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Current assumptions are used in the formulation of pseudo-first (PFO) and second-order (PSO) models to describe the kinetic data of filtration based on ideal operating conditions. This paper presents a new model developed with pseudo  order and based on real assumption. A comparison was performed between PFO, PSO and the new model to highlight their performance and the optimisation of the pseudo-order equation, using MATLAB software. Adsorption characteristic of bovine serum albumin adsorption on the track-etched membrane are used as a medium based on protein filtration data were extracted from the literature for different concentrations to demonstrate the comparison between PFO/PSO and the new model. The pseudo first and second-order kinetic models were applied to test the experimental data and they did not provide reasonable values. The results show that the predicted values are consistent with experimental values giving a good correlation coefficient R = 0.997 and a minimum root mean squared error RMSE = 0.0171. Indeed, the experimental results follow the new model and the optimal pseudo equation order  = 1.115, the most suitable curves for the new model. As a result, we used different experimental adsorption data from the literature to examine and check the applicability and validity of the model.

Novel adsorption model of filtration process in polycarbonate track-etched membrane: Comparative study