References

  1. R. Baker, Membrane Technology and Application, John Wiley & Sons, New York, 2012.
  2. S.V. Jadhav, K.V. Marathe, V.K. Rathod, A pilot scale concurrent removal of fluoride, arsenic, sulfate and nitrate by using nanofiltration: competing ion interaction and modelling approach, J. Water Process Eng., 13 (2016) 153–167.
  3. T. Uragami, Science and Technology of Separation Membranes, John Wiley & Sons, Chichester, UK, 2017.
  4. Y. Dermirel, Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems, Elsevier, Amsterdam, 2007.
  5. V. Gerbaud, N. Shcherbakova, S. Da Cunha, A nonequilibrium thermodynamics perspective on nature-inspired chemical engineering processes, Chem. Eng. Res. Des., 154 (2020) 316–330.
  6. S. Raghuvanshi, B. La Prairie, S. Rajagopal, V.G. Yadav, Chapter 11 – Polymeric Nanomaterials for Ocular Drug Delivery, A.K. Bajpai, R.K. Saini, Eds., Advances in Polymeric Nanomaterials for Biomedical Applications: Micro and Nano Technologies, Elsevier, Amsterdam, 2021.
  7. J. Rewak-Soroczynska, P. Sobierajska, S. Targonska, A. Piecuch, L. Grosman, J. Rachuna, S. Wasik, M. Arabski, R. Ogorek, R.J. Wiglusz, New approach to antifungal activity of fluconazole incorporated into the porous
    6-anhydro-α-l-galacto-β-dgalactan structures modified with nanohydroxyapatite for chronic-wound treatments-in vitro evaluation, Int. J. Mol. Sci., 22 (2021) 3112, doi: 10.3390/ijms22063112.
  8. D. Rana, T. Matsuura, S. Sourirajan, Physicochemical and Engineering Properties of Food in Membrane Separation Processes, M.A. Rao, S.S.H. Rizvi, A.K. Datta, J. Ahmed, Eds., Engineering Properties of Foods, Taylor & Francis/CRC Press, Boca Raton, FL, 2014, pp. 437–525.
  9. D. Rana, T. Matsuura, State of the art reviews in membrane science and research, J. Membr. Sci. Res., 3 (2017) 118–119.
  10. D. Rana, T. Matsuura, Membrane Transport Models, D.R. Heldman, C.I. Moraru, Eds., Encyclopedia of Agriculture, Food and Biological Engineering, Taylor & Francis, New York, NY, 2010, pp. 1041–1047.
  11. D. Rana, T. Matsuura, M.A. Kassim, A.F. Ismail, Reverse Osmosis Membrane, A.K. Pabby, S.S.H. Rizvi, A.M. Sastre, Eds., Handbook of Membrane Separations: Chemical, Pharmaceutical, Food, and Biotechnological Applications, Taylor & Francis/CRC Press, Boca Raton, FL, 2015, pp. 35–52.
  12. A. Katchalsky, P.F. Curran, Nonequilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge, MA, USA, 1965.
  13. D. Kondepudi, I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wiley & Sons, Chichester, 2006.
  14. J.G. Wijmans, R.W. Baker, The solution–diffusion model: a review, J. Membr. Sci., 107 (1995) 1–21.
  15. M.A. Al-Obaidi, C. Kara-Zaitri, I.M. Mujtaba, Scope and limitation of the irreversible thermodynamics and the solution diffusion models for the separation of binary and multicomponent systems in reverse osmosis process, Comput. Chem. Eng., 100 (2017) 48–79.
  16. K.S. Spiegler, Transport processes in ionic membranes, Trans. Faraday Soc., 54 (1958) 1408–1428.
  17. O. Kedem, A. Katchalsky, A physical interpretation of the phenomenological coefficients of membrane permeability, J. Gen. Physiol., 45 (1961) 143–179.
  18. A. Ślęzak, A frictional interpretation of the phenomenological coefficients of membrane permeability for multicomponent, non-ionic solutions, J. Biol. Phys., 23 (1997) 239–250.
  19. M.H. Friedman, R.A. Meyer, Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. I. Inequality of reflection coefficients for volume flow and solute flow, Biophys. J., 34 (1981) 535–544.
  20. E.A. Mason, H.K. Lonsdale, Statistical-mechanical theory of membrane transport, J. Membr. Sci., 51 (1990) 1–81.
  21. 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, doi: 10.1371/journal.pone.0145422.
  22. L. Peusner, The Principles of Network Thermodynamics: Theory and Biophysical Applications, Ph.D. Thesis, Harvard University, Cambridge, MA, USA, 1970.
  23. G. Oster, A. Perelson, A. Katchalsky, Network thermodynamics, Nature, 234 (1971) 239–399.
  24. L. Peusner, Hierarchies of irreversible energy conversion systems: a network thermodynamic approach. I. Linear steady state without storage, J. Theor. Biol., 10 (1983) 27–39.
  25. L. Peusner, Hierarchies of irreversible energy conversion systems. II. Network derivation of linear transport equations, J. Theor. Biol., 115 (1985) 319–335.
  26. L. Peusner, Network representation yielding the evolution of Brownian motion with multiple particle interactions, Phys. Rev. A, 32 (1985) 1237–1238.
  27. L. Peusner, D.C. Mikulecky, B. Bunow; S. Roy Caplan, A network thermodynamic approach to Hill and King–Altman reaction– diffusion kinetics, J. Chem. Phys., 83 (1985) 5559–5566.
  28. L. Peusner, Studies in Network Thermodynamics, Elsevier, Amsterdam, 1986.
  29. L. Peusner, Hierarchies of energy conversion processes III. Why are Onsager equations reciprocal? The euclidean geometry of fluctuation–dissipation space, J. Theor. Biol., 122 (1983) 125–155.
  30. L. Peusner, Premetric thermodynamics. A topological graphical model, J. Chem. Soc., Faraday Trans., 81 (1985) 1151–1161.
  31. A. Ślęzak, S. Grzegorczyn, K.M. Batko, Resistance coefficients of polymer membrane with concentration polarization, Transp. Porous Media, 95 (2012) 151–170.
  32. 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.
  33. I. Ślęzak-Prochazka, K.M. Batko, S. Wąsik, A. Ślęzak, H* Peusner’s form of the Kedem–Katchalsky equations for nonhomogenous non-electrolyte binary solutions, Transp. Porous Media, 111 (2016) 457–477.
  34. 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.
  35. 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) 5629259, doi: 10.1155/2019/5629259.
  36. M. Kargol, A. Kargol, Mechanistic equations for membrane substance transport and their identity with Kedem–Katchalsky equations, Biophys. Chem., 103 (2003) 117–127.
  37. 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.
  38. J. Meixner, Thermodynamics of electrical networks and Onsager–Casimir reciprocal relations, J. Math. Phys., 4 (1963) 154–159.
  39. A. Ślęzak, S. Grzegorczyn, K.M. Batko, W.M. Bajdur, M. Włodarczyk-Makuła, M. Applicability of the Lr form of the Kedem–Katchalsky–Peusner equations for membrane transport in water purification technology, Desal. Water Treat., 202 (2020) 48–60.
  40. K.M. Batko, A. Ślęzak, S. Grzegorczyn, W.M. Bajdur, The Rr form of the Kedem–Katchalsky–Peusner model equations for description of the membrane transport in concentration polarization conditions, Entropy, 22 (2020) 857, doi: 10.3390/ e22080857.
  41. K. Batko, I. Ślęzak-Prochazka, A. Ślęzak, W.M. Bajdur, M. Makuła-Włodarczyk, Management of energy conversion processes in membrane system, Energies, 15 (2022) 1661, doi: 10.3390/en15051661.
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. A. Ślęzak, Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane, Biophys. Chem., 34 (1989) 91–102.
  47. 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.
  48. A. Ślęzak, K. Dworecki, J.E. Anderson, Gravitational effects on transmembrane flux: the Rayleigh—Taylor convective instability, J. Membr. Sci., 23 (1985) 71–81.
  49. H. Klinkman, M. Holtz, W. Wilgerodt, G. Wilke, D. Schoenfelder, Nephrophan–Eine neue dialysemembranen, Z. Urol. Nephrol., 62 (1969) 285–292.
  50. T. Richter, S. Keipert, In vitro permeation studies comparing bovine nasal mucosa, porcine cornea and artificial membrane: androstenedione in microemulsions and their components, Eur. J. Pharm. Biopharm., 58 (2004) 137–143.
  51. Th. F. Vandamme, Microemulsions as ocular drug delivery systems: recent developments and future challenges, Prog. Retin. Eye Res., 21 (2002) 15–34.
  52. O. Kedem, S.R. Caplan, Degree of coupling and its relation to efficiency of energy conversion, Trans. Faraday Soc., 61 (1965) 1897–1911.
  53. S. Bason, O. Kedem, V. Freger, Determination of concentrationdependent transport coefficients in nanofiltration: experimental evaluation of coefficients, J. Membr. Sci., 310 (2008) 326–204.
  54. I. Ślęzak-Prochazka, K.M. Batko, A. Ślęzak, evaluation of transport properties and energy conversion of bacterial cellulose membrane using Peusner network thermodynamics, Entropy, 25 (2023) 3, doi: 10.3390/e25010003.
  55. K. Dworecki, Interferometric investigation of near-membrane diffusion layers, J. Biol. Phys., 21 (1995) 37–49.
  56. 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.
  57. K. Dworecki, A. Ślęzak, M. Drabik, B. Ornal-Wąsik, S. Wąsik, Determination of the membrane permeability coefficient under concentration polarisation conditions, Desalination, 198 (2006) 326–334.