Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter August 25, 2020

Membrane Transport in Concentration Polarization Conditions: Evaluation of S-Entropy Production for Ternary Non-Electrolyte Solutions

  • Andrzej Ślęzak ORCID logo , Sławomir Grzegorczyn ORCID logo EMAIL logo , Kornelia M. Batko ORCID logo , Wiesław Pilis and Robert Biczak

Abstract

A model of the S-entropy production in a system with a membrane which separates non-electrolyte aqueous solutions was presented. The differences between fluxes in non-homogeneous and homogeneous conditions for volume and solute fluxes, respectively, are non-linear functions of the glucose osmotic pressure difference (OPD) in ranges dependent on the initial ethanol OPD. A decrease of ethanol OPD causes a shift of this range into the lower values of glucose OPD; this shift is also observed for negative values of glucose and ethanol OPDs. The coefficient of concentration polarization of the membrane as a function of glucose OPD has a sigmoidal shape. For suitably great negative values of glucose OPD this coefficient is very small, while for suitably high positive glucose OPD this coefficient is equal to 0.5. An increase of ethanol OPD at the initial moment causes a shift of this curve towards the direction of positive values of glucose OPD. In turn the S-entropy production in non-homogeneous conditions has low values for negative values of glucose OPD (convective range) while for suitably high positive glucose OPD it has greater values (diffusive and convective range). A change of ethanol OPD at the initial moment causes a shift of this curve along the horizontal axis.


Article note

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


  1. Conflict of interest: None declared.

References

[1] Katchalsky and P. F. Curran, Nonequilibrium Thermodynamics in Biophysics, Harvard, Cambridge, 1965.10.4159/harvard.9780674494121Search in Google Scholar

[2] G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations, Wiley-Interscience, New York, 1977.Search in Google Scholar

[3] Y. Demirel, Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical and Biological System, Elsevier, Amsterdam, 2002.10.1016/B978-044450886-7/50002-3Search in Google Scholar

[4] D. Kondepudi, Introduction to Modern Thermodynamics, J Wiley & Sons, Chichester, 2008.Search in Google Scholar

[5] L. M. Martyushev and V. D. Seleznev, Maximum entropy production principle in physics, chemistry and biology, Phys. Rep.426 (2006), no. 1, 1–45.10.1016/j.physrep.2005.12.001Search in Google Scholar

[6] L. Peusner, Studies in Network Thermodynamics, Elsevier, Amsterdam, 1986.Search in Google Scholar

[7] T. Tome and M. J. Oliveira, Entropy production in nonequilibrium systems at stationary state, Phys. Rev. Lett.108 (2012), 020601.10.1103/PhysRevLett.108.020601Search in Google Scholar

[8] S. R. De Groot and P. Mazur, Non-Equilibrium Thermodynamics, Dover, New York, 1984.Search in Google Scholar

[9] M. Delmotte and J. Chanu, Non-equilibrium thermodynamics and membrane potential measurement in biology, in: G. Millazzo, editor, Topics Bioelectrochemistry and Bioenergetics, John Wiley Publish & Sons, Chichester, (1979), 307–359.Search in Google Scholar

[10] B. Z. Ginzburg and A. Katchalsky, The frictional coefficients of the flows of non-electrolytes through artificial membranes, J. Gen. Physiol.47 (1963), no. 2, 403–418.10.1085/jgp.47.2.403Search in Google Scholar

[11] A. Ślęzak, K. Dworecki and J. A. Anderson, Gravitational effects on transmembrane flux: The Rayleigh–Taylor convective instability, J. Membr. Sci.23 (1985), no. 1, 71–81.10.1016/S0376-7388(00)83135-XSearch in Google Scholar

[12] A. Ślęzak, Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane, Biophys. Chem.34 (1989), no. 2, 91–102.10.1016/0301-4622(89)80047-XSearch in Google Scholar

[13] S. Przestalski and M. Kargol, Graviosmotic volume flow through membrane systems, Stud. Biophys.34 (1972), no. 1, 7–14.Search in Google Scholar

[14] M. Kargol, K. Dworecki and S. Przestalski, Graviosmotic flow amplification effects in a series membrane system, Stud. Biophys.76 (1979), no. 2, 137–144.Search in Google Scholar

[15] K. Dworecki, S. Wąsik and A. Ślęzak, Temporal and spatial structure of the concentration boundary layers in membrane system, Physica A326 (2003) no. 3–4, 360–369.10.1016/S0378-4371(03)00266-8Search in Google Scholar

[16] K. Dworecki, A. Ślęzak, B. Ornal-Wąsik and S. Wąsik, Effect of hydrodynamic instabilities on solute transport in a membrane system, J. Membr. Sci.265 (2005), no. 1–2, 94–100.10.1016/j.memsci.2005.04.041Search in Google Scholar

[17] A. Ślęzak, K. Dworecki, I. H. Ślęzak and S. Wąsik, Permeability coefficient model equations of the complex: membrane-concentration boundary layers for ternary nonelectrolyte solutions, J. Membr. Sci.267 (2005), no. 1–2, 50–57.10.1016/j.memsci.2005.05.023Search in Google Scholar

[18] A. Ślęzak, I. Ślęzak-Prochazka, S. Grzegorczyn and J. Jasik-Ślęzak, Evaluation of S-entropy production in a single-membrane system in concentration polarization conditions, Transp. Porous Media116 (2017), no. 2, 941–957.10.1007/s11242-016-0807-7Search in Google Scholar

[19] A. Ślęzak, S. Grzegorczyn, J. Jasik-Ślęzak and K. Michalska-Małecka, Natural convection as an asymmetrical factor of the transport through porous membrane, Transp. Porous Media84 (2010) no. 3, 685–698.10.1007/s11242-010-9534-7Search in Google Scholar

[20] A. Ślęzak, I. H. Ślęzak and K. M. Ślęzak, Influence of the concentration boundary layers on membrane potential in single-membrane system, Desalination184 (2005), no. 1–3, 113–123.10.1016/j.desal.2005.03.064Search in Google Scholar

[21] A. Kargol, Effect of boundary layers on reverse osmosis through a horizontal membrane, J. Membr. Sci.159 (1999), 177–184.10.1016/S0376-7388(99)00053-8Search in Google Scholar

[22] P. H. Barry and J. M. Diamond, Effects of unstirred layers on membrane phenomena, Physiol. Rev.647 (1984), no. 3, 763–872.10.1152/physrev.1984.64.3.763Search in Google Scholar

[23] J. Jasik-Ślęzak, K. Olszówka and A. Ślęzak, Estimation of thickness of concentration boundary layers by osmotic volume flux determination, Gen. Physiol. Biophys.30 (2011), 186–195.10.4149/gpb_2011_02_186Search in Google Scholar

[24] Y. Demirel and S. I. Sandler, Thermodynamics and bioenergetics, Biophys. Chem.97 (2002), no. 2–3, 87–111.10.1016/S0301-4622(02)00069-8Search in Google Scholar

[25] A. Ślęzak, S. Grzegorczyn and K. M. Batko, Resistance coefficients of polymer membrane with concentration polarization, Transp. Porous Media95 (2012), no. 1, 151–170.10.1007/s11242-012-0038-5Search in Google Scholar

[26] K. Batko, I. Ślęzak-Prochazka, S. Grzegorczyn and A. Ślęzak, Membrane transport in concentration polarization conditions: network thermodynamics model equations, J. Porous Media17 (2014), no. 7, 573–586.10.1615/JPorMedia.v17.i7.20Search in Google Scholar

[27] K. Batko, I. Ślęzak-Prochazka and A. Ślęzak, Network hybrid form of the Kedem–Katchalsky equations for non-homogeneous binary non-electrolyte solutions: evaluation of Pij Peusner’s coefficients, Transp. Porous Media106 (2015), no. 1, 1–20.10.1007/s11242-014-0352-1Search in Google Scholar

[28] S. Grzegorczyn, A. Ślęzak, K. Michalska-Małecka and I. Ślęzak-Prochazka, Conditions of hydrodynamic instability appearance in fluid thin layers with changes in time thickness and density gradient, J. Non-Equilib. Thermodyn.37 (2012), no. 1, 77–99.10.1515/jnetdy.2011.027Search in Google Scholar

[29] S. Grzegorczyn and A. Ślezak, Time characteristics of electromotive force in single-membrane cell for stable and unstable conditions of reconstructing of concentration boundary layers, J. Membr. Sci.280 (2006), no. 1–2, 485–493.10.1016/j.memsci.2006.02.004Search in Google Scholar

[30] J. de Valenca, M. Jogi, R. M. Wagterveld, E. Karatay, J. A. Wood and R. G. H. Lammertink, Cobfined electroconvective vortices at structured ion exchange membranes, Langmuir34 (2018), no. 7, 2455–2463.10.1021/acs.langmuir.7b04135Search in Google Scholar PubMed PubMed Central

[31] V. V. Nikonenko, A. V. Kovalenko, M. K. Urtenov, N. D. Pismenskaya, J. Han, P. Sistat, et al., Desalination at overlimiting currents: state-of-the-art and perspectives, Desalination342 (2014), no. 2, 85–106.10.1016/j.desal.2014.01.008Search in Google Scholar

[32] T. Lohaus, N. Herkenhoff, R. Shankar and M. Wessling, Feed flow patterns of combined Rayleigh–Bénard convection and membrane permeation, J. Membr. Sci.549 (2018), no. 1, 60–66.10.1016/j.memsci.2017.11.061Search in Google Scholar

Received: 2020-02-04
Revised: 2020-07-21
Accepted: 2020-07-31
Published Online: 2020-08-25
Published in Print: 2020-10-25

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 26.4.2024 from https://www.degruyter.com/document/doi/10.1515/jnet-2020-0012/html
Scroll to top button