References

  1. J. Kheriji, D. Tabassi, B. Hamrouni, Removal of Cd(II) ions from aqueous solution and industrial effluent using reverse osmosis and nanofiltration membranes, Water Sci. Technol., 72 (2015) 1206–1216.
  2. H. Al-Zoubi, N. Hilal, N.A. Darwish, A.W. Mohammad Rejection and modelling of sulphate and potassium salts by nanofiltration membranes: neural network and Spiegler–Kedem model, Desalination, 206 (2007) 42–60.
  3. A.M. Hidalgo, G. Leon, M. Gomez, M.D. Murcia, E. Gomez, J.L. Gomez, Application of the Spiegler–Kedem–Kachalsky model to the removal of 4-chlorophenol by different nanofiltration membranes, Desalination, 315 (2013) 70–75.
  4. Z.V.P. Murthy, L.B. Chaudhari, Separation of binary heavy metals from aqueous solutions by nanofiltration and characterization of the membrane using Spiegler–Kedem model, J. Chem. Eng., 150 (2009) 181–187.
  5. A.L. Ahmad, M.F. Chong, S. Bhatia, Mathematical modeling and simulation of the multiple solutes system for nanofiltration process, J. Membr. Sci., 253 (2005) 103–115.
  6. L. Malaeb, G.M. Ayoub, Reverse osmosis technology for water treatment: state of the art review, Desalination, 267 (2011) 1–8.
  7. A. Suárez, F.A. Riera Using the Spiegler–Kedem model to predict solute rejection in the treatment of industrial UHT condensates by reverse osmosis, Desal. Water Treat., 57 (2016) 24176–24186.
  8. O. Kedem, A. Katchalsky, Thermodynamic analysis of the permeability of biological membranes
    to non-electrolytes, Biochem. Biophys. Acta, 27 (1958) 229–246.
  9. S. Jain, S.K. Gupta, Analysis of modified surface force pore flow model with concentration polarization and comparison with Spiegler–Kedem model in reverse osmosis systems, J. Membr. Sci., 232 (2004) 45–62.
  10. J.J. Wu, On the application of the Spiegler–Kedem model to forward osmosis, BMC Chem. Eng., 1 (2019) 1–15.
  11. J.J. Wu, R.W. field, On the understanding and feasibility of “Breakthrough” osmosis, Sci. Rep., 9 (2019) 16464, doi: 10.1038/s41598-019-53417-6.
  12. I. Koyuncu, M. Yazgan, Application of nanofiltration and reverse osmosis membranes to the salty and polluted surface water, J. Environ. Sci. Health. Part A Toxic/Hazard. Subst. Environ. Eng., 36 (2000) 1321–1333.
  13. C. Rodrigues, A.I. Cavaco Morão, M.N. de Pinho, V. Geraldes, On the prediction of permeate flux for nanofiltration of concentrated aqueous solution with thin-film composite polyamide membranes, J. Membr. Sci., 346 (2010) 1–7.
  14. Z.V.P. Murthy, S.K. Gupta, Estimation of mass transfer coefficient using a combined nonlinear membrane transport and film theory model, Desalination, 109 (1997) 39–49.
  15. J. Gilron, N. Gara, O. Kedem, Experimental analysis of negative salt rejection in nanofiltration membranes, J. Membr. Sci., 185 (2001) 223–236.
  16. W.R. Bowen, J.S. Welfoot, Modeling the performance of membrane nonofiltration-critical assessment and model development, Chem. Eng. Sci., 57 (2002) 1121–1137.
  17. S.Y. Vaidya, A.V. Simaria, Z.V.P Murthy, Reverse osmosis transport model evaluation: a new approach, Indian Chem. Eng., 8 (2001) 335–343.
  18. A.M. Hidalgo, G. León, M. Gómez, M.D. Murcia, E. Gómez, J.L. Gómez, Application of the Spiegler–Kedem–Kachalsky model to the removal of 4-chlorophenol by different nanofiltration membranes, Desalination, 315 (2013) 70–75.
  19. F. Ahmed, Modified Spiegler–Kedem Model to Predict the Rejection and Flux of Nanofiltration Processes at High NaCl Concentrations, MSc. Thesis, University of Ottawa, 2013.
  20. A.E. Yaroshchuc, Solution–diffusion–imperfection model revised, J. Membr. Sci., 101 (1995) 83–87.