Cascade Continuum Micromechanics Model for the Effective Diffusivity of Porous Materials: Exponential Hierarchy across Cascade Levels. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Timothy, Jithender J.; Meschke, Günther
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 471
• Page End: 472
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510226
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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)