Отправлено: 10.09.08 03:42. Заголовок: Investigation of Donnan equilibrium in charged porous materials—a scale transition analysis

Investigation of Donnan equilibrium in charged porous materials—a scale transition analysis
Журнал Transport in Porous Media
Springer Netherlands
ISSN 0169-3913 (Print) 1573-1634 (Online)
Volume 69, Number 2 / Сентябрь 2007 г.
DOI 10.1007/s11242-006-9071-6
pp 215-237

Investigation of Donnan equilibrium in charged porous materials—a scale transition analysis
Peter Pivonka1 , David Smith1 and Bruce Gardiner1

(1) Department of Civil and Environmental Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia

Received: 28 June 2004 Accepted: 4 October 2006 Published online: 14 December 2006

Abstract We propose a new theory describing how the macroscopic Donnan equilibrium potential can be derived from the microscale by a scale transition analysis. Knowledge of the location and magnitude of the charge density, together with the morphology of the pore space allows one to calculate the Donnan potential, characterizing ion exclusion in charged porous materials. Use of the electrochemical potential together with Gauss’ electrostatic theorem allows the computation of the ion and voltage distribution at the microscale. On the other hand, commonly used macroscopic counterparts of these equations allow the estimation of the Donnan potential and ion concentration on the macroscale. However, the classical macroscopic equations describing phase equilibrium do not account for the non-homogeneous distribution of ions and voltage at the microscale, leading to inconsistencies in determining the Donnan potential (at the macroscale). A new generalized macroscopic equilibrium equation is derived by means of volume averaging of the microscale electrochemical potential. These equations show that the macroscopic voltage is linked to so-called “effective ion concentrations”, which for ideal solutions are related to logarithmic volume averages of the ion concentration at the microscale. The effective ion concentrations must be linked to an effective fixed charge concentration by means of a generalized Poisson equation in order to deliver the correct Donnan potential. The theory is verified analytically and numerically for the case of two monovalent electrolytic solutions separated by a charged porous material. For the numerical analysis a hierarchical modeling approach is employed using a one-dimensional (1D)macroscale model and a two-dimensional (2D)microscale model. The influence of various parameters such as surface charge density and ion concentration on the Donnan potential are investigated.
Keywords Donnan potential - Anion exclusion - Electrochemical potential - Poisson equation - Charged porous materials - Volume averaging


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Peter Pivonka (Corresponding author)
Email: ppivonka@unimelb.edu.au

David Smith
Email: david.smith@unimelb.edu.au

Bruce Gardiner
Email: bgardine@unimelb.edu.au


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