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Quantitative relationships between microstructure and effective transport properties based on virtual materials testing
Author(s) -
Gaiselmann Gerd,
Neumann Matthias,
Schmidt Volker,
Pecho Omar,
Hocker Thomas,
Holzer Lorenz
Publication year - 2014
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.14416
Subject(s) - tortuosity , microstructure , convection–diffusion equation , diffusion equation , porosity , macro , porous medium , diffusion , materials science , statistical physics , conductivity , mechanics , computer science , mathematics , thermodynamics , physics , chemistry , engineering , composite material , metric (unit) , operations management , programming language
The microstructure influence on conductive transport processes is described in terms of volume fraction ε, tortuosity τ, and constrictivity β. Virtual microstructures with different parameter constellations are produced using methods from stochastic geometry. Effective conductivitiesσ eff are obtained from solving the diffusion equation in a finite element model. In this way, a large database is generated which is used to test expressions describing different micro–macro relationships such as Archie's law, tortuosity, and constrictivity equations. It turns out that the constrictivity equation has the highest accuracy indicating that all three parameters ( ε , τ , β ) are necessary to capture the microstructure influence correctly. The predictive capability of the constrictivity equation is improved by introducing modifications of it and using error‐minimization, which leads to the following expression:σ eff = σ 0 2.03 ε 1.57β 0.72 / τ 2with intrinsic conductivityσ 0 . The equation is important for future studies in, for example, batteries, fuel cells, and for transport processes in porous materials. © 2014 American Institute of Chemical Engineers AIChE J , 60: 1983–1999, 2014