CALCULATION OF THE HELFFERICH NUMBER TO IDENTIFY THE RATE-CONTROLLING STEP OF ION-EXCHANGE FOR A BATCH PROCESS

The Helfferich number He is used frequently as a valuable criterion to decide whether for an ion exchange process film diffusion or particle diffusion of the ions is the rate-determining step. The corresponding equation given by Helfferich is restricted, however, for the boundary condition of an infinite solution volume. In the present paper, the Helfferich number is calculated also for a finite solution volume, i.e., for a typical batch process. Because the resulting equation can be solved only numerically, the results are presented in graphical form. It is also examined for which batch processes the conventional Helfferich number already yields a conservative and thus a very simple and useful estimate of the rate-determining step.