Immersed Interface and Diffuse-Domain Approach for Current-Potential Distributions and Electrodeposition Problems

Abstract

Several numerical approaches are being developed to solve the moving boundary models which predict the morphological evolution of the electrode surface during electrodeposition. Despite these significant research efforts over a broad range of materials, scales, and purposes, the prediction of the shape evolution of the electrodes over time is still a challenging problem. One needs to solve these moving boundary problems, as the potential and current distributions within the cell get affected by the geometry.1-2 In this work, we will demonstrate a recently developed numerical framework based on the diffused domain approach using phase-field models for two classical example, Hull cell and copper deposition in trenches.3 The original model equation was carefully reformulated as a diffuse-domain/immerse domain approach for steady state current-potential distribution problems.4-5 Then the shape change problem is cast as a transient phase-field problem to predict the shape changes of the electrode during electrodeposition. A comparative analysis has also been performed for the efficiency, accuracy, speed, and convergence of the present solutions for the Hull cell with other available numerical and even analytical methods. It can be stated that the present phase-field model is robust and efficient for predicting the shape changes of the electrode over time without oscillations. Acknowledgments This research was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy (DoE) through the Advanced Battery Materials Research Program (Battery500 Consortium) References V. R. Subramanian, and R. E. White, J. Electrochem. Soc, 149(10) C498 (2002).R. Alkire, T. Bergh, and R. L. Sani, J. Electrochem. Soc., 125, 1981 (1978).T. Jang, L. Mishra, S. A. Roberts, A. Subramaniam, M. Uppaluri, M. P. Gururajan, J. Zhang, and V. R. Subramanian, “BattPhase – A convergent, non-oscillatory, efficient algorithm and code for predicting shape changes in lithium metal batteries using phase-field models – 1. Secondary Current Distribution,” ECSarXiv (2022), doi:10.1149/osf.io/k2vu6C. S. Peskin, Acta Numer., 11, 479 (2003).X. Li, J. Lowengrub, A. Ratz and A. Voigt, Commun. Math. Sci., 7, 81 (2009).