Electroosmosis of the Second Kind on Flat Charged Surfaces – a Direct Numerical Simulation Study
Main Article Content
Abstract
While the electroosmosis of the first kind (equilibrium) is accepted widely, the electroosmosis of the second kind (nonequilibrium) is still controversial. In this work, the theory of electroosmosis slip, of either the first kind or of the second kind at electrolyte membrane system is revisited via our direct numerical simulation. The obtained results show that above a certain voltage threshold, the basic conduction state becomes electroconvectively unstable. This instability provides a mechanism for explaining the over-limiting conductance in concentration polarization at a permselective membrane. The most important work in our study is to examine the famous electroosmosis of the second kind formula suggested by Rubinstein and Zaltzman in 1999. Although their formula has been presented for a long time, there has no work to validate its accuracy experimentally or numerically due to the difficulty in pinpointing exactly the extended space charge layer in their formula. By using direct numerical simulation, we could solve this problem and inspect the application range of their formula. This also helps to strongly confirm the relationship between the electroosmosis of the second kind and the instability in concentration polarization at electrodialysis membranes.
Keywords
electroosmosis, concentration polarization, permselective membrane
Article Details
References
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[3] T. Pundik, I. Rubinstein, B. Zaltzman, Bulk electroconvection in electrolyte, Physical Review E, vol. 72, no. 061502, Dec. 2005 https://doi.org/10.1103/PhysRevE.72.061502.
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[5] E. V. Dydek, B. Zaltzman, I. Rubinstein, D. S. Deng, A. Mani, M. Z. Bazant, Over-limiting current in a microchannel, Physical Review Letters, vol. 107, no. 118301, Sep. 2011 https://doi.org/10.1103/PhysRevLett.107.118301
[6] Block M, Kitchener JA. J, Polarization phenomena in commercial ion‐exchange membranes, J. Electrochem Soc, 113-947, 1966. https://doi.org/10.1149/1.2424162
[7] Maletzki F, Rossler HW, Staude E. J, Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability, Membr Sci, 71:105, Sep. 2011 https://doi.org/10.1103/PhysRevE.84.036318.
[8] S. S. Dukhin, Electro-kinetic phenomena of the second kind and their applications, Adv. Coll. Interf. Sci. 35, pp. 173-196, 1991. https://doi.org/10.1016/0001-8686(91)80022-C
[9] I. Rubinstein and L. Shtilman, Voltage against current curves of cation exchange membrane, J. Chem. Soc., vol. 75, pp. 231-246, 1979. https://doi.org/10.1039/f29797500231
[10] E. K. Zholkovskij, M. A. Vorotynsev, E. Staude, Electro-kinetic instability of solution in a plane-parallel electrochemical cell, J. Colloid Interf. Sci, vol. 181, pp. 28-33, July. 1996 https://doi.org/10.1006/jcis.1996.0353.
[11] S. S. Dukhin and B. V. Derjaguin, Electrophoresis, Moscow, Nauka 1976.
[12] Pham, V. S., Li, Z., Lim, K. M., White, J. K., Han J., Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a perm-selective membrane, Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys, vol. 86, no. 4, pp. 1–11. 2012 https://doi.org/10.1103/PhysRevE.86.046310
[2] I. Rubinstein, Electro-convection at an electrically inhomogeneous perm-selective interface, Phys. Fluids A, vol. 3, no. 10, pp. 2301-2309, Jan. 1991, https://doi.org/10.1063/1.857869.
[3] T. Pundik, I. Rubinstein, B. Zaltzman, Bulk electroconvection in electrolyte, Physical Review E, vol. 72, no. 061502, Dec. 2005 https://doi.org/10.1103/PhysRevE.72.061502.
[4] V. V. Nikonenko, N. D. Pismenskaya, E. I. Belova, P. Sistat, P. Huguet, G. Pourcelly, C. Larchet, Intensive current transfer in membrane systems: modeling, mechanisms and application in electro-dialysis., Advances in Colloid and Interface Science, vol. 160, no. 1-2, pp. 101-123, Aug. 2010 https://doi.org/10.1016/j.cis.2010.08.001.
[5] E. V. Dydek, B. Zaltzman, I. Rubinstein, D. S. Deng, A. Mani, M. Z. Bazant, Over-limiting current in a microchannel, Physical Review Letters, vol. 107, no. 118301, Sep. 2011 https://doi.org/10.1103/PhysRevLett.107.118301
[6] Block M, Kitchener JA. J, Polarization phenomena in commercial ion‐exchange membranes, J. Electrochem Soc, 113-947, 1966. https://doi.org/10.1149/1.2424162
[7] Maletzki F, Rossler HW, Staude E. J, Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability, Membr Sci, 71:105, Sep. 2011 https://doi.org/10.1103/PhysRevE.84.036318.
[8] S. S. Dukhin, Electro-kinetic phenomena of the second kind and their applications, Adv. Coll. Interf. Sci. 35, pp. 173-196, 1991. https://doi.org/10.1016/0001-8686(91)80022-C
[9] I. Rubinstein and L. Shtilman, Voltage against current curves of cation exchange membrane, J. Chem. Soc., vol. 75, pp. 231-246, 1979. https://doi.org/10.1039/f29797500231
[10] E. K. Zholkovskij, M. A. Vorotynsev, E. Staude, Electro-kinetic instability of solution in a plane-parallel electrochemical cell, J. Colloid Interf. Sci, vol. 181, pp. 28-33, July. 1996 https://doi.org/10.1006/jcis.1996.0353.
[11] S. S. Dukhin and B. V. Derjaguin, Electrophoresis, Moscow, Nauka 1976.
[12] Pham, V. S., Li, Z., Lim, K. M., White, J. K., Han J., Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a perm-selective membrane, Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys, vol. 86, no. 4, pp. 1–11. 2012 https://doi.org/10.1103/PhysRevE.86.046310