The Analytical Transport Network Model for Diffusive-Reactive Flow in 3-D Microstructural Networks: A Computationally Economical Model for Potential Use in Multi-Scale Modeling Efforts

Abstract

Electrochemical energy materials are those used in electrochemical energy conversion and storage technologies, such as batteries, fuel cells, and electrochemical capacitors. Their development is complicated by the fact that they must simultaneously satisfy a diverse set of design criteria, which in turn depend on multiple, interacting physical processes occurring across multiple length and time scales. An energy material’s microstructure adds to its complexity: in addition to occurring across multiple length and time scales, the physical processes that determine its performance also occur within a geometrically complex, often 3-D, domain. Then, if one wishes to integrate molecular-scale knowledge (e.g., from molecular dynamics simulations, etc.) into a multi-scale design framework, it would be advantageous to have a robust, computationally inexpensive means of accounting for the geometrical complexity of a typical energy material microstructure. In this work, we consider energy material microstructures comprised of interwoven, 3-D networks and present a heuristic, fully analytical model – the Analytical Transport Network (ATN) Model – that explicitly relates the morphology and topology of a given network’s channels to its effective transport coefficient and, in an approximate manner, its electrochemical activity. ATN’s effective transport coefficient estimates obtained for conserved flow within a set of artificially-generated and real energy material microstructures exhibited good agreement with those obtained from electrochemical fin theory and finite element analysis, but were computed 1.5 and 6 orders of magnitude faster, respectively. In addition, the theory explicitly relates a number of morphological and topological parameters directly to the effective transport coefficient, whereby the distributions that characterize the structure are readily available for, e.g., morphological/topological optimization studies or further topological characterization by network science. In considering reacting flow, the ATN model is used to identify morphological and topological features that influence the flow consumed by reactions per the flow entering the network. In this talk, we will present the ATN model, compare its predictions to those from existing techniques as well as to experimental measurements, and discuss how it can potentially be extended to elucidate the influence of channel morphology and topology on multi-component and transient flow.