Existing battery modeling works have limitations in addressing the dependence of transport properties on local field variations and characterizing the response of anisotropic media. These limitations are tackled by means of a nested finite element (FE²) multiscale framework in which microscale simulations are employed to comprehensively characterize an anisotropic medium (macroscale). The approach is applied to the numerical simulation of transport processes in lithium ion battery separators. From the microscale solution, homogenized fluxes and their dependence on the downscaled macroscale variables are upscaled, thereby replacing otherwise assumed macroscale constitutive laws. The tensorial nature of macroscale effective transport properties stems from the numerical treatment. The proposed approach is verified against full-scale simulations. Several numerical examples are used to demonstrate the perils associated with accepted procedures, leading in some cases to severe discrepancies in the prediction of field quantities (from differences in the potential drop across the separator of about 27% for a fixed microstructure to more than 100% in the case of an evolving microstructure). Despite the use of simplified assumptions (e.g., synthetic microstructures), the numerical results demonstrate the importance of a tensorial description of transport properties in the modeling of battery processes.

In the study of transient heat conduction in heterogeneous two-phase media, the local thermal non-equilibrium condition calls for the use of a two-equation model to appropriately describe different temperatures in the two phases. We propose for the two-equation model an FE² multi-scale framework that is capable of addressing nonlinear conduction problems. The FE² framework consists of volume-averaged macroscale equations, well-defined microscale problems, and the information exchange between the two scales. Compared to a traditional FE² method for the one-equation model, the proposed FE² framework introduces an additional source term at the macroscale that is upscaled from the microscale interfacial heat transfer. At variance with the tangent matrices (i.e., effective conductivity) of the heat flux, the tangent matrices of the interfacial heat transfer depend on the microscopic length scale. The proposed FE² framework is validated against single-scale direct numerical simulations, and some numerical examples are employed to demonstrate its potential.

This study presents a three-dimensional computational model to evaluate effective conductivity and capacity of fiber-based battery electrodes. We employ electrodes composed of conductive and active material nanofibers dispersed in an electrolyte matrix. The effective conductivity is calculated by means of an equivalent resistor network model, while capacity evaluation is based on the identification of active material fibers that are accessible to electrons (i.e., those connected with the electronically conductive network). When a constraint is applied to the total fiber content, an optimal active-conductive material ratio is determined that maximizes the active material utilization and the electrode capacity. We also study fiber orientation effects on the electrode electrochemical properties. It is found that fiber orientation has a strong impact on the percolation threshold, and this impact also reflects on the active material utilization: the more the fiber orientation deviates from the ideal isotropic distribution, the lower the utilization of active material fibers. This is of special interest for practical applications where geometrical constraints on fiber orientation arise, as in the case of electrospun fibers deposited on a substrate. The results of this study are therefore meant to give an insight into how a fibrous electrode architecture performs and suggest effective design solutions.