Radioactive nuclides (radionuclides) are separate from an aqueous radioactive liquid by feeding the liquid into a chamber between a porous anode and a porous cathode of a shock electrodialysis device. Meanwhile, an anolyte is fed through the porous anode, and a catholyte is fed through the porous cathode. A voltage is applied to the porous anode and to the porous cathode to create a voltage differential across the chamber. The liquid is passed through the chamber, and cations are selectively driven from the liquid into the cathode by the voltage differential. The voltage differential creates a desalination shock that produces an ion-enriched zone on one side of the desalination shock and a deionized zone on an opposite side. A brine including the radioactive cations is extracted from the ion-enriched zone through a brine outlet, and fresh water is extracted from the deionized zone through a fresh-water outlet.

A flow electrode capacitive deionization system and a method for recovering phosphorus in phosphogypsum leachate and synchronous performing brine desalination belong to the technical field of wastewater treatment and recycling. The flow electrode capacitive deionization system includes a phosphorus recovery electrodeionization module and a desalination electrodeionization module. A first flow electrode solution reservoir, a phosphorus recovery electrodeionization module cathode flow electrode chamber, and a desalination electrodeionization module anode flow electrode chamber are interconnected in a circulation. A second flow electrode solution reservoir, a phosphorus recovery electrodeionization module anode flow electrode chamber, and a desalination electrodeionization module cathode flow electrode chamber are interconnected in a circulation. Two independent flow electrode solution circulation loops are formed. The phosphogypsum leachate enters the phosphorus recovery electrodeionization module and phosphorus is enriched into a flow electrode solution. A phosphorus-rich solution is reacted with a ferrous solution under an oxygen-free condition to generate vivianite [Fe.sub.3(PO.sub.4).sub.2.Math.8H.sub.2O].