Channel size distribution of complex three-dimensional microstructures calculated from the topological characterization of isodistance structures

We present a novel approach for quantifying the channel size distribution (CSD) of complex three-dimensional microstructures. The CSD, which characterizes the probability of finding a channel bottleneck with a given size, is difficult to measure for materials with complex microstructures that are extensively interconnected. More importantly, insights about the physical properties of these materials, such as transport properties, may be provided by their CSD. The CSD is measured by topological characterization of a distance function, which is calculated from complex microstructural data using the level set method. The newly developed method for calculating CSD is shown to be robust such that it is applicable to both smooth and discontinuous (bi-level) data. The method is demonstrated by calculating the CSDs for three-dimensional microstructures formed through conserved (Cahn-Hilliard) and nonconserved (Allen-Cahn) dynamics. We found significant differences between the two structures in their characteristic channel size and the width of their distributions, even though their genera, a measure of connectivity, are almost identical. The CSD, which was not previously available for complex microstructures, will provide a new means to correlate properties of composite materials with their performance.