First-Principles Modeling of an Electrolytic Cell for Lithium Hydroxide Production: A Multiscale ODE-PDE Framework

This study presents a first-principles dynamic model for the electrochemical production of lithium hydroxide (LiOH) in a bench-scale cation exchange membrane (CEM) cell. Its distinguishing feature is a single, dynamically coupled description of the whole cell, in which the lumped Ordinary Differential Equation (ODE) dynamics of the anodic and cathodic chambers are coupled to a spatially resolved Nernst–Planck (PDE) model of membrane ion transport. The model resolves the transient induction period of ion crossover and captures the association kinetics of Li+ and OH−, cathodic water reduction, and the back-migration and neutralization of OH− at the anode, with the local electric field represented by a non-linear potential gradient. Solved by the Method of Lines and reduced through symbolic treatment of the Robin boundary conditions to a consistent ODE system, it yields a numerically robust framework for this stiff, strongly coupled problem. Two process-level results emerge: the membrane strongly attenuates cross-chamber disturbances, largely decoupling the anode and cathode, and it reaches a quasi-steady state far faster than the bulk chambers—a separation of time scales expected to widen at larger volume-to-surface-area ratios. These insights inform scale-up strategies and multiscale control architectures for the cell.