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Cascade Continuum Micromechanics Model for the Effective Diffusivity of Porous Materials: Exponential Hierarchy across Cascade Levels
Author(s) -
Timothy Jithender J.,
Meschke Günther
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510226
Subject(s) - micromechanics , thermal diffusivity , cascade , statistical physics , representative elementary volume , materials science , exponential function , mechanics , porosity , physics , mathematics , thermodynamics , composite material , chemistry , mathematical analysis , microstructure , composite number , chromatography
The effective molecular diffusivity of porous materials such as cementitious, geological or synthetic materials is strongly affected by the complexity of the pore‐space which may span across multiple scales from the nanometer to the sub‐millimeter range. Recently, a semi‐analytical Cascade Continuum Micromechanics (CCM) Model [1,2] was proposed, which allows to compute estimates of the effective diffusivity given the porosity ϕ, the intrinsic diffusivity of molecules in the pore‐fluid D and a complexity parameter n . In contrast to existing micromechanics models, the CCM model is able to predict a physically consistent percolation threshold. In this paper, the classical CCM model is generalized so as to characterize a pore‐volume distribution and its influence on the effective diffusivity at a particular cascade level. The generalized CCM model shows an exponential pore‐volume distribution across cascade levels that is implicitly included in the classical CCM model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)