Determination of the Kinetic Rate Law of Rare-Earth Solvent Extraction Using Interferometry: The Case of Samarium(III)

The growing demand for rare-earths, which are processed by using costly and environmentally unfriendly solvent extraction methods, requires a better understanding of the underlying reaction kinetics in order to achieve further process optimizations. For this purpose, we present a novel approach to determine the complete reaction rate law of a liquid–liquid solvent extraction system. Therefore, extraction experiments with the strategically important rare-earth element samarium are carried out in a Hele–Shaw cell using PC88A diluted in low-viscosity paraffin oil. To analyze the diffusive mass transfer of the samarium ions from the aqueous phase into the extractant-loaded organic phase, the concentration profile in the aqueous phase is measured using a Mach–Zehnder interferometer. By applying the method of initial rates, the concentration data enable the semiempirical reaction rate law to be determined. The rate law is quasi-first-order for Sm(III), a quasi-second-order for the extractant PC88A, and a partial order of −0.11 for the hydrogen concentration. This experimental procedure is combined with a complementary numerical approach, based on simulating the one-dimensional reaction–diffusion equation, to quantify the complete reaction kinetics. Using the backward rate law of the current iteration, the deviation of the following numerical results from the experimental data is determined in order to find the minimum deviation. Consequently, a third-order reaction was observed for the samarium complex and a partial reaction order of 0.2 for the hydrogen concentration. In this way, a new method is proposed and validated to precisely quantify the reaction kinetics with a low chemical consumption.