A method of recovering daughter isotopes from a radioisotope mixture. The method comprises providing a radioisotope mixture solution comprising at least one parent isotope. The at least one parent isotope is extracted into an organic phase, which comprises an extractant and a solvent. The organic phase is substantially continuously contacted with an aqueous phase to extract at least one daughter isotope into the aqueous phase. The aqueous phase is separated from the organic phase, such as by using an annular centrifugal contactor. The at least one daughter isotope is purified from the aqueous phase, such as by ion exchange chromatography or extraction chromatography. The at least one daughter isotope may include actinium-225, radium-225, bismuth-213, or mixtures thereof. A liquid-liquid extraction system for recovering at least one daughter isotope from a source material is also disclosed.