as a function of pH for H = 4 nm and two salinities

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Fig. 13

Swelling index in the free swelling experiment as a function of pH for different salinities

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