Abstract
Electrochemically switched ion membrane extraction (ESIME) technology enables continuous Nd(III) extraction, using an electrochemical–chemical dual-functional di(2-ethylhexyl) phosphoric acid-incorporated multi-walled carbon nanotubes (P204-MWCNTs) membrane. To elucidate the electrochemical–chemical transmembrane transport in ESIME, a dynamic model for Nd(III) extraction was developed and validated. This model quantitatively reveals the coupled extraction–diffusion–stripping transmembrane process. In the model, the electroactive carrier concentration and the ion-exchange carrier concentration bridge the external driving forces (electric field and H+ concentration gradient) and the spatiotemporal evolution of Nd-complexes. Simulation results indicate that the rate-limiting step of the transmembrane process alternates between extraction and diffusion, while stripping remains rapid. To quantify the extraction-diffusion competition, a dynamic Damköhler number (DaII) is introduced, revealing that the rate-limiting step shifts from diffusion control (DaII>1) to extraction control (DaII<1) at an extraction efficiency () of ∼67% (membrane thickness: 95 μm). Parameter analysis further indicates that a voltage of 0.9 V maximizes the synergistic electrochemical and chemical contribution (53% and 47%, respectively), achieving an of 93%. Multi-parameter optimization identifies an optimal operational window achieving >95% stripping efficiency. Finally, the model was successfully extended to multi-ion systems and validated in simulated NdFeB recovery solution. This DaII-based framework serves as an efficient in-silico tool for evaluating and optimizing rare-earth separation process in ESIME systems.
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•A dynamic model for electrochemically switched ion membrane extraction is developed and validated.•ECC and ICC bridge driving forces and spatiotemporal evolution of Nd-complexes.•Electrochemical-chemical synergy is quantitatively elucidated.•Dynamic Damköhler number diagnoses evolving rate-limiting regimes.•Multi-parameter analysis defines an optimal space with stripping efficiency >95%.