Transport of copper ions through nanocomposite chitosan/polyvinyl alcohol thin adsorptive membranes has been mathematically investigated in the current study. Unsteady-state diffusive transport model was coupled with the Freundlich isotherm to predict the concentration of the ions in dialysis permeation operation. Pristine model was not successful in predicting the experimental data based upon its low coefficients of determination (0.1 < R-2 < 0.65). Well-behaved polynomial and exponential functions were used to describe time-dependency of the inlet-concentration in the first extension of themodel with a little improvement in the model adjustment (0.4 < R-2 < 0.69). Similar time-dependent functions were employed for tracking the ion diffusivity and then applied in combination with the optimized functions of inlet-concentration in the second extension of the model. A sensible enhancement was obtained in the adjustment of the second extended models as a result of this combination (0.73 < R-2 < 0.93). APRE, AAPRE, RSME, RMSE, STD and R-square statistical analyses were performed to verify the agreement of the models with the experimental results. Concentration distribution versus time and location (inside the membrane) was obtained as 3D plots with the help of the optimized models. Modeling results emphasized on the transiency of diffusivity and feed-side concentration in dialysis permeation through chitosan membranes. (C) 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.