Estimation of geodesic tortuosity and constrictivity in stationary random closed sets

TL;DR

This paper develops and proves the consistency of estimators for geodesic tortuosity and constrictivity, key structural features affecting transport in porous materials, with applications demonstrated in fuel cell materials.

Contribution

It introduces precise definitions and consistent estimators for geodesic tortuosity and constrictivity in stationary random closed sets, addressing edge effects in real data.

Findings

Strong consistency of estimators for unbounded sampling windows

Application to multi-phase fuel cell materials

Control of edge effects demonstrated

Abstract

We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous or composite materials. Loosely speaking, geodesic tortuosity measures the windedness of paths whereas the notion of constrictivity captures the appearance of bottlenecks resulting from narrow passages within a given materials phase. We first provide mathematically precise definitions of these quantities and introduce appropriate estimators. Then, we show strong consistency of these estimators for unboundedly growing sampling windows. In order to apply our estimators to real datasets, the extent of edge effects needs to be controlled. This is illustrated using a model for a multi-phase material that is incorporated in solid oxid fuel cells.