Ionic diffusion and kinetic homogeneous chemical reactions in the pore solution of porous materials with moisture transport

Abstract

Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a rigid porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form accounts for electroquasistatics. The derived macroscopic field equations (conservation of mass, linear and angular momentum, energy and Maxwell’s equations) for the multiphase, multicomponent system are combined with the entropy inequality to obtain restrictions on constitutive equations. The so-called near equilibrium results obtained from this analysis (using Lagrange multipliers to identify properties) are obtained by expanding linearly about equilibrium. The approach leads to the development of the explicit expressions for the constitutive equations. In this work the derived generalized Fick’s law of diffusion and the generalized Darcy’s law will be used together with derived constitutive equations for chemical reactions within phases. The mass balance equations for the constituents and the phases together with the constitutive equations gives the coupled set of non-linear differential equations describing the theoretical behaviour of the system under consideration. A finite element procedure is described capable of solving the coupled set of governing differential equations. A novel approach on how to arrange the stiffness matrix of the global problem to take into account for a quite general description of chemical reactions among constituents is described. The Petrov–Galerkin approach is used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton–Raphson scheme is derived for the non-linear global matrix formulation. The developed model and its numerical solution procedure are checked by running test examples which results demonstrates robustness of the proposed approach.