An asymptotically exact nonlinear driving force model of intra-particle mass-transfer rate for nonlinear isotherm systems with macropore diffusion control is presented. The obtained expression is compared with the solutions of the Fickian diffusion and adsorption model and excellent accuracy over the entire time (fractional uptake) domain is demonstrated. In the case of an irreversible isotherm the model reduces to the equations resulting from the shrinking core model a fact that guarantees its accuracy for highly nonlinear systems. The high accuracy of the model is further demonstrated by comparison with experimental data under various operational conditions. (C) 2004 Elsevier Ltd. All rights reserved.