Phosphoric acid sludge contains acid (similar to 54% P2O5) and solid precipitates including rare earth elements (REEs) at concentrations of similar to 2200 ppm. Low-cost recovery of valuable P2O5 and simultaneous solid separation could be an economically feasible approach to recovering REEs while increasing the production of phosphoric acid. The sludge, however, is a complicated stream that cannot be separated by traditional technologies because of high viscosity and a large solid content (30-40%). Guided by a force balance model, an efficient solid/liquid separation method is demonstrated, using a continuous-flow centrifugal contactor. The shear regime is bypassed by introducing the sludge directly into the rotor where a centrifugal force is exerted on the fluid, inducing phase separation. Solid particles are trapped in the contactor. High liquid recovery is demonstrated and the effects of process parameters on solid capture are investigated. Three contactors in series yield 94% recovery of solids containing 1500-2895 ppm of REEs.