A systematic model-based approach is used for development of an efficient carousel ion-exchange process for the selective removal of radioactive Cs-137(+) from alkaline nuclear waste solutions. Equilibrium data for two resorcinol-formaldehyde (R-F) cation-exchange resins are correlated by an empirical equation of the Freundlich-Langmuir type over cesium/sodium concentration ratios of 10(-9) to 10(-2) and sodium concentrations of 1 to 6 N. The standard deviations are 3.5 and 6.6%, respectively. The data cannot be accurately described by mass action equations. A detailed rate model, developed in this study for the periodic countercurrent multicolumn operation of carousel systems, is used with the equilibrium correlations to simulate cesium breakthrough curves from R-F resin columns. Results show that accuracy of the predicted breakthrough curves are directly related to the accuracy of the isotherm data and correlations. Cesium breakthrough position is generally predicted to within 5% or less far 10 of 13 runs over linear superficial velocities of 0.16 to 8.8 cm/min, column lengths of 3.14 to 118.5 cm, and particle radii of 145 to 200 mu m. One run shows later breakthrough than predicted as a result of a low potassium concentration in the feed. Two other runs show early breakthroughs as a result of channeling in poorly packed columns of a carousel system. Despite the channeling, strong thermodynamic self-sharpening effects helped establish constant pattern waves in the downstream columns. A case study for a pilot-scale carousel unit shows that 100% utilization of cesium capacity and maximum throughput can be achieved while containing the mass transfer zone within the downstream columns. Since intraparticle diffusion controls spreading of the breakthrough curves, reducing the particle radius from 200 to 145 mu m increases throughput by 40%.