## 2 Materials and Methods
### Procedures and Analytics  
Batch solvent extraction experiments were carried out using equal volumes of 500 \(\upmu\)L of each phase. The aqueous and organic phases were pipetted into screw-cap vials and contacted for 30 min on an IKA VIBRAX VXR, IKA(r)-Werke GmbH & Co. KG (Staufen, Germany) basic automatic shaker at 2200 rpm and 22 \({}^{\circ}\)C. The temperature was controlled by a HAAKE F3 thermostat, Thermo Scientific HAAKE (Geel, Belgium). After mixing, the phases were disengaged with a Hettich EBA 8s centrifuge, Andreas Hettich GmbH & Co.KG (Tuttlingen, Germany), for 5 min. The phases were then separated manually using a fine tipped transfer micropipette. Gamma measurements of \({}^{241}\)Am (60 keV) and \({}^{152}\)Eu (122 keV) were carried out using an Eurisys EGC 35-195-R germanium coaxial N-type detector, and spectra were evaluated using the GammaVision Software. Samples were measured directly without further treatment of the samples. Alpha measurements were carried out for \({}^{241}\)Am (5486 keV) and \({}^{244}\)Cm (5805 keV) using an ORTEC Octete-pc eight chamber alpha measurement system equipped with PIPS detectors. Sample preparation for alpha measurement was done by homogenizing a 10 \(\upmu\)L alpha spectroscopy sample in 100 \(\upmu\)L of a mixture of Zapon varnish and acetone (1:100 \(v\)/\(v\)). This mixture was distributed over a stainless-steel plate obtained from Berthold, Bad Wildbad, Germany. The sample was dried under a heating lamp and annealed into the stainless-steel plate using a gas-flame burner. For stable elements, inductively coupled plasma mass spectrometry (ICP-MS) was applied using a Perkin Elmer NexION 2000C. Aqueous samples were measured after dilution in 1% \(v\)/\(v\) nitric acid solution without further treatment. Organic samples were measured directly in a tensile matrix (Triton-X-100) in 1% \(v\)/\(v\) HNO\({}_{3}\) after dilution. Acid concentration was measured by titration against 0.1 mol L\({}^{-1}\) NaOH using a 798 MPT Titrino, purchased from Metrohm GmbH & Co. KG (Filderstadt, Germany). The pH of aqueous solutions was measured with a Metrohm 691 pH Meter, purchased from Metrohm GmbH & Co. KG (Filderstadt, Germany). The calibration of the pH meter was done using commercial buffer solutions purchased from Merck AG (Darmstadt, Germany). Distribution ratios \(D\) were calculated as the ratio of activity or concentration of a metal ion in the organic phase vs. the activity or concentration of the metal ion in the aqueous phase. The separation factor \(SF\) between two metal ions was calculated as the ratio of the corresponding distribution ratios (\(SF_{\text{M1/M2}}=D_{\text{M1}}/D_{\text{M2}}\)). Distribution ratios between 0.01 and 100 exhibit an uncertainty of \(\pm\)5%, whereas lower/higher values exhibit larger uncertainties. Mass balances were calculated as the sum of aqueous and organic concentrations divided by the initial concentration. Stage efficiencies in the single centrifugal contactor experiments were calculated depending on the extraction mode. For the forward extraction tests (extraction section and Ln re-extraction section), the stage efficiency was calculated as the metal ion distribution ratio in steady state divided by the metal ion distribution ratio in equilibrium. For the backward extraction tests (Scrub 2, An stripping, and Ln stripping sections), the stage efficiency was calculated as the metal ion distribution ratio in equilibrium divided by the metal ion distribution ratio in steady state. The equilibrium distribution ratios in all single centrifugal contactor tests were determined after stopping the contactor by transferring the content of its mixing chamber into a test tube and shaking it for 15-30 min on a test tube shaker (Heidolph rear top test tube shaker, purchased from Heidolph Instruments GmbH Co. KG, Schwabach, Germany). Then, the test tubes were centrifuged with a Hettich EBA 8s centrifuge, Andreas Hettich GmbH & Co.KG (Tuttlingen, Germany), and the phases were separated and sampled individually.