Theory for dynamic ion transport in ion-shuttling electrodes for electrochemical ion pumping

Abstract Electrochemical ion pumping (EIP) enables unidirectional ion transport, like electrodialysis, but operates via capacitive ion storage, as in capacitive deionization. This functionality is achieved through circuit switching, which dynamically alternates the connections of each ion-shuttling electrode with its neighbouring electrodes. Here we present a mathematical model that captures the spatiotemporal ion transport dynamics in EIP by coupling the Nernst–Planck equation for ion transport through ion-exchange polymers with an extended Donnan model for ion storage in porous electrodes. Simulations reveal unique ion transport behaviours not observed in conventional capacitive deionization or electrodialysis. The model is validated by experiments using EIP cells with single and multiple ion-shuttling electrodes. This work provides a theoretical foundation for EIP, enabling future advances in system design, operational optimization and selective ion separation.