Homogenisation of spirally-wound high-contrast layered materials

Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the need for simplified models of the electrical and thermal behaviour of lithium-ion cells, accounting for the highly conductive metallic current collectors and relatively poorly conductive electrodes. We identify and study three distinguished limits, and then describe two composite models which each provide a uniform approximation spanning two distinguished limits. We compare the results of the various reduced-order models with calculations of the full model on a detailed geometry to give a guide to the accuracy of the approximations.