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The separation efficiencies of aqueous solutions containing nitric salts of Zn, Cu, Fe or Pb at various pH in process of nanofiltration have been investigated experimentally. These results were used to obtain the total volume membrane charge densities, through mathematical modelling based on the Donnan–Steric partitioning Model. The experimentally obtained retention values of individual heavy metal ions varied between 36% (Zn2+ at pH = 2), 57% (Pb2+ at pH = 2), 80% (Fe3+ at pH = 9), and up to 97% (Cu2+ at pH = 9). The mathematical modelling allowed for fitting the total volume membrane charge density (Xd), which yielded values ranging from −451.90 to +900.16 mol/m3 for different non-symmetric ions. This study presents the application of nanofiltration (NF) modelling, including a consideration of each ion present in the NF system—even those originating from solutions used to adjust the pH values of the feed.

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Nanofiltration of aqueous solutions of succinic acid with the addition of sodium hydroxide or magnesium hydroxycarbonate has been investigated experimentally and modeled with the comprehensively described Donnan-Steric partitioning model. The experimental retentions of acid at the same pH varied between 16% and 78%, while the estimated total volume membrane charge densities were in the range of −35.73 and +875.69 mol/m 3 . This work presents a novel insight into the modeling of nanofiltration and investigates the relations between the estimated total volume membrane charge densities, ionic strength, and component concentration on the performance of ceramic membrane. In addition, this study takes into consideration other parameters such as pH regulation and viscosities of solutions.

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The study presents results of rheological tests and measurements of pressure drops occurring during the flow of aqueous solutions of a mixture of drag reducing surfactants: cocamidopropyl betaine (CAPB, zwitterionic surfactant) and cocamide DEA (nonionic surfactant) through straight pipes. Tests were carried out at different CAPB/DEA weight ratios and different total concentrations of surfactants in the solution. Rheological measurements demonstrate the formation of a shear-induced structure (SIS) in the temperature range below 10 °C, which provides evidence for the presence of wormlike micelles in CAPB/DEA solutions. Drag reduction was observed during the flow of CAPB/DEA solutions in the temperature range from 3 to 45 °C, however, above 25 °C the degree of drag reduction was markedly decreased. The lower temperature limit at which drag reduction occurs depends on the CAPB and DEA weight ratio in the solution. In the range of higher temperatures, during the flow of CAPB/DEA solutions (similarly to flexible-chain polymer solutions) the onset of drag reduction is noted above a certain critical value of the Rec,0 number, whose value depends on the temperature of the solution, diameter of the pipe and the weight ratio of surfactants. At the same time, the critical value of wall shear stress τw,c0 corresponding to the critical value of Rec,0 is approximately independent of pipe diameter. The critical value of the Rec,0 number has been linked to the clouding of CAPB/DEA solutions.

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