Skip to main content
SpringerLink
Log in

Theoretical Analysis of the Effect of Ion Concentration in Solution Bulk and at Membrane Surface on the Mass Transfer at Overlimiting Currents

  • Published:
Russian Journal of Electrochemistry Aims and scope Submit manuscript

Abstract

Overlimiting current modes are of considerable interest for the practice of electrodialysis (ED). However, the economical expedience of such ED modes is evident only for desalination of dilute solutions. Here, we show the theoretical analysis of the effect of concentration on the behavior of an ED cell with homogeneous ion-exchange membranes. The study is based on numerical solution of the two-dimensional system of coupled equations of Nernst–Planck–Poisson–Navier–Stokes. It is shown that as the electrolyte concentration in solution that enters the ED desalination chamber increases, the intensity of electroconvection decreases, which induces a decrease in the relative mass-transfer rate (the decrease in the ratio of current density to its limiting value). This effect is stronger in the region of high potential differences where the electroconvective instability of Rubinstein–Zaltzman is realized under the conditions of a nonuniform concentration field caused by solution desalination. In contrast, the increase in the counterion concentration at the membrane surface (associated with the increase in the surface charge) intensifies the electroconvection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Maletzki, F., Rösler, H.W., and Staude, E., Ion transfer across electrodialysis membranes in the overlimiting current range: stationary voltage current characteristics and current noise power spectra under different conditions of free convection, J. Membr. Sci., 1992, vol. 71, p. 105.

    Article  CAS  Google Scholar 

  2. Pismenskaya, N.D. Nikonenko, V.V., Belova, E.I., Lopatkova, G.Yu., Sistat, P., Pourcelly, G., and Larshe, K., Coupled convection of solution near the surface of ionexchange membranes in intensive current regimes, Russ. J. Electrochem., 2007, vol. 43, p. 307.

    Article  CAS  Google Scholar 

  3. Rubinstein, S.M., Manukyan, G., Staicu, A., Rubinstein, I., Zaltzman, B., Lammertink, R.G.H., Mugele, F., and Wessling, M., Direct observation of a nonequilibrium electro-osmotic instability, Phys. Rev. Lett., 2008, vol. 101, 236101.

    Article  CAS  Google Scholar 

  4. Vasil’eva, V.I., Zhiltsova, A.V., Malykhin, M.D., Zabolotskii, V.I., Lebedev, K.A., Chermit, R.Kh., and Sharafan, M.V., Effect of the chemical nature of the ionogenic groups of ion-exchange membranes on the size of the electroconvective instability region in highcurrent modes, Russ. J. Electrochem., 2014, vol. 50, p. 120.

    Article  Google Scholar 

  5. Rubinstein, I. and Zaltzman, B., Electro-osmotically induced convection at a permselective membrane, Phys. Rev. E, 2000, vol. 62, no. 2, p. 2238.

    Article  CAS  Google Scholar 

  6. Kwak, R., Pham, V.S., Lim, K.M., and Han, J., Shear flow of an electrically charged fluid by ion concentration polarization: scaling laws for convection vortices, Phys. Rev. Lett., 2013, vol. 110, 114501.

    Article  Google Scholar 

  7. Urtenov, M.K., Uzdenova, A.M., Kovalenko, A.V., Nikonenko, V.V., Pismenskaya, N.D., Vasil’eva, V.I., Sistat, P., and Pourcelly, G., Basic mathematical model of overlimiting transfer enhanced by electroconvection in flow-through electrodialysis membrane cells, J. Membr. Sci., 2013, vol. 447, p. 190.

    Article  CAS  Google Scholar 

  8. Daiguji, H., Yang, P.D., and Majumdar, A., Ion transport in nanofluidic channels, Nano Letters, 2004, vol. 4, no. 1, p. 137.

    Article  CAS  Google Scholar 

  9. Dukhin, S.S. and Mishchuk, N.A., Unlimited increase in the current through ionite granes, Kolloidn. Zh., 1988, vol. 49, no. 6, p. 1047.

    Google Scholar 

  10. Dukhin, S.S., Electrokinetic phenomena of second kind and their applications, Adv. Colloid Interface Sci., 1991, vol. 35, p. 173.

    Article  CAS  Google Scholar 

  11. Mishchuk, N.A., Concentration polarization of interface and non-linear electrokinetic phenomena, Adv. Colloid Interface Sci., 2010, vol. 160, p. 16.

    Article  CAS  Google Scholar 

  12. Rubinstein, I. and Zaltzman, B., Equilibrium electroconvective instability, Phys. Rev. Lett., 2015, vol. 114, 114502.

    Article  CAS  Google Scholar 

  13. Zaltzman, B. and Rubinstein, I., Electro-osmotic slip and electroconvective instability, J. Fluid Mech., 2007, vol. 579, p. 173.

    Article  Google Scholar 

  14. Wessling, M., Morcillo, L.G., and Abdu, S., Nanometer-thick lateral polyelectrolyte micropatterns induce macrosopic electro-osmotic chaotic fluid instabilities, Sci. Rep., 2014, vol. 4, p. 4294.

    Article  CAS  Google Scholar 

  15. Dukhin, S.S. and Mishchuk, N.A., Intensification of electrodialysis based on electroosmosis of the second kind, J. Membr. Sci., 1993, vol. 79, p. 199.

    Article  CAS  Google Scholar 

  16. Nikonenko, V.V., Vasil’eva, V.I., Akberova, E.M., Uzdenova, A.M., Urtenov, M.K., Kovalenko, A.V., Pismenskaya, N.P., Mareev, S.A., and Pourcelly, G., Competition between diffusion and electroconvection at an ion-selective surface in intensive current regimes, Adv. Colloid Interface Sci., 2016, vol. 235, p. 233.

    Article  CAS  Google Scholar 

  17. Rubinstein, I., Staude, E., and Kedem, O., Role of the membrane surface in concentration polarization at ionexchange membranes, Desalination, 1988, vol. 69, p. 101.

    Article  CAS  Google Scholar 

  18. Rubinstein, I. and Shtilman, L., Voltage against current curves of cation-exchange membranes, J. Chem. Soc., Faraday Trans., 1979, vol. 75, p. 231.

    Article  CAS  Google Scholar 

  19. Rubinstein, I., Zaltzman, B., and Pundik, T., Ionexchange funneling in thin-film coating modification of heterogeneous electrodialysis membranes, Phys. Rev. E, 2002, vol. 65, 041507.

    Article  Google Scholar 

  20. Belova, E.I., Lopatkova, G.Yu., Pismenskaya, N.D., Nikonenko, V.V., Larchet, C., and Pourcelly, G., The effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer, J. Phys. Chem. B, 2006, vol. 110, p. 13458.

    Article  CAS  Google Scholar 

  21. Dydek, E.V., Zaltzman, B., Rubinstein, I., Deng, D.S., Mani, A., and Bazant, M.Z., Overlimiting current in a microchannel, Phys. Rev. Lett., 2011, vol. 107, 118301.

    Article  Google Scholar 

  22. Green, Y. and Yossifon, G., Dynamical trapping of colloids at the stagnation points of electro-osmotic vortices of the second kind, Phys. Rev. E, 2013, vol. 87, no. 3, 033005.

    Article  Google Scholar 

  23. Demekhin, E.A., Shelistov, V.S., and Polyanskikh, S.V., Linear and nonlinear evolution and diffusion layer selection in V.S. electrokinetic instability, Phys. Rev. E, 2011, vol. 84, 036318.

    Article  CAS  Google Scholar 

  24. Shelistov, V., Nikitin, N., Ganchenko, G., and Demekhin, E., Numerical modeling of electrokinetic instability in semipermeable membranes, Dokl. Phys., 2011, vol. 56, p. 538.

    Article  CAS  Google Scholar 

  25. Pham, S.V., Li, Z., Lim, K.M., White, J.K., and Han, J., Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of permselective membrane, Phys. Rev. E, 2012, vol. 86, 046310.

    Article  Google Scholar 

  26. Druzgalski, C.L., Andersen, M.B., and Mani, A., Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface, Phys. Fluids, 2013, vol. 25, 110804.

    Article  Google Scholar 

  27. Dukhin, S.S., Electrokinetic phenomena of the second kind and their applications, Adv. Colloid Interface Sci., 1991, vol. 35, p. 173.

    Article  CAS  Google Scholar 

  28. Mishchuk, N.A. and Takhistov, P.V., Electroosmosis of the second kind and current through curved interface, Colloids Surf. A, 1995, vol. 95, p. 119.

    Article  CAS  Google Scholar 

  29. Mishchuk, N.A., Electro-osmosis of the second kind near the heterogeneous ion-exchange membrane, Colloids Surf. A, 1998, vol. 140, p. 75.

    Article  CAS  Google Scholar 

  30. Chang, H.-C., Demekhin, E.A., and Shelistov, V.S., Competition between Dukhin’s and Rubinstein’s electrokinetic modes, Phys. Rev. E, 2012, vol. 86, 046319.

    Article  Google Scholar 

  31. Uzdenova, A.M., Kovalenko, A.V., and Urtenov, M.Kh., Matematicheskie modeli elektrokonvektsii v elektromembrannykh sistemakh (Mathematical Models of Electroconvection in Electrochemical Systems), Karachaevsk: KChGU, 2011.

    Google Scholar 

  32. Nikonenko, V.V., Kovalenko, A.V., Urtenov, M.K., Pismenskaya, N.D., Han, J., Sistat, P., and Pourcelly, G., Desalination at overlimiting currents: state-of-the-art and perspectives, Desalination, 2014, vol. 342, p. 85.

    Article  CAS  Google Scholar 

  33. Uzdenova, A.M., Kovalenko, A.V., Urtenov, M.K., and Nikonenko, V.V., Effect of electroconvection during pulsed electric field electrodialysis. Numerical experiments, Electrochem. Commun., 2015, vol. 51, p. 1.

    Article  CAS  Google Scholar 

  34. Uzdenova, A.M., Kovalenko, A.V., and Urtenov, M.Kh., Matematicheskoe modelirovanie membrannykh protsessov s ispol’zovaniem Comsol Multiphysics 4.3 (Mathematical Simulation of Membrane Processes with the Use of Comsol Multiphysics 4.3), Krasnodar: KGU, 2013.

    Google Scholar 

  35. Newman, J.S., Electrochemical, Systems, New York: Prentice Hall, 1991, 2nd Ed.

    Google Scholar 

  36. Gnusin, N.P., Zabolotskii, V.I., Nikonenko, V.V., and Urtenov, M.Kh., Convective-diffusion model of the process of electrodialysis desalination. Overlimiting current and diffusion layer, Elektrokhimiya, 1986, vol. 22, p. 298.

    CAS  Google Scholar 

  37. Karatay, E., Druzgalski, C.L., and Mani, A., Simulation of chaotic electrokinetic transport: performance of commercial software versus custom-built direct numerical simulation codes, J. Colloid Interface Sci., 2015, vol. 446, p. 67.

    Article  CAS  Google Scholar 

  38. Urtenov, M.A.K., Kirillova, E.V., Seidova, N.M., and Nikonenko, V.V., Decoupling of the Nernst-Planck and Poisson equations. Application to a membrane system at overlimiting currents, J. Phys. Chem. B., 2007, vol. 111, p. 14208.

    Article  CAS  Google Scholar 

  39. Belashova, E.D., Melnik, N.A., Pismenskaya, N.D., Shevtsova, K.A., Nebavsky, A.V., Lebedev, K.A., and Nikonenko, V.V., Overlimiting mass transfer through cation-exchange membranes modified by Nafion film and carbon nanotubes, Electrochim. Acta, 2012, vol. 59, p. 412.

    Article  CAS  Google Scholar 

  40. Rubinstein, I., Zaltzman, B., Futerman, A., Gitis, V., and Nikonenko, V., Reexamination of electrodiffusion time scales, Phys. Rev. E, 2009, vol. 79, no. 2, 021506.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karachaevo-Cherkessky State University Named after U.D. Aliev, Karachaevsk, 369202, Russia

    A. M. Uzdenova

  2. Kuban State University, Krasnodar, 350040, Russia

    A. V. Kovalenko, M. Kh. Urtenov & V. V. Nikonenko

Authors
  1. A. M. Uzdenova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Kovalenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Kh. Urtenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. V. Nikonenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Uzdenova.

Additional information

Original Russian Text © A.M. Uzdenova, A.V. Kovalenko, M.Kh. Urtenov, V.V. Nikonenko, 2017, published in Elektrokhimiya, 2017, Vol. 53, No. 11.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Uzdenova, A.M., Kovalenko, A.V., Urtenov, M.K. et al. Theoretical Analysis of the Effect of Ion Concentration in Solution Bulk and at Membrane Surface on the Mass Transfer at Overlimiting Currents. Russ J Electrochem 53, 1254–1265 (2017). https://doi.org/10.1134/S1023193517110179

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1023193517110179

Keywords

Search

Navigation