References

1. Y. Demirel, V. Gerbaud, Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems, Elsevier, Amsterdam, 2014.
2. M. Aguilella-Arzo, M. Queralt-Martín, M.-L. Lopez, A. Alcaraz, Fluctuation-driven transport in biological nanopores. A 3D Poisson–Nernst–Planck study, Entropy, 19 (2017) e19030116.
3. Z. Siwy, F. Fornasiero, Improving on aquaporins, Science, 357 (2017) 753
4. B.Y. Huang, H.K. Wang, B.X. Yang, Water Transport Mediated by Other Membrane Proteins, B.X. Young, Ed., Aquaporins. Advances in Experimental Medicine and Biology, Vol. 969, Springer, Dordrecht, 2017, pp. 251–261.
5. V.V. Nikonenko, A.V. Kovalenko, M.K. Urtenov, N.D. Pismenskaya, J.Y. Han, P. Sistat, G. Pourcelly, Desalination at overlimiting currents: state-of-the-art and perspectives, Desalination, 342 (2014) 85–106.
6. S.J. Park, H.J. Kim, D.H. Seol, T.J. Park, M. Leem, H.W. Ha, H.S. An, H. You Kim, S.-J. Jeong, S.J. Park, H.S. Kim, Y.S. Kim, Evenly transferred single-layered graphene membrane assisted by strong substrate adhesion, Nanotechnology, 28 (2017) 145706.
7. A. Katchalsky, P.F. Curran, Nonequilibrium Thermodynamics in Biophysics, Harvard, Cambridge, 1965.
8. H.Y. Elmoazzen, J.A.W. Elliot, L.E. McGann, Osmotic transport across cell membranes in nondilute solutions: a new nondilute solute transport equation, Biophys. J., 96 (2009) 2559–2571.
9. O. Kedem, A. Katchalsky, Thermodynamic analysis of the permeability of biological membranes to non-electrolytes, Biochim. Biophys. Acta, 27 (1958) 229–246.
10. I.W. Richardson, E.A.D. Foster, S. Miękisz, Nonlinear generalizations of the Kedem–Katchalsky equations for ionic fluxes, Bull. Math. Biol., 44 (1982) 761–775.
11. X. Cheng, P.M. Pinsky, The balance of fluid and osmotic pressures across active biological membranes with application to the corneal endothelium, PLoS One, 10 (2015) e0145422.
12. S.S.S. Cardoso, J.H.E. Cartwright, Dynamics of osmosis in a porous medium, R. Soc. Open Sci., 1 (2017) 140352.
13. A. Kargol, A mechanistic model of transport processes in porous membranes generated by osmotic and hydrostatic pressure, J. Membr. Sci., 191 (2001) 61–69.
14. M. Kargol, A. Kargol, Mechanistic formalism for membrane transport generated by osmotic and mechanical pressure, Gen. Physiol. Biophys., 22 (2003) 51–68.
15. L. Peusner, Studies in Network Thermodynamics, Elsevier, Amsterdam, 1986.
16. O. Kedem, S.R. Caplan, Degree of coupling and its relation to efficiency of energy conversion, Trans. Faraday Soc., 61 (1965) 1897–1911.
17. K.M. Batko, I. Ślęzak-Prochazka, S. Grzegorczyn, A. Ślęzak, Membrane transport in concentration polarization conditions: network thermodynamics model equations, J. Porous Media, 17 (2014) 573–586.
18. K.M. Batko, I. Ślęzak-Prochazka, A. Ślęzak, Network form of the Kedem–Katchalsky equations for ternary non-electrolyte solutions. 2. Evaluation of Lij Peusner’s coefficients for polymeric membrane, Polim. Med., 43 (2013) 103–109.
19. A. Ślęzak, S. Grzegorczyn, K.M. Batko, Resistance coefficients of polymer membrane with concentration polarization, Transp. Porous Media, 95 (2012) 151–170.
20. K.M. Batko, I. Ślęzak-Prochazka, A. Ślęzak, Network hybrid form of the Kedem–Katchalsky equations for non-homogenous binary non-electrolyte solutions: evaluation of Pij * Peusner’s tensor coefficients, Transp. Porous Media, 106 (2015) 1–20.
21. I. Ślęzak-Prochazka, K.M. Batko, S. Wąsik, A. Ślęzak, H* Peusner’s form of the Kedem–Katchalsky equations for on-homogeneous non-electrolyte binary solutions, Transp. Porous Media, 111 (2016) 457–477.
22. K.M. Batko, A. Ślęzak, Membrane transport of non-electrolyte solutions in concentration polarization conditions: Hr form of the Kedem–Katchalsky–Peusner equations, Int. J. Chem. Eng., 2019 (2019) 10 pages, https://doi.org/10.1155/2019/5629259.
23. A. Ślęzak, Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane, Biophys. Chem., 34 (1989) 91–102.
24. A. Ślęzak, S. Grzegorczyn, J. Jasik-Ślęzak, K. Michalska-Małecka, Natural convection as an asymmetrical factor of the transport through porous membrane, Transp. Porous Media, 84 (2010) 685–698.
25. K. Dworecki, A. Ślęzak, B. Ornal-Wąsik, S. Wąsik, Effect of hydrodynamic instabilities on solute transport in a membrane system, J. Membr. Sci., 265 (2005) 94–100.
26. J.S. Jasik-Ślęzak, K.M. Olszówka, A. Ślęzak, Estimation of thickness of concentration boundary layers by osmotic volume flux determination, Gen. Physiol. Biophys., 30 (2011) 186–195.
27. A. Ślęzak, K. Dworecki, I.H. Ślęzak, S. Wąsik, Permeability coefficient model equations of the complex: membraneconcentration boundary layers for ternary non-electrolyte solutions, J. Membr. Sci., 267 (2005) 50–57.
28. A. Ślęzak, K. Dworecki, J. Jasik-Ślęzak, J. Wąsik, Method to determine the critical concentration Rayleigh number in isothermal passive membrane transport processes, Desalination, 168 (2004) 397–412.
29. A. Ślęzak, K. Dworecki, J.E. Anderson, Gravitational effects on transmembrane flux: the Rayleigh—Taylor convective instability, J. Membr. Sci., 23 (1985) 71–81.
30. K. Dworecki, S. Wąsik, A. Ślęzak, Temporal and spatial structure of the concentration boundary layers in a membrane system, Physica A, 326 (2003) 360–369.
31. G. Lebon, D. Jou, J. Casas-Vasquez, Understanding Non- Equilibrium Thermodynamics. Foundations, Applications, Frontiers, Springer, Berlin, 2008.
32. M. Bodzek, Chapter 15 – Membrane Technologies for the Removal of Micropollutants in Water Treatment, A. Basile, A. Cassano, N.K. Rastogi, Eds., Advances in Membrane Technologies for Water Treatment: Materials, Processes and Applications, Elsevier Science, Woodhead Publishing Ltd., Cambridge, 2015, pp. 465–517.
33. M. Bodzek, M. Dudziak, K. Luks-Betlej, Application of membrane techniques to water purification. Removal of phthalates, Desalination, 162 (2004) 121–128.
34. K. Mielczarek, J. Bohdziewicz, M. Włodarczyk-Makuła, M. Smol, Modeling performance of commercial membranes in the low-pressure filtration coking wastewater treatment based on mathematical filtration models, Desal. Water Treat., 52 (2014) 3743–3752.
35. M. Dudziak, M. Bodzek, A study of selected phytoestrogens retention by reverse osmosis and nanofiltration membranes - the role of fouling and scaling, Chem. Pap., 64 (2010) 139–146.
36. M. Wilf, L. Awerbuch, G. Pearce, C. Bartels, M. Mickley, N. Voutchkov, Membrane Desalination Technology, Balaban Desalination Publications, L’Aquila, Italy, 2006.