Cake washing of freely mobile ions was described by an advection-dispersion equation combined with the Donnan equilibrium and an overall ion transfer model between the external liquid phase and the fiber phase of kraft pulp. The ion exchange rate coefficients between the phases were determined from the earlier published leaching test results for an oxygen delignified Scandinavian hardwood kraft pulp. The time constant of the first order process model was about 19 s for calcium and manganese and about 6 s for sodium and magnesium. The calculated results for various elements during the acid displacement were compared with the published displacement experiments. Calculated concentrations and pH profiles in wash effluent and cake were shown. Moreover, changes in pH values and redistribution of ions between the external phase and the fiber phase in the cake during the acid displacement were also demonstrated. (c) 2005 Elsevier Ltd. All rights reserved.