The Analytical Transport Network Model for Energy Materials Design and Characterization: Extensions for the Modeling of Coupled Flows and Structural Mechanics
Authors: Cocco Alex P. , Grew Kyle N. 
Published: February 2020

The design and characterization of next-generation, heterogeneous materials for application in energy technologies (batteries, fuel cells, etc.) increasingly relies on a fundamental understanding of how the 3-D properties of a material’s microstructure influences its performance. The Analytical Transport Network (ATN) Model was developed to offer a computationally quick and inexpensive means for analytically examining the link between 3-D structure and performance in such materials [1], [2]. In this talk, we present recent extensions of the model to constant-property, coupled, flow phenomena that conform to Onsager reciprocity (e.g., thermoelectric or electrokinetic phenomena). In addition, we discuss the development of a mechanics of materials model written in ATN nomenclature, which makes it possible to characterize a network’s flow and mechanical properties using the same analytical formalism. Finally, we present refinements and extensions to our software for applying the model to 3-D, voxel-based images, which can be artificially generated or obtained by 3-D imaging techniques, such as x-ray tomography.
The ATN model is a lumped-element approach for modeling potential flow (and recently structural mechanics) in microstructural networks, e.g., in porous materials, heterogeneous materials, or, generally, in any composite whose components comprise multiple, interwoven networks of channels [1], [2]. The central question that ATN aims to address is: How does the relative arrangement and the individual geometric characteristics of a network’s channels, i.e., their topology and morphology, impact the network’s flow behavior? The question is motivated by the longer-term goal of rationally designing microstructural networks to obtain desired material properties.
In [1]and [2], steady-state, diffusive potential flow of a single-entity was considered, e.g., electrical/heat conduction or trace species diffusion. In [2], the model additionally accounted for the loss or gain of flow across channel boundaries, e.g., heat loss due to surface convection or species consumption due to 1storder surface reactions. ATN predictions of effective network resistance and surface exchange were calculated, with minimal additional error, up to 6 orders of magnitude faster than Finite Element Analysis (FEA). Furthermore, because ATN’s fundamental modeling element is a physical channel, as opposed to sub-channel-scale element, graph theory could be used to mathematically examine how the interplay of channel morphology and topology impact network flow. These advantages carry into the model’s extensions presented in this talk.
[1] A. P. Cocco, A. Nakajo, and W. K. S. Chiu, “Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 1. Flow without reactions,” J. Power Sources, vol. 372, 2017.
[2] A. P. Cocco and W. K. S. Chiu, “Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 2. Flow with reactions,” J. Power Sources, 2017.