Empirical relationships between effective conductivities in porous and composite materials and their geometric characteristics such as volume fraction e, tortuosity s and constrictivity b are established. (simplified formula) with intrinsic conductivity r 0 , geodesic tortuosity s geod and relative prediction errors of 19% and 18%, respectively. We critically analyze the methodologies used to determine tortuosity and constrictivity. Comparing geometric tortuosity and geodesic tortuosity, our results indicate that geometric tortuosity has a tendency to overestimate the windedness of transport paths. Analyzing various definitions of constrictivity, we find that the established definition describes the effect of bottlenecks well. In summary, the established relationships are important for a purposeful optimization of materials with specific transport properties, such as porous electrodes in fuel cells and batteries.

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 conductivities σeff  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: σeff =σ02.03ε1.57β0.72/τ2 with intrinsic conductivity σ0. 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

A parametric stochastic 3D model for the description of complex three-phase microstructures is developed. Such materials occur for example in anodes of solid oxide fuel cells (SOFC) which consist of pores, nickel (Ni) and yttriastabilized zirconia (YSZ). The model is constructed using tools from stochastic geometry. More precisely, we model the backbones of the three phases by a certain class of random geometric graphs called beta-skeletons. This allows us to reproduce complete connectivity of all three phases as observed in experimental image data of a pristine Ni-YSZ anode as well as the prediction of volume fractions by model parameters. Finally a slightly generalized version of this model enables a good fit to experimental image data with respect to transport relevant microstructure characteristics and the length of triple phase boundary. Model validation is performed by comparing effective transport properties from finite element (FE) simulations based on 3D-data from the stochastic model and from tomography of real Ni-YSZ anodes. Moreover, the virtual, but realistic Ni-YSZ microstructures can be used for investigating the quantitative influence of microstructure characteristics on various physical properties and consequently on the performance of the

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The analysis of big data is changing industries, businesses and research as large amounts of data are available nowadays. In the area of microstructures, acquisition of (3-D tomographic image) data is difficult and time-consuming. It is shown that large amounts of data representing the geometry of virtual, but realistic 3-D microstructures can be generated using stochastic microstructure modeling. Combining the model output with physical simulations and data mining techniques, microstructure-property relationships can be quantitatively characterized. Exemplarily, we aim to predict effective conductivities given the microstructure characteristics volume fraction, mean geodesic tortuosity, and constrictivity. Therefore, we analyze 8119 microstructures generated by two different stochastic 3-D microstructure models. This is-to the best of our knowledge-by far the largest set of microstructures that has ever been analyzed. Fitting artificial neural networks, random forests and classical equations, the prediction of effective conductivities based on geometric microstructure characteristics is possible.