**5. Conclusions**

The main goal of the performed computer-aided simulations was to estimate the membrane surface charge densities with the use of the comprehensively described Donnan–Steric partitioning model, which is derived from the extended Nernst–Planck equation with Donnan partitioning assumption. The obtained total volume membrane charge densities *Xd* are consistent with experimental values of retention. Values such as charge density of the membrane are very important for explanation of the mechanism of ions transport across the membrane, defining retention, and describing influences on electrostatic repulsion between ions and membrane.

The presented work can be summarized in the following points: (1) separation of organic acids, such as succinic acid, on the ceramic membrane is affected by the acid concentration and the type of used pH regulator; (2) experiments clearly show that increase of the concentration of components can decrease the retention of separated components (MS1 and MS2); (3) use of a different pH regulator can dramatically change the performance of the separation (MS1 and MS3); (4) in case of low succinic acid concentration, the membrane functional group (-TiO2) dissociation has the greatest impact on the charge formation, whereas in case of higher succinic acid concentrations, it is postulated that the charge formation is determined by adsorption of specific ions on the membrane active layer; (5) defining separation performance at certain pH can be totally different in the vicinity of other components or impurities; (6) detailed description of experiments is required in order to compute *Xd*, even reporting the amount of added pH regulator; (7) including all components in mathematical modeling can allow for better understanding of nanofiltration separation.

Based on the obtained results and authors knowledge, it is impossible to state which modeling approach is the best, however it is clear to recommend the comprehensively described Donnan–Steric partitioning model to analyze the separation of multicomponent mixtures as it gives reasonable results and takes into account all components present in the mixture.

**Author Contributions:** Conceptualization, A.M.-M., P.T.M. and K.P.; Methodology, K.P., P.T.M., and J.R.; Modeling and simulation, A.M.-M.; Validation, A.M.-M. and P.T.M.; Experimental investigation, A.M.-M. and J.A.; Resources, K.P. and J.R.; Writing—original draft preparation, A.M.-M.; Writing—review and editing, A.M.-M., P.T.M., K.P., and J.R.; Supervision, P.T.M.

**Funding:** This research was supported by the Ministry of Science and Higher Education in Poland subsidy for Poznan University of Technology, Faculty of Chemical Technology (grant nos. 03/32/SBAD/0902 and 03/32/SBAD/0901).

**Conflicts of Interest:** The authors declare no conflict of interest.
