Why is the film model fundamentally wrong but still able to correlate the experimental data in membrane processes?

The film model that predicts a logarithmic dependence of permeate velocity on feed solute concentration in membrane separation processes is fundamentally wrong because the primary mass balance equation in the model is inapplicable to the total solute. Based on mass balance relationships on the retained solute, The permeate velocity in crossflow membrane separation processes can be rigorously shown to be a cube root function of the retained solute concentration. Furthermore, the reported good fitness of the film model to the experimental permeate velocities can be shown just to be a delusion of curve fitting mainly due to the adjustable parameters in the model.