Identification of 'replacement' microstructure for porous medium from thermal conductivity measurements: Problem formulation and numerical solution

The problem of reconstruction and quantitative characterization of the microstructure of random composites, as a fundamental problem of material sciences, has been a subject of a considerable amount of literature. Thus far, previous studies used for the reconstruction either statistical microstructure descriptors or the overall property of real material. This paper makes a major contribution to research on reconstruction by formulating a procedure to recover the micro-structure that produces the same effective thermal conductivity as the real composite material. In particular, our goal is to find a binary representation of 'replacement' microstructure that, being a two-phase statistically isotropic medium, produces minimal disagreement with the experimental data. Such a binary microstructure is invariant with respect to the conductivity of fluid occupying the porous space. Thus, in some sense, the paper is an extension of the concept proposed by Lydzba et al. (2018), who showed, in the framework of analytical homogenization, that any isotropic microstructure can be represented by randomly oriented spheroids of certain distribu-tion over the aspect ratios. The efficiency of our methodology was illustrated by examples including Wiener and Hashin-Shtrikman bounds as well as the microstructure created by the system of non-overlapping disks. Finally, we use our algorithm to construct the 'replacement' microstructure for the real porous medium, i.e., medium sand. The main advantage of the digital representation of 'replacement' microstructure over the analytical one, is that it can be further used in computational modeling as well as in 3D printing applications.