Ponce F Ranena V, Murad Márcio A, Lima Sidarta A
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:
Laboratório Nacional de Computacao Científica LNCC/MCT , Av Getúlio Vargas 333 , 25651-070 Petrópolis, RJ , Brazil e-mail:
J Appl Mech. 2013 Mar;80(2):0209031-2090314. doi: 10.1115/1.4023011. Epub 2013 Feb 4.
We propose a new two-scale model to compute the swelling pressure in colloidal systems with microstructure sensitive to 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 [Formula: see text]. Ion exchange reactions occur at the surface of the particles leading to a -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 -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.
我们提出了一种新的双尺度模型，用于计算胶体系统中的溶胀压力，该胶体系统的微观结构对与纳米孔中电解质溶液处于热力学平衡的外部主体流体的变化敏感。该模型基于为一种双相多孔介质建立微观孔隙尺度控制方程，该双相多孔介质由被含有四种单价离子[公式：见原文]的水性电解质溶液饱和的表面带电大分子组成。离子交换反应发生在颗粒表面，导致表面电荷密度依赖于[具体变量]，从而为双电层电位的泊松 - 玻尔兹曼问题产生一个非线性诺伊曼条件。基于形式匹配渐近展开的均匀化过程被应用于将孔隙尺度模型向上扩展到宏观尺度。从均匀化过程中严格推导出修正形式的太沙基有效应力原理和固相质量平衡，包括一个附加应力张量和电化学压缩性。针对这些包含[具体变量]依赖性的量构建了新的本构定律。通过有限元方法对双尺度模型进行离散化，并应用于数值模拟由外部主体溶液的化学刺激引起的自由溶胀实验。
