- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Thermoelectrokinetic instability and salt superconcentration near permselective electric membranes

E. N. Kalaydin1,2, N. Yu. Ganchenko2, G. S. Ganchenko3, N. V. Nikitin4, and E. A. Demekhin1,3,4,*

  • 1Department of Mathematics and Informatics, Financial University, Krasnodar 350051, Russian Federation
  • 2Department of Mathematical and Computer Methods, Kuban State University, Krasnodar 350040, Russian Federation
  • 3Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University, Krasnodar 350051, Russian Federation
  • 4Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, Moscow 119192, Russian Federation

  • *edemekhi@gmail.com
PDF

Phys. Rev. Fluids 2, 114201 – Published 14 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114201

Abstract

A sophisticated type of electrohydrodynamic instability, the thermoelectrokinetic instability, in an electrolyte solution near ion-selective surfaces in an external electric field was discovered and investigated theoretically. The investigation used parallel computing on the SKIF MSU Lomonosov supercomputer and it was based on the direct numerical simulation of the Nernst-Planck-Poisson-Navier-Stokes system, along with the energy equation and corresponding boundary conditions. Although the physical mechanism of the instability is connected with Joule heating, it dramatically differs from the well-known Raleigh-Bénard convection: The instability is caused by nonuniformity of the electric current and electric conductivity and, in contrast to the Raleigh-Bénard instability, it occurs when the heating is from above. The thermoelectrokinetic instability prevails in long microchannels and a good enough thermal insulation of the system and it can be an additional factor for the overlimiting current mode. Initial unstable small random disturbances of the unknowns evolve towards rather unusual coherent structures. For the cation-exchange membranes, the salt concentration was eventually localized in long narrow fingers that are similar to stalactites and that stretched from the anode in the direction of the cathode. Outside the stalactites, the salt concentration was practically zero, while inside the stalactites it could reach hundreds from the initial concentration. Consequently, it is possible to talk about its superconcentration. The electric current propagates in a narrow needle along the stalactite with maximal electric conductivity and this gives rise to Joule heating in this region. The space charge forms crownlike micropatterns near the cathode. Note that the regime of chaotic motion that is characteristic of the electrokinetic instability was not observed for the thermoelectrokinetic instability.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (58)

  1. Y.-C Wang, A. L. Stevens, and J. Han, Million-fold preconcentration of proteins and peptides by nanofluidic filter, Anal. Chem. 77, 4293 (2005).
  2. R. B. Schoch, J. Han, and P. Renaud, Transport phenomena in nanofluidics, Rev. Mod. Phys. 80, 839 (2008).
  3. V. V. Nikonenko, N. D. Pismenskaya, E. I. Belova, P. Sistat, P. Huguet, G. Pourcelly, and C. Larchet, Intensive current transfer in membrane systems: Modelling, mechanisms and application in electrodialysis, Adv. Colloid Interface Sci. 160, 101 (2010).
  4. S. J. Kim, S. H. Ko, K. H. Kang, and J. Han, Direct seawater desalination by ion concentration polarization, Nat. Nanotech. 5, 297 (2010).
  5. T. A. Zangle, A. Mani, and J. G. Santiago, Theory and experiments of concentration polarization and ion focusing at microchannel and nanochannel interfaces, Chem. Soc. Rev. 39, 1014 (2010).
  6. A. Mani and M. Z. Bazant, Deionization shocks in microstructures, Phys. Rev. E 84, 061504 (2011).
  7. M. E. Suss, T. F. Baumann, W. L. Bourcier, C. M. Spadaccini, K. A. Rose, J. G. Santiago, and M. Stadermann, Capacitive desalination with flow-through electrodes, Energy Environ. Sci. 5, 9511 (2012).
  8. H.-C. Chang, G. Yossifon, and E. A. Demekhin, Nanoscale electrokinetics and microvortices: How microhydrodynamics affects nanofluidic ion flux, Annu. Rev. Fluid Mech. 44, 401 (2012).
  9. V. V. Nikonenko, A. V. Kovalenko, M. K. Urtenov, N. D. Pismenskaya, J. Han, P. Sistat, and G. Pourcelly, Desalination at overlimiting currents: State-of-the-art and perspectives, Desalination 342, 85 (2014).
  10. R. Kwak, G. Guan, W. K. Peng, and J. Han, Microscale electrodialysis: Concentration profiling and vortex visualization, Desalination 308, 138 (2013).
  11. R. Kwak, V. S. Pham, K. M. Lim, and J. Han, Shear Flow of an Electrically Charged Fluid by Ion Concentration Polarization: Scaling Laws for Electroconvective Vortices, Phys. Rev. Lett. 110, 114501 (2013).
  12. D. Deng, W. Aouad, W. A. Braff, S. Schlumpberger, M. E. Suss, and M. Z. Bazant, Water purification by shock electrodialysis: Deionization, filtration, separation, and disinfection, Desalination 357, 77 (2015).
  13. V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, 1962).
  14. R. F. Probstein, Physicochemical Hydrodynamics, An Introduction (Wiley-Interscience, New York, 2005).
  15. I. Rubinstein and L. Shtilman, Voltage against current curves of cation exchange membranes, J. Chem. Soc. Faraday Trans. 2 75, 231 (1979).
  16. J. Balster, M. H. Yildirim, D. F. Stamatialis, R. Ibanez, R. G. H. Lammertink, V. Jordan, and M. Wessling, Morphology and microtopology of cation-exchange polymers and the origin of the overlimiting current, J. Phys. Chem. B 111, 2152 (2007).
  17. V. I. Zabolotsky, V. V. Nikonenko, N. D. Pismenskaya, E. V. Laktionov, M. K. Urtenov, H. Strathmann, M. Wessling, and G. H. Koops, Coupled transport phenomena in overlimiting current electrodialysis, Sep. Purif. Technol. 14, 255 (1998).
  18. E. I. Belova, G. Y. Lopatkova, N. D. Pismenskaya, V. V. Nikonenko, C. Larchet, and G. Pourcelly, Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer, J. Phys. Chem. B 110, 13458 (2006).
  19. B. Zaltzman and I. Rubinstein, Electro-osmotic slip and electroconvective instability, J. Fluid Mech. 579, 173 (2007).
  20. V. A. Shaposhnik, V. I. Vasil'eva, and O. V. Grigorchuk, The interferometric investigations of electromembrane processes, Adv. Colloid Interface Sci. 139, 74 (2008).
  21. N. D. Pismenskaya, V. V. Nikonenko, E. I. Belova, G. Y. Lopatkova, P. Sistat, G. Pourcelly, and K. Larshe, Coupled convection of solution near the surface of ion-exchange membranes in intensive current regimes, Russ. J. Electrochem. 43, 307 (2007).
  22. Y. Kharkats, Mechanism of “supralimiting” currents at ion-exchange membrane/electrolyte interfaces. Sov. Electrochem. 21, 917 (1985).
  23. H.-C. Chang, E. A. Demekhin, and V. S. Shelistov, Competition between Dukhin's and Rubinstein's electrokinetic modes, Phys. Rev. E 86, 046319 (2012).
  24. S. M. Davidson, M. Wessling, and A. Mani, On the dynamical regimes of pattern-accelerated electroconvection, Sci. Rep. 6, 22505 (2016).
  25. V. A. Kirii, V. S. Shelistov, and E. A. Demekhin, Hydrodynamics of spatially inhomogeneous real membranes, J. Appl. Mech. Tech. Phys. 58, 635 (2017).
  26. V. A. Kiriy, V. S. Shelistov, E. N. Kalaidin, and E. A. Demekhin, Hydrodynamics, electroosmosis, and electrokinetic instability in imperfect electric membranes, Dokl. Phys. 62, 222 (2017).
  27. E. D. Belashova, N. A. Melnik, N. D. Pismenskaya, K. A. Shestova, A. V. Nebavky, K. A. Lebedev, and V. V. Nikonenko, Overlimiting mass transfer through cation-exchange membranes modified by nafion film and carbon nanotubes, Electrochim. Acta 59, 412 (2012).
  28. V. S. Shelistov, E. A. Demekhin, and G. S. Ganchenko, Electrokinetic instability near charge-selective hydrophobic surfaces, Phys. Rev. E 90, 013001 (2014).
  29. I. Rubinstein and B. Zaltzman, Electro-osmotically induced convection at a permselective membrane, Phys. Rev. E 62, 2238 (2000).
  30. E. A. Demekhin, V. S. Shelistov, and S. V. Polyanskikh, Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability, Phys. Rev. E 84, 036318 (2011).
  31. E. A. Demekhin, N. V. Nikitin, and V. S. Shelistov, Direct numerical simulation of electrokinetic instability and transition to chaotic motion, Phys. Fluids 25, 122001 (2013).
  32. E. A. Demekhin, N. V. Nikitin, and V. S. Shelistov, Three-dimensional coherent structures of electrokinetic instability, Phys. Rev. E 90, 013031 (2014).
  33. V. S. Pham, Z. Li, K. M. Lim, J. K. White, and J. Han, Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a permselective membrane, Phys. Rev. E 86, 046310 (2012).
  34. C. L. Druzgalski, M. B. Andersen, and A. Mani, Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface, Phys. Fluids 25, 110804 (2013).
  35. A. T. Pérez and A. Castellanos, Role of charge diffusion in finite-amplitude electroconvection, Phys. Rev. A 40, 5844 (1989).
  36. I. Rubinstein, Electroconvection at an electrically inhomogeneous permselective interface, Phys. Fluids A 3, 2301 (1991).
  37. I. Rehberg, F. Horner, and G. Hartung, The measurement of subcritical electroconvection, J. Stat. Phys. 64, 1017 (1991).
  38. J. D. Posner and J. G. Santiago, Convective instability of electrokinetic flows in a cross-shaped microchannel, J. Fluid Mech. 555, 1 (2006).
  39. E. Karatay, M. B. Andersen, M. Wessling, and A. Mani, Coupling Between Buoyancy Forces and Electroconvective Instability near Ion-Selective Surfaces, Phys. Rev. Lett. 116, 194501 (2016).
  40. J. C. de Valenca, A. Kurniawan, R. M. Wagterveld, J. A. Wood, and R. G. H. Lammertink, Influence of Rayleigh-Bénard convection on electrokinetic instability in overlimiting current conditions, Phys. Rev. Fluids 2, 033701 (2017).
  41. W. M. Saslow, Joule heating rate need not equal I2R, where R is the Ohmic resistance: The case of voltaic cells, Phys. Rev. E 59, R1343 (1999).
  42. R. Dey, T. Ghonge, and S. Chakraborty, Steric-effect-induced alteration of thermal transport phenomenon for mixed electroosmotic and pressure driven flows through narrow confinements, Int. J. Heat Mass Transfer 56, 251 (2013).
  43. E. A. Demekhin, S. Amiroudine, G. S. Ganchenko, and N. Y. Khasmatulina, Thermoelectroconvection near charge-selective surfaces, Phys. Rev. E 91, 063006 (2015).
  44. R. abu Rjal, L. Prigozhin, I. Rubinstein, and B. Zaltzman, Equilibrium electro-convective instability in concentration polarization: The effect of non-equal ionic diffusivities and longitudinal flow, Russ. J. Electrochem. 53, 903 (2017).
  45. C. Soret, Sur l'état d'équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homohéne dont deux parties sont portées á des temprétures différentes, Arch. Sci. Phys. Nat. 2, 48 (1879).
  46. A. Würger, Transport in Charged Colloids Driven by Thermoelectricity, Phys. Rev. Lett. 101, 108302 (2008).
  47. I. Chikina, V. Shikin, and A. A. Varlamov, Seebeck effect in electrolytes, Phys. Rev. E 86, 011505 (2012).
  48. R. F. Stout and A. S. Khair, Diffuse charge dynamics in ionic thermoelectrochemical systems, Phys. Rev. E 96, 022604 (2017).
  49. CRC Handbook of Chemistry and Physics, edited by D. Lide (CRC, New York, 1994).
  50. Z. R. Garnon and H.-C. Chang, Electrothermal ac electro-osmosis, Appl. Phys. Lett. 94, 024101 (2009).
  51. P. Garcia-Sanchez, A. Ramos, and F. Mugele, Electrothermally driven flows in ac electrowetting, Phys. Rev. E 81, 015303 (2010).
  52. I. Rubinstein and B. Zaltzman, Wave number selection in a nonequilibrium electro-osmotic instability, Phys. Rev. E 68, 032501 (2003).
  53. M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851 (1993).
  54. H.-C. Chang and E. A. Demekhin, Complex Wave Dynamics on Thin Films (Elsevier, Amsterdam, 2002), Vol. 14 .
  55. I. Rubinstein and B. Zaltzman, Equilibrium Electroconvective Instability, Phys. Rev. Lett. 114, 114502 (2015).
  56. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, 1987), p. 556.
  57. V. S. Shelistov, E. A. Demekhin, and G. S. Ganchenko, Self-similar solution to the problem of electrokinetic instability in semipermeable membranes, Moscow Univ. Mech. Bull. 69, 119 (2014).
  58. S. C. Wang, H. H. Wei, H. P. Chen, M. H. Tsai, C. C. Yu, and H.-C. Chang, Dynamic superconcentration at critical-point double-layer gates of conducting nanoporous granules due to asymmetric tangential fluxes, Biomicrofluidics 2, 014102 (2008).

Outline

Information

Phys. Rev. Fluids 2, 114201– Published 14 November, 2017
  • Received 25 July 2017

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation