Variationally consistent homogenization of electrochemical ion transport in a porous structural battery electrolyte

In this paper, we develop a multi-scale modeling framework for a multiphysics problem characterized by electro-chemically coupled ion transport in a Structural Battery Electrolyte (SBE). The governing equations of the problem are established by coupling Gauss law with mass conservation for each mobile species. By utilizing variationally consistent homogenization, we are able to establish a two-scale model where both the macro-scale and sub-scale equations are deduced from a single-scale problem. Investigations of the sub-scale RVE problem show that the transient effects are negligible for the length scales relevant to the studied application, which motivates the assumption of micro-stationarity. In the special case of linear constitutive response, we get a numerically efficient solution scheme for the macro-scale problem that is based on a priori upscaling. As a final step, we demonstrate the numerically efficient solution scheme by solving a 2D macro-scale problem using upscaled constitutive quantities based on a 3D RVE.

Automated summary

In this study, a multi-scale modeling framework is developed to address the electro-chemically coupled ion transport in a Structural Battery Electrolyte (SBE). The governing equations are established by coupling Gauss law with mass conservation for each species. Through variationally consistent homogenization, a two-scale model is formulated where both macro-scale and sub-scale equations are derived from a single-scale problem. The transient effects in the investigated sub-scale RVE problem are found to be negligible, leading to the assumption of micro-stationarity. In the case of linear constitutive response, a numerically efficient solution scheme for the macro-scale problem is obtained based on a priori upscaling. Finally, the efficiency of the solution scheme is demonstrated by solving a 2D macro-scale problem using upscaled constitutive quantities from a 3D RVE.