Approximations for intraparticle diffusion rates in cyclic adsorption and desorption

Numerical solutions of the intraparticle diffusion equation subjected to cyclic adsorption/desorption are compared with predictions by three approximations: Glueckauf's LDF, the Nakao-Suzuki LDF and the extended LDF. Glueckauf's LDF contains no empirical parameter, whereas each of the other two contains one empirical parameter. The practically important range of the half-cycle time of θ_c = 0.001-1 is considered. It is shown that only the extended LDF yields correct predictions for the instantaneous intraparticle diffusion rates as well as the correct instantaneous amounts adsorbed. The extended LDF is also capable of predicting the interesting phenomenon of the existence of two fluxes in opposite directions within the particle shortly after the step change (and hence the existence of a counterproductive region).