Smoothed particle hydrodynamics modeling of electrodeposition and dendritic growth under migration- and diffusion-controlled mass transport

Abstract

In many electrochemical processes, the transport of charged species is governed by the Nernst-Planck equation, which includes terms for both diffusion and electrochemical migration. In this work, a multi-physics, multi-species model based on the smoothed particle hydrodynamics (SPH) method is presented to model the Nernst-Planck equation in systems with electrodeposition. Electrodeposition occurs when ions are deposited onto an electrode. These deposits create complex boundary geometries, which can be challenging for numerical methods to resolve. SPH is a particularly effective numerical method for systems with moving and deforming boundaries due to its particle nature. This paper discusses the SPH implementation of the Nernst-Planck equations with electrodeposition and verifies the model with an analytical solution and a numerical integrator. A convergence study of migration and precipitation is presented to illustrate the model’s accuracy, along with comparisons of the deposition growth front to experimental results.