It is well known that phase formation by electrodeposition yields films of poorly controllable morphology. This typically leads to a range of technological issues in many fields of electrochemical technology. Presently, a particularly relevant case is that of high-energy density next-generation batteries with metal anodes, that cannot yet reach practical cyclability targets, owing to uncontrolled elelctrode shape evolution. In this scenario, mathematical modelling is a key tool to lay the knowledge-base for materials-science advancements liable to lead to concretely stable battery material architectures. In this work, we introduce the Evolving Surface DIB (ESDIB) model, a reaction-diffusion system posed on a dynamically evolving electrode surface. Unlike previous fixed-surface formulations, the ESDIB model couples surface evolution to the local concentration of electrochemical species, allowing the geometry of the electrode itself to adapt in response to deposition. To handle the challenges related to the coupling between surface motion and species transport, we numerically solve the system by proposing an extension of the Lumped Evolving Surface Finite Element Method (LESFEM) for spatial discretisation, combined with an IMEX Euler scheme for time integration. The model is validated through six numerical experiments, each compared with laboratory images of electrodeposition. Results demonstrate that the ESDIB framework accurately captures branching and dendritic growth, providing a predictive and physically consistent tool for studying metal deposition phenomena in energy storage devices.

翻译：众所周知，电沉积形成的相通常会产生形态难以控制的薄膜，这通常会导致电化学技术许多领域中出现一系列技术问题。当前一个特别相关的案例是采用金属负极的高能量密度下一代电池，由于电极形状的不可控演化，这些电池尚无法达到实际可循环性目标。在此背景下，数学建模是建立知识基础的关键工具，这些知识基础有望推动材料科学的进步，从而最终实现具体稳定的电池材料结构。在本工作中，我们提出了演化表面DIB（ESDIB）模型，这是一个建立在动态演化电极表面上的反应-扩散系统。与以往固定表面的公式不同，ESDIB模型将表面演化与电化学物种的局部浓度耦合，使得电极本身的几何形状能够根据沉积过程自适应调整。为应对表面运动与物种传输之间耦合带来的挑战，我们通过扩展集总演化表面有限元方法（LESFEM）进行空间离散化，并结合IMEX欧拉格式进行时间积分，从而数值求解该系统。该模型通过六次数值实验进行验证，每次实验均与电沉积的实验室图像进行对比。结果表明，ESDIB框架能够准确捕捉分支和枝晶生长现象，为研究储能装置中的金属沉积现象提供了一个具有预测性且物理一致的工具。