Atom- and energy-efficient chemical separations are urgently needed to meet the surging demand for critical materials that has strained supply chains and threatened environmental damage. In this study, we used reaction-diffusion coupling to separate iron, neodymium, and dysprosium ions from model feedstocks of permanent magnets, which are typically found in electronic wastes. Feedstock solutions were placed in contact with a hydrogel loaded with potassium hydroxide and/or dibutyl phosphate, resulting in complex precipitation patterns as the various metal ions diffused into the reaction medium. Specifically, we observed the precipitation of up to 40 mM of iron from the feedstock, followed by the enrichment of 73 % dysprosium, and the extraction of >
95 % neodymium product at a further distance from the solution-gel interface. We designed a series of experiments and simulations to determine the relevant ion diffusivities, D