Статья
2017

Effect of electroconvection and its use in intensifying the mass transfer in electrodialysis (Review)


V. V. Nikonenko V. V. Nikonenko , S. A. Mareev S. A. Mareev , N. D. Pis’menskaya N. D. Pis’menskaya , A. M. Uzdenova A. M. Uzdenova , A. V. Kovalenko A. V. Kovalenko , M. Kh. Urtenov M. Kh. Urtenov , G. Pourcelly G. Pourcelly
Российский электрохимический журнал
https://doi.org/10.1134/S1023193517090099
Abstract / Full Text

The modern concepts on the origin of electroconvection (EC) are surveyed briefly and the known mechanisms of this phenomenon are classified. Factors that influence the EC character and intensity at the surface of ion-exchange membranes are analyzed, such as electrical and geometrical heterogeneity of the membrane surface, its degree of hydrophobicity, and the surface charge. The EC mechanism is shown also to depend on the applied potential difference and the rate of solution flow between membranes. The mechanism of the EC-induced gain in the mass transfer is elucidated, the possible gain in the mass transfer is estimated, and the prospects for using the EC for reducing the membrane fouling caused by sedimentation and formation of organic deposits are assessed.

Author information
  • Kuban State University, Krasnodar, 350040, Russia

    V. V. Nikonenko, S. A. Mareev, N. D. Pis’menskaya, A. V. Kovalenko & M. Kh. Urtenov

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

    A. M. Uzdenova

  • Institute European of the Membranes, University of Montpellier, ENSCM, CNRS, СС047, Montpellier, 34095, France

    G. Pourcelly

References
  1. Strathmann, H., Electrodialysis, a mature technology with a multitude of new applications, Desalination, 2010, vol. 264, p. 268.
  2. Strathmann, H., Grabowski, A., and Eigenberger, G., Ion-exchange membranes in the chemical process industry. industrial and engineering chemistry research, Ind. Eng. Chem. Res., 2013, vol. 52, no. 31, p. 10364.
  3. 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.
  4. Cifuentes-Araya, N., Pourcelly, G., and Bazinet, L., Impact of pulsed electric field on electrodialysis process performance and membrane fouling during consecutive demineralization of a model salt solution containing a high magnesium/calcium ratio, J. Colloid Interface Sci., 2011, vol. 361, p. 79.
  5. Mikhaylin, S., Nikonenko, V., Pourcelly, G., and Bazinet, L., Intensification of demineralization process and decrease in scaling by application of pulsed electric field with short pulse/pause conditions, J. Membr. Sci., 2014, vol. 468, p. 389.
  6. Mikhaylin, S., Nikonenko, V., Pourcelly, G., and Bazinet, L., Hybrid bipolar membrane electrodialysis/ultrafiltration technology assisted by a pulsed electric field for casein production, Green Chem., 2016, vol. 18, no. 1, p. 307.
  7. Kim, S.J., Wang, Y.-C., Lee, J.H., Jang, H., and Han, J., Concentration polarization and nonlinear electrokinetic flow near a nanofluidic channel, Phys. Rev. Lett., 2007, vol. 99, p. 44501.
  8. Biesheuvel, P.M. and van der Wal, A., Membrane capacity deionization, J. Membr. Sci., 2010, vol. 346, p. 256.
  9. Phan, D.-T., Shaegh, S.A.M., Yang, C., and Nguyen, N.-T., Sample concentration in a microfluidic paper-based analytical device using ion concentration polarization, Sens. Actuators B, 2016, vol. 222, p. 735.
  10. de Jong, J., Lammertink, R.G.H., and Wessling, M., Membranes and microfluidics: a review, Lab Chip, 2006, vol. 6, p. 1125.
  11. Wang, Y.-C., Stevens, A.L., and Han, J., Million-fold preconcentration of proteins and peptides by nanofluidic filter, Anal. Chem., 2005, vol. 77, p. 4293.
  12. Kwak, R., Pham, V.S., Kim, B., Chen, L., and Han, J., Enhanced salt removal by unipolar ion conduction in ion concentration polarization desalination, Sci. Rep., 2016, vol. 6, p. 25349.
  13. Zangle, T.A., Mani, A., and Santiago, J.G., On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part II: numerical and experimental study, Langmuir, 2009, vol. 25, no. 6, p. 3909.
  14. Zangle, T.A., Mani, A., and Santiago, J.G., Theory and experiments of concentration polarization and ion focusing at microchannel and nanochannel interfaces, Chem. Soc. Rev., 2010, vol. 39, no. 3, p. 1014.
  15. Yaroshchuk, A., Over-limiting currents and deionization shocks in current-induced polarization: localequilibrium analysis, Adv. Colloid Interface Sci., 2012, vol. 183–184, p. 68.
  16. Mani, A. and Bazant, M.Z., Deionization shocks in microstructures, Phys. Rev. E, 2011, vol. 84, p. 061504.
  17. Bazant, M.Z., Dydek, E.V., Deng, D., and Mani, A., US Patent 0308953 A1, 2011.
  18. Kim, S.-J., Ko, S.-H., Kang, K.H., and Han, J., Direct seawater desalination by ion concentration polarization, Nat. Nanotechnol., 2010, vol. 5, p. 297.
  19. Stone, H.A., Stroock, A.D., and Ajdari, A., Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech., 2004, vol. 36, p. 381.
  20. Schoch, R.B., Han, J., and Renaud, P., Transport phenomena in nanofluidics, Rev. Mod. Phys., 2008, vol. 80, p. 839.
  21. Chang, H.C., Yossifon, G., and Demekhin, E.A., Nanoscale electrokinetics and microvortices: how hydrodynamics affects nanofluidic ion flow, Annu. Rev. Fluid Mech., 2012, vol. 44, p. 401.
  22. Yeo, L.Y., Chang, H.C., Chan, P.P.Y., and Friend, J.R., Microfluidic devices for bioapplications, Small, 2011, vol. 7, p. 12.
  23. Slouka, Z., Senapati, S., and Chang, H.C., Microfluidic systems with ion-selective membranes, Annu. Rev. Anal. Chem., 2014, vol. 7, p. 317.
  24. Bazant, M.Z., Kilic, M.S., Storey, B.D., and Ajdari, A., Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions, Adv. Colloid Interface Sci., 2009, vol. 152, p. 48.
  25. Frilette, V.J., Electrogravitational transport at synthetic ion exchange membrane surfaces, J. Phys. Chem., 1957, vol. 61, p. 168.
  26. Rubinstein, I. and Shtilman, L., Voltage against current curves of cation exchange membranes, J. Chem. Soc., Faraday Trans., 1979, vol. 75, p. 231.
  27. Rubinstein, I., Warshawsky, A., Schechtman, L., and Kedem, O., Elimination of acid–base generation (“water-splitting”) in electrodialysis, Desalination, 1984, vol. 51, p. 55.
  28. Rubinstein, I. and Zaltzman, B., Electro-osmotically induced convection at a permselective membrane, Phys. Rev. E, 2000, vol. 62, no. 2, 2238.
  29. Zaltzman, B. and Rubinstein, I., Electro-osmotic slip and electroconvective instability, J. Fluid Mech., 2007, vol. 579, p. 173.
  30. Dukhin, S.S., Mishchuk, N.A., Tarovskii, A.A., and Baran, A.A., Electrophoresis of the second kind, Kolloidn. Zh., 1987, vol. 49, p. 616.
  31. Dukhin, S.S. and Mishchuk, H.A., Strong concentration polarization of a thin double layer of a spherical particle in external electric field, Kolloidn. Zh., 1988, vol. 50, no. 2, p. 237.
  32. Dukhin, S.S., Electrokinetic phenomena of the second kind and their applications, Adv. Colloid Interface Sci., 1991, vol. 35, p. 173.
  33. 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.
  34. Mishchuk, N.A., Concentration polarization of interface and non-linear electrokinetic phenomena, Adv. Colloid Interface Sci., 2010, vol. 160, p. 16.
  35. Zabolotsky, V.I., Nikonenko, V.V., and Pismenskaya, N.D., On the role of gravitational convection in the transfer enhancement of salt ions in the course of dilute solution electrodialysis, J. Membr. Sci., 1996, vol. 119, p. 171.
  36. Zabolotsky, V.I., Nikonenko, V.V., Pismenskaya, N.D., Laktionov, E.V., Urtenov, M.K., Strathmann, H., Wessling, M., and Koops, G.H., Coupled transport phenomena in overlimiting current electrodialysis, Sep. Purif. Technol., 1998, vol. 14, no. 1–3, p. 255.
  37. 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 ion-exchange membranes in intensive current regimes, Russ. J. Electrochem., 2007, vol. 43, p. 307.
  38. Nikonenko, V.V., Pismenskaya, N.D., Belova, E.I., Sistat, P., Huguet, P., Pourcelly, G., and Larchet, C., Intensive current transfer in membrane systems: modeling, mechanisms and application in electrodialysis, Adv. Colloid and Interface Sci., 2010, vol. 160, p. 101.
  39. Kwak, R., Guan, G., Peng, W.K., and Han, J., Microscale electrodialysis: concentration profiling and vortex visualization, Desalination, 2013, vol. 308, p. 138.
  40. Deng, D., Dydek, E.V., Han, J.H., Schlumpberger, S., Mani, A., Zaltzman, B., and Bazant, M.Z., Overlimiting current and shock electrodialysis in porous media, Langmuir, 2013, vol. 29, no. 52, p. 16167.
  41. Levich, V.G. Fiziko-khimicheskaya gidrodinamika (Physicochemical Hydrodynamics), Moscow: Fizmatgiz, 1959, p. 700
  42. Levich, V.G., Physicochemical Hydrodynamics, New York: Prentice Hall, 1962.
  43. Dukhin, S.S. and Deryagin, B.V., Elektroforez (Electrophoresis), Moscow: Nauka, 1976.
  44. Probstein, R.F., Physicochemical Hydrodynamics, New York: Wiley, 1994.
  45. Rubinstein, I., Staude, E., and Kedem, O., Role of the membrane surface in concentration polarization at ion-exchange membrane, Desalination, 1988, vol. 69, p. 101.
  46. Rubinshtein, I., Zaltzman, B., Pretz, J., and Linder, C. Experimental verification of the electroosmotic mechanism of overlimiting conductance through a cation exchange electrodialysis membrane, Russ. J. Electrochem, 2002, vol. 38, p. 853.
  47. Tanaka, Y., Concentration polarization in ionexchange membrane electrodialysis: the events arising in an unforced flowing solution in a desalting cell, J. Membr. Sci., 2004, vol. 244, p. 1.
  48. Volgin, V.M., and Davydov, A.D., Natural-convective instability of electrochemical systems: a review, Russ. J. Electrochem., 2006, vol. 42, p. 567.
  49. Martí-Calatayud, M.C., García-Gabaldón, M., and Pérez-Herranz, V., Effect of the equilibria of multivalent metal sulfates on the transport through cationexchange membranes at different current regimes, J. Membr. Sci., 2013, vol. 443, p. 181.
  50. Pismenskiy, A., Urtenov, M., Kovalenko, A., and Mareev, S., Electrodialysis desalination process in conditions of mixed convection, Desalin. Water Treat., 2015, vol. 56, p. 3211.
  51. Levich, V.G., Theory of nonequilibrium double layer, Dokl. Akad. Nauk SSSR, 1949, vol. 67, no. 2, p. 309.
  52. Levich, V.G., On the theory of nonequilibrium double layer, Dokl. Akad. Nauk SSSR, 1959, vol. 124, no. 4, p. 869.
  53. Grafov, B.M. and Chernenko, A.A., Theory of direct current flow through binary-electrolyte solution, Dokl. Akad. Nauk SSSR, 1962, vol. 146, no. 1, p. 135.
  54. Grafov, B.M. and Chernenko, A.A., Direct current flow through binary-electrolyte solution, Zh. Fiz. Khim., 1963, vol. 37, no. 3, p. 664.
  55. Newman, J., The polarized diffuse double layer, Trans. Faraday Soc., 1965, vol. 61, no. 10, p. 2229.
  56. Smyrl, W.H. and Newman, J., Double layer structure at the limiting current, Trans. Faraday Soc., 1967, vol. 62, no. 1, p. 207.
  57. Chernenko, A.A., On the theory of direct current flow through binary-electrolyte solution, Dokl. Akad. Nauk SSSR, 1963, vol. 153, p. 1129.
  58. Grigin, A.P., Coulomb convection in electrochemical systems, Elektrokhimiya, 1992, vol. 28, no. 3, p. 307.
  59. 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.
  60. Bazant, M., Chu, K.T., and Bayly, B.J., Current–voltage relations for electrochemical thin films, SIAM J. Appl. Math., 2005, vol. 65, p. 1463.
  61. Chu, K.T. and Bazant, M.Z., Electrochemical thin films at and above the classical limiting current, SIAM J. Appl. Math., 2005, vol. 65, p. 1485.
  62. Dukhin, S.S. and Mishchuk, N.A., Unlimited increase in the current through ionite grains, Kolloidn. Zh., 1988, vol. 49, no. 6, p. 1197.
  63. Rubinstein, I. and Zaltzman, B., Extended space charge in concentration polarization, Adv. Colloid Interface Sci., 2010, vol. 159, p. 117.
  64. Rubinstein, I., Electroconvection at an electrically inhomogeneous permselective interface, Phys. Fluids A, 1991, vol. 3, p. 2301.
  65. Mishchuk, N.A., Electroosmosis of second kind near heterogeneous ion-exchange membranes, Colloids Surf., A, 1998, vol. 140, pp. 75–89.
  66. 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 a permselective membrane, Phys. Rev. E, 2012, vol. 86, 046310.
  67. Demekhin, E.A., Shelistov, V.S., and Polyanskikh, S.V., Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability, Phys. Rev. E, 2011, vol. 84, no. 3, 036318.
  68. Zabolotskii, V.V., Urtenov, M.K., Lebedev, K.A., and Bugakov, V.V., Electroconvection in systems with heterogeneous ion-exchange membranes, Russ. J. Electrochem., 2012, vol. 48, no. 7, p. 692.
  69. Zabolotskii, V.I., Lebedev, K.A., Urtenov, M.Kh. Nikonenko, V.V., Vasilenko, P.A., Shaposhnik, V.A., and Vasill’eva, V.I., A mathematical model describing voltammograms and transport numbers under intensive electrodialysis modes, Russ. J. Electrochem., 2013, vol. 49, no. 4, p. 369.
  70. Urtenov, M.K., Uzdenova, A.M., Kovalenko, A.V., Nikonenko, V.V., and 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.
  71. 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.
  72. Shelistov, V.S., Nikitin, N.V., Kiry, V.A., and Demekhin, E.A., A sequence of electrokinetic instability bifurcations resulting in a chaotic flow regime, Dokl. Phys., 2014, vol. 59, no. 4, p. 166.
  73. Ganchenko, G.S., Kalaydin, E.N., Schiffbauer, J., and Demekhin, E.A., Document modes of electrokinetic instability for imperfect electric membranes, Phys.Rev. E, 2016, vol. 94, 063106.
  74. Andersen, M., Wang, K., Schiffbauer, J., Mani, A., Confinement effects on electroconvective instability, Electrophoresis, 2016 (in press). doi 10.1002/elps.201600391
  75. Pham, S.V., Kwon, H., Kim, B., White, J.K., Lim, G., and Han, J., Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes, Phys. Rev. E, 2016, vol. 93, no. 3, 033114.
  76. Sonin, A.A. and Probstein, R.F., Hydrodynamic theory of desalination by electrodialysis, Desalination, 1968, vol. 5, p. 293.
  77. Gnusin, N.P., Zabolotskii, V.I., Nikonenko, V.V., and Urtenov, M.K., Convective-diffusion model of electrodialytic desalination. Limiting current and diffusion layer, Sov. Electrochem., 1986, vol. 23, no. 3, p. 273.
  78. Shaposhnik, V.A., Kuzminykh, V.A., Grigorchuk, O.V., and Vasil’eva, V.I., Analytical model of laminar flow electrodialysis with ion-exchange membranes, J. Membr. Sci, 1997, vol. 133, no. 1, p. 27.
  79. Belova, E.I., Lopatkova, G.Y., Pismenskaya, N.D., Nikonenko, V.V., Larchet, C., and Pourcelly, G., Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer, J. Phys. Chem. B, 2006, vol. 110, no. 27, p. 13458.
  80. Sistat, P., Kozmai, A., Pismenskaya, N., Larchet, C., Pourcelly, G., and Nikonenko, V., Low-frequency impedance of an ion-exchange membrane system, Electrochim. Acta, 2008, vol. 53, no. 22, p. 6380.
  81. Balster, J., Yildirim, M.H., Stamatialis, D.F., Ibanez, R., Lammertink, R.G.H., Jordan, V., and Wessling, M., Morphology and microtopology of cation-exchange polymers and the origin of the overlimiting current, J. Phys. Chem. B, 2007, vol. 111, p. 2152.
  82. Rubinstein, I. and Zaltzman, B., Equilibrium electroconvective instability, Phys. Rev. Lett., 2015, vol. 114, 114502.
  83. Mishchuk, N.A. and Takhistov, P.V., Electroosmosis of the second kind, Colloids Surf. A, 1995, vol. 95, p. 119.
  84. Uzdenova, A.M., Kovalenko, A.V., Urtenov, M.K., and Nikonenko V.V., Theoretical analysis of the effect of ion concentration in solution bulk and at the membrane surface on the mass transfer at overlimiting currents, Russ. J. Electrochem., 2017, vol. 53; in press.
  85. Zholkovskij, E.K., Vorotynsev, M.A., and Staude, E., Electrokinetic instability of solution in a plane-parallel electrochemical cell, J. Colloid Interface Sci., 1996, vol. 181, no. 1, p. 28.
  86. Abu-Rjal, R., Rubinstein, I., and Zaltzman, B., Driving factors of electro-convective instability in concentration polarization, Phys. Rev. Fluids, 2016, vol. 1, 023601.
  87. Bruinsma, R. and Alexander, S., Theory of electrohydrodynamic instabilities in electrolytic cells, J. Chem. Phys., 1990, vol. 92, p. 3074.
  88. Aleksandrov, R.S., Grigin, A.P., and Davydov, A.D. Numerical study of electroconvective instability of binary electrolyte in a cell with plane parallel electrodes, Russ. J. Electrochem., 2002, vol. 38, no. 10, p. 1097.
  89. Lerman, I., Rubinstein, I., and Zaltzman, B., Absence of bulk electroconvective instability in concentration polarization, Phys. Rev. E, 2005, vol.71.
  90. Rubinstein, S.M., Manukyan, G., Staicu, A., Rubinstein, I., Zaltzman, B., Lammertink, R., Mugele, F., and Wessling, M., Direct observation of a nonequilibrium electro-osmotic instability, Phys. Rev. Lett., 2008, vol. 101, 236101.
  91. Yossifon, G. and Chang, H.C., Selection of nonequilibrium overlimiting currents: universal depletion layer formation dynamics and vortex instability, Phys. Rev. Lett, 2008, vol. 101, 254501
  92. Kwak, R., Guan, G., Peng, W.K., and Han, J., Microscale electrodialysis: concentration profiling and vortex visualization, Desalination, 2013, vol. 308, p. 138.
  93. Green, Y., Park, S., and Yossifon, G., Bridging the gap between an isolated nanochannel and a communicating multipore heterogeneous membrane, Phys. Rev. E, 2015, vol. 91, no. 1, 011002.
  94. de Valença, J.C., Wagterveld, R.M., Lammertink, R.G.H., and Tsai, P.A., Dynamics of microvortices induced by ion concentration polarization, Phys. Rev. E, 2015, vol. 92, no. 3, 031003.
  95. Vasil’eva, V.I., Shaposhnik, V.A., Grigorchuk, O.V., and Petrunya, I.P., The membrane-solution interface under high-performance current regimes of electrodialysis by means of laser interferometry, Desalination, 2006, vol. 192, p. 408.
  96. Shaposhnik, V.A., Vasil’eva, V.I., and Praslov, D.B., Concentration fields of solutions under electrodialysis with ion-exchange membranes, J. Membr. Sci., 1995, vol. 101, nos. 1–2, p. 23.
  97. Shaposhnik, V.A., Vasil’eva, V.I., and Grigorchuk, O.V., The interferometric investigations of electromembrane processes, Adv. Colloid Interface Sci., 2008, vol. 139, p. 74.
  98. Vasil’eva, V.I., Zhil’tsova, A.V., Malykhin, M.D., Zabolotskii, V.I., Lebedev, K.A., Chermit, R.K., 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, no. 2, p. 120.
  99. 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.
  100. Kozmai, A.E., Nikonenko, V.V., Pismenskaya, N.D., Pryakhina, O.D., Sistat, P., and Pourcelly, G., Diffusion layer thickness in a membrane system as determined from voltammetric and chronopotentiometric data, Russ. J. Electrochem, 2010, vol. 46, no. 12, p. 1383.
  101. Nam, S., Cho, I., Heo, J., Lim, G., Bazant, M.Z., Moon, D.J., Sung, G.Y., and Kim, S.J., Experimental verification of overlimiting current by surface conduction and electro-270 osmotic flow in microchannels, Phys. Rev. Lett., 2015, vol. 114, 114501.
  102. Cortelezzi, L. and Karogozian, A.R., On the formation of the counter-rotating vortex pair in transverse jets, J. Fluid Mech., 2001, vol. 446, p. 347.
  103. Schlegel, F., Wee, D., Marzouk, Y.M., and Ghoniem, A.F., Contributions of the wall boundary layer to the formation of the counter-rotating vortex pair in transverse jets, J. Fluid Mech., 2011, vol. 676, p. 461.
  104. del Alamo, J.C., Jimenez, J., Zandonade, P., and Moser, R.D., Self-similar vortex clusters in the turbulent logarithmic region, J. Fluid Mech., 2006, vol. 561, p. 329.
  105. Pawlowski, S., Geraldes, V., Crespo, J.G., and Velizarov, S., Computational fluid dynamics (CFD) assisted analysis of profiled membranes performance in reverse electrodialysis, J. Membr. Sci, 2016, vol. 502, pp. 179.
  106. 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.
  107. Choi, J-H., Lee, H.-J., and Moon, S.-H., Effects of electrolytes on the transport phenomena in a cationexchange membrane, J. Colloid Interface Sci., 2001, vol. 238, p. 188.
  108. Gil, V.V., Andreeva, M.A., Pismenskaya, N.D., Nikonenko, V.V., Larchet, C., and Dammak, L., Effect of counterion hydration numbers on the development of electroconvection at the surface of heterogeneous cation-exchange membrane modified with an MF-4SK film, Petrol. Chem., 2016, vol. 56, no. 5, p. 440.
  109. Mishchuk, N.A., Polarization of systems with complex geometry, Curr. Opin. Colloid Interface Sci., 2013, vol. 18, no. 2, p. 137.
  110. Rubinstein, I., Zaltzman, B., and Kedem, O., Document electric fields in and around ion-exchange membranes, J. Membr. Sci., 1997, vol. 125, p. 17.
  111. Rubinstein, I. and Maletzki, F., Electroconvection at an electrically inhomogeneous permselective membrane surface, J. Chem. Soc., Faraday Trans., 1991, vol. 87, p. 2079.
  112. 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.
  113. Green, Y. and Yossifon, G., Time-dependent ion transport in heterogeneous permselective systems, Phys. Rev. E, 2015, vol. 91, 063001.
  114. Green, Y. and Yossifon, G., Effects of three-dimensional geometric field focusing on concentration polarization in a heterogeneous permselective system, Phys. Rev. E, 2014, vol. 89, 013024.
  115. Mareev, S.A., Nichka, V.S., Butylskii, D.Y., Urtenov, M.K., Pismenskaya, N.D., Apel, P.Y., and Nikonenko, V.V., Chronopotentiometric response of an electrically heterogeneous permselective surface: 3D modeling of transition time and experiment, J. Phys. Chem. C, 2016, vol. 120, no. 24, p. 13113.
  116. 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.
  117. Davidson, S.M., Wessling, M., and Mani, A., On the dynamical regimes of pattern-accelerated electroconvection, Sci. Rep., 2016, vol. 6, 22505.
  118. Nikonenko, V.V., Pismenskaya, N.D., Belova, E.I., Pourcelly, G., and Larchet, C., Proceedings of XVIII Mendeleev Congress on General and Applied Chemistry, Moscow, 2007, vol. 2, p. 43.
  119. Pismenskaya, N., Melnik, N., Nevakshenova, E., Nebavskaya, K., and Nikonenko, V., Document enhancing ion transfer in overlimiting electrodialysis of dilute solutions by modifying the surface of heterogeneous ion-exchange membranes, Int. J. Chem. Eng., 2012, vol. 2, 528290.
  120. 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.
  121. Korzhova, E., Pismenskaya, N., Lopatin, D., Baranov, O., Dammak, L., and Nikonenko, V., Effect of surface hydrophobization on chronopotentiometric behavior of an AMX anion–exchange membrane at overlimiting currents, J. Membr. Sci., 2016, vol. 500, p. 161.
  122. Pismenskaya, N.D., Nikonenko, V.V., Pourcelly, G., Dammak, L., and Larchet, C., Evolution with time of hydrophobicity and microrelief of a cation-exchange membrane surface and its impact on overlimiting mass transfer, J. Phys. Chem. B, 2012, vol. 116, no. 7, p. 2145.
  123. Gnusin, N.P., Pevnitskaya, M.V., Varentsov, V.K., and Grebenyuk, V.D., RF Patent 216622 (1972).
  124. Belobaba, A.G., Pevnitskaya, M.V., and Kozina, A.A., Electrodialysis of dilute solutions in apparatus with profiled ion-exchange membranes, Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Khim. Nauk, 1980, no. 9(4), p. 161.
  125. Edardo, P., US Patent 291713 (1975).
  126. Belobaba, A.G., Plekhanov, L.A., and Pevnitskaya, M.V., RF Patent 990256 (1983).
  127. Eigenberger, G., Strathmann, H., and Grabovskiy, A., FRG Patent 009596 (2005); B01D 61/44.
  128. Zabolotskii, V.I., Nikonenko, V.V., Pis’menskaya, N.D., Pis’menskii, V.F., and Laktionov, E.V., RF Patent 2033850 (1995).
  129. Larchet, C., Zabolotsky, V.I., Pismenskaya, N., Nikonenko, V.V., Tskhay, A., TastanovK., and Pourcelly, G., Comparison of different ED stack conceptions when applied for drinking water production from brackish waters, Desalination, 2008, vol. 222, nos. 1–3, p. 489.
  130. Zabolotskii, V.I., Loza, S.A., and Sharafan, M.V., Physicochemical properties of profiled heterogeneous ion-exchange membranes, Russ. J. Electrochem., 2005, vol. 41, no. 10, p. 1053.
  131. van Baak, W., Saakes, M., and Nijmeijer, K., Monovalent-ion-selective membranes for reverse electrodialysis, J. Membr. Sci., 2014, vol. 455, p. 254.
  132. Vasil'eva, V.I., Bityutskaya, L.A., Zaichenko, N.A., Grechkina, M.V., Botova, T.S., and Agapov, B.L., Microscopic analysis of surface morphology of ionexchange membranes, Sorbtsionnye Khromatogr. Protsessy, 2008, vol. 8, no. 2, p. 260.
  133. Vasil’eva, V.I., Kranina, N.A., Malykhin, M.D., Akberova, E.M., and Zhil’tsova, A.V., Surface heterogeneity of ion-exchange membranes according to data of methods STM and AFM, Poverkhnost, 2013, no. 2, p. 51.
  134. Knyaginicheva, E.V., Belashova, E.D., Sarapulova, V.V., and Pis’menskaya, N.D., Effect of MA-41 membrane modification on its electrochemical characteristics, Kondens. Sredy Mezhfazny Granitsy, 2014, vo. 16, no. 3, p. 282.
  135. Belova, E., Lopatkova, G., Pismenskaya, N., Nikonenko, V., and Larchet, C., Role of water splitting in development of electroconvection in ion-exchange membrane systems, Desalination, 2006, vol. 199, nos. 1–3, p. 59.
  136. Slouka, Z., Senapati, S., Yan, Y., and Chang, H.C., Charge inversion, water splitting, and vortex suppression due to DNA sorption on ion-selective membranes and their ion-current signatures, Langmuir, 2013, vol. 29, no. 26, p. 8275.
  137. Nebavskaya, K.A., Sabbatovskiy, K.G., Sobolev, V.D., Pismenskaya, N.D., Cretin, M., and Nikonenko, V.V., Impact of ion exchange membrane surface charge and hydrophobicity on electroconvection at underlimiting and overlimiting currents, J. Membr. Sci., 2017, vol. 523, p. 36.
  138. Ibl, N.D., Some theoretical aspects of pulse electrolysis, Surf. Technol., 1980, vol. 10, no. 2, p. 81.
  139. Puippe, J.C. and Leaman, F.H., Theory and practice of pulse plating. Research Parkway, Orlando (Florida): AESF, 1986.
  140. Berezin, N.B., Gudin, N.V., Filippova, A.G., Chevela, V.V., Mezhevich, Zh.V., Yakh’yaev, E.D., and Sagdeev, K.A., Elektroosazhdenie metallov i splavov iz vodnykh rastvorov kompleksnykh soedinenii (Electrodeposition of Metals and Alloys from Aqueous Solutions of Complex Compounds), Kazan: KGTU, 2006.
  141. Wasekar, N.P., Latha, S.M., Ramakrishna, M., Rao, D.S., and Sundararajan, G., Pulsed electrodeposition and mechanical properties of Ni–W/SiC nano-composite coatings, Mater. Des., 2016, vol. 112, p. 140.
  142. Mikhaylin, S. and Bazinet, L., Fouling on ionexchange membranes: classification, characterization and strategies of prevention and control, Adv. Colloid and Interface Sci., 2016, vol. 229, p. 34.
  143. Mishchuk, N.A. and Koopal, L.K., Intensification of electrodialysis by applying a non-stationary electric field, Colloids Surf. A, 2001, vol. 176, nos. 2–3, p. 195.
  144. Sistat, P., Huguet, P., Ruiz, B., Pourcelly, G., Mareev, S.A., and Nikonenko, V.V., Effect of pulsed electric field on electrodialysis of a NaCl solution in sub-limiting current regime, Electrochim. Acta, 2015, vol. 164, p. 267.
  145. Lee, H.-J., Moon, S.-H., and Tsai, S.-P., Effects of pulsed electric fields on membrane fouling in electrodialysis of NaCl solution containing humate, Sep. Purif. Technol, 2002, vol. 27, no. 2, p. 89.
  146. Ruiz, B., Sistat, P., Huguet, P., Pourcelly, G., Araya-Farias, M., and Bazinet, L., Document application of relaxation periods during electrodialysis of a casein solution: impact on anion-exchange membrane fouling, J. Membr. Sci., 2007, vol. 287, no. 1, p. 41.
  147. Suwal, S., Amiot, J., Beaulieu, L., and Bazinet, L., Effect of pulsed electric field and polarity reversal on peptide/amino acid migration, selectivity and fouling mitigation, J. Membr. Sci., 2016, vol. 510, p. 405.
  148. Malek, P., Ortiz, J.M., Richards, B.S., and Schäfer, A.I., Electrodialytic removal of NaCl from water: Impacts of using pulsed electric potential on ion transport and water dissociation phenomena, J. Membr. Sci., 2013, vol. 435, p. 99.
  149. Cifuentes-Araya, N., Pourcelly, G., and Bazinet, L., Water splitting proton-barriers for mineral membrane fouling control and their optimization by accurate pulsed modes of electrodialysis, J. Membr. Sci., 2013, vol. 447, p. 433.
  150. Chandrasekar, M.S. and Pushpavanam, M., Pulse and pulse reverse plating–Conceptual, advantages and applications, Electrochim. Acta, 2008, vol. 53, p. 3313.
  151. Cheh, H.Y., Electrodeposition of gold by pulsed current, J. Electrochem. Soc., 1971, vol. 118, no. 4, p. 551.
  152. Yin, K.-M., Duplex diffusion layer model for pulse with reverse plating, Surf. Coat. Technol., 1997, vol. 88, p. 162.
  153. Mishchuk, N.A., Perspectives of the electrodialysis intensification, Desalination, 1998, vol. 117, p. 283.
  154. Mishchuk, N.A., Verbich, S.V., and Gonzalez-Caballero, F., Concentration polarization and specific selectivity of membranes in pulse mode, Colloid J., 2001, vol. 63, p. 586.
  155. Vermaas, D.A., Saakes, M., and Nijmeijer, K., Power generation using profiled membranes in reverse electrodialysis, J. Membr. Sci., 2011, vols. 385–386, p. 234.