Simulated Diffusion Spreadability for Characterizing the Structure and Transport Properties of Materials

In multiphase heterogeneous media, time-dependent diffusion processes between phases are widespread in physical, chemical, and biological systems. Examples of such media include composites, porous media, and complex fluids. The recently developed diffusion spreadability, ${cal S}(t)$, provides a direct link between time-dependent interphase diffusive transport and the microstructure of two-phase media across length scales [1]; thus making ${cal S}(t)$ a powerful tool for classifying the (non)hyperuniformity of microstructures. In this work, we develop a computationally efficient algorithm for ascertaining ${cal S}(t)$ and its associated entropy production rate directly from digitized representations of microstructures via simulated random walks. We apply our algorithm to a variety of two- and three-dimensional (non)hyperuniform microstructures to assess their non-equilibrium transport properties. Overall, our algorithm has practical use in the discovery and design of materials with desirable time-dependent diffusion properties.

[1] Torquato, S., Phys. Rev. E., 104 054102 (2021)