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Electro-osmotic slip and electroconvective instability

Published online by Cambridge University Press:  02 May 2007

B. ZALTZMAN  and
I. RUBINSTEIN
B. ZALTZMAN
Affiliation:
DSEEP, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede-Boqer Campus, 84990, Israel
I. RUBINSTEIN
Affiliation:
DSEEP, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede-Boqer Campus, 84990, Israel
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Abstract

Electric conduction from an electrolyte solution into a charge selective solid, such as ion exchange membrane or electrode, becomes unstable when the electrolyte concentration near the interface approaches zero owing to diffusion limitation. The sequence of events leading to instability is as follows: upon the decrease of the interface concentration, the electric double layer at the interface transforms from its common quasi-equilibrium structure to a different, non-equilibrium one. The key feature of this new structure is an extended space charge added to the usual one of the quasi-equilibrium electric double layer. The non-equilibrium electro-osmotic slip related to this extended space charge renders the quiescent conductance unstable. A unified asymptotic picture of the electric double-layer undercurrent, encompassing all regimes from quasi-equilibrium to the extreme non-equilibrium one, is developed and employed for derivation of a universal electro-osmotic slip formula. This formula is used for a linear stability study of quiescent electric conduction, yielding the precise parameter range of instability, compared with that in the full electroconvective formulation. The physical mechanism of instability is traced both kinematically, in terms of non-equilibrium electro-osmotic slip, and dynamically, in terms of forces acting in the electric double layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 579 , 25 May 2007 , pp. 173 - 226
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Alexandrov, R. S., Grigin, A. P. & Davydov, A. P. 2002 Numerical study of electroconvective instability of binary electrolyte in a cell with plane parallel electrodes. Russ. J. Electrochem. 38, 1216–1222.Google Scholar
Baygents, J. C. & Baldessari, F. 1998 Electrohydrodynamic instability in a thin fluid layer with an electrical conductivity gradient. Phys. Fluids 10, 301–311.CrossRefGoogle Scholar
Bazant, M. Z. & Squires, T. M. 2004 a Induced-charge electro-osmosis. J. Fluid Mech. 509, 217–252.Google Scholar
Bazant, M. Z. & Squires, T. M. 2004 b Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92, 066101.CrossRefGoogle ScholarPubMed
Bazant, M. Z., Thornton, K. & Ajdari, A. 2004 Diffuse-charge dynamics in electrochemical systems. Phys. Rev. E 70, 021506.Google ScholarPubMed
Belova, E. I., Lopatkova, G. Y., Pismenskaya, N. D., Nikonenko, V. V., Larchet, C. & Pourcelly, G. 2006 Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer. J. Phys. Chem. B 110, 13458–13469.CrossRefGoogle ScholarPubMed
Ben, Y. & Chang, H. C. 2002 Nonlinear Smoluchowski slip velocity and micro-vortex generation. J. Fluid Mech. 461, 229–238.CrossRefGoogle Scholar
Block, M. & Kitchener, J. A. 1966 Polarization phenomena in commercial ion-exchange membranes. J. ElectroChem. Soc. 113, 947–953.CrossRefGoogle Scholar
Bruinsma, R. & Alexander, S. 1990 Theory of electrohydrodynamic instabilities in electrolytic cells. J. Chem. Phys. 92, 3074–3085.CrossRefGoogle Scholar
Buchanan, M. E. & Saville, D. A. 1999 Electrohydrodynamic stability in electrochemical systems. In Proc. AIChE Annual Meeting (ed. APS Meeting Abstracts), pp. D8+. Am. Phys. Soc.Google Scholar
Buck, R. P. 1973 Steady-state space-charge effects in symmetric cells with concentration polarized electrodes. J. Electroanal. Chem. 46, 1–23.CrossRefGoogle Scholar
Castellanos, A. & Velarde, M. G. 1981 Electrohydrodynamic stability in the presence of a thermal gradient. Phys. Fluids 24, 1784–1786.CrossRefGoogle Scholar
Chen, C. H., Lin, H., Lele, S. K. & Santiago, J. G. 2005 Convective and absolute electrokinetic instability with conductivity gradients. J. Fluid Mech 524, 263–303.CrossRefGoogle Scholar
Chu, K. T. & Bazant, M. Z. 2005 Electrochemical thin films at and above the classical limiting current. SIAM J. Appl. Math 65, 1485–1505.CrossRefGoogle Scholar
Dukhin, S. S. 1991 Electrokinetic phenomena of the second kind and their applications. Adv. Colloid Interface Sci. 35, 173–196.CrossRefGoogle Scholar
Dukhin, S. S. & Derjaguin, B. V. 1976 Electrophoresis, 2nd edn. Nauka, Moscow (in Russian).Google Scholar
Dukhin, S. S. & Mishchuk, N. A. 1989 Disappearance of limiting current phenomenon in the case of a granule of an ion-exchanger. Coll. J. USSR 51, 570–581 (in Russian).Google Scholar
Dukhin, S. S., Mishchuk, N. A. & Takhistov, P. B. 1989 Electro-Osmosis of the second kind and unrestricted current increase in the mixed monolayer of an ion-exchanger. Coll. J. USSR 51, 616–618 (in Russian).Google Scholar
Fleury, V., Chazalviel, J.-N. & Rosso, M. 1993 Coupling of drift, diffusion, and electroconvection, in the vicinity of growing electrodeposits. Phys. Rev. E 48, 1279–1295.Google ScholarPubMed
Fleury, V., Kaufman, J. H. & Hibbert, D. B. 1994 Mechanism of a morphology transition in ramified electrochemical growth. Nature 367, 435–438.CrossRefGoogle Scholar
Frillete, V. J. 1957 Electrogravitational transport at synthetic ion exchange membrane surfaces. J. Phys. Chem. 61, 168–174.CrossRefGoogle Scholar
Grafov, B. M. & Chernenko, A. A. 1962 Theory of the passage of a constant current through a solution of a binary electrolyte. Dokl. Akad. Nauk SSSR 146, 135–138 (in Russian).Google Scholar
Grigin, A. P. 1985 The convective coulombic instability of binary electrolytes in cells with plane-parallel electrodes. Sov. Electrochem. 21, 48–53.Google Scholar
Grigin, A. P. 1992 Coulomb convection in electrochemical systems. Sov. Electrochem. 28, 247–269.Google Scholar
Helmholtz, H. 1879 Studien uber electrische grenzschichten. Ann. Phys. Chem. 7, 337–382.CrossRefGoogle Scholar
Kamin, S., Peletier, L. A. & Vazquez, J. L. 1989 Classification of singular solutions of a nonlinear heat-equation. Duke Math. J. 58, 610–615.CrossRefGoogle Scholar
Lerman, I., Rubinstein, I. & Zaltzman, B. 2005 Absence of bulk electroconvective instability in concentration polarization. Phys. Rev. E 71, 011506.Google ScholarPubMed
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice–Hall.Google Scholar
Li, Q., Fang, Y. & Green, M. 1983 Turbulent light scattering fluctuation spectra near a cation electrodialysis membranes. J. Colloid Interface Sci. 91, 412–417.CrossRefGoogle Scholar
Lifson, S., Gavish, B. & Reich, S. 1977 Current noise of ion-selective membranes and turbulent convection in the depleted layer. In Physicochemical Hydrodynamics II (ed. Spalding, D. B.), pp. 141–146. Advance Publications, London.Google Scholar
Listovnichy, A. V. 1989 Passage of currents higher than the limiting one through the electrode–electrolyte solution system. Elektrokhimia 25, 1651–1658 (in Russian).Google Scholar
Livermore, C. & Wong, P. Z. 1994 Convection and turbulence effects in strongly driven electrochemical deposition. Phys. Rev. Lett. 72, 3847–3850.CrossRefGoogle ScholarPubMed
Maletzki, F., Rosler, H. W. & Staude, E. 1992 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. 71, 105–116.CrossRefGoogle Scholar
Manzanares, J. A., Murphy, W. D., Mafe, S. & Reiss, H. 1993 Numerical simulation of the nonequilibrium diffuse double layer in ion-exchange membranes. J. Phys. Chem. 97, 8524–8530.CrossRefGoogle Scholar
Melcher, J. R. 1981 Continuum Electromechanics, 1st edn. MIT Press.Google Scholar
Mishchuk, N., Gonzalez-Caballero, F. & Takhistov, P. 2001 Electro-Osmosis of the second kind and current through curved interface. Colloids Surfaces A 181, 131–144.CrossRefGoogle Scholar
Nasumo, S. & Kai, S. 1991 Instabilities and transition to defect turbulence in electrohydrodynamic convection of nematics. Europhys. Lett. 14, 779–783.CrossRefGoogle Scholar
Nikonenko, V. V., Zabolotsky, V. I. & Gnusin, N. P. 1989 Electric transport of ions through diffusion layers with impaired electroneutrality. Sov. Electrochem. 25, 262–266.Google Scholar
Perez, A. T. & Castellanos, A. 1989 Role of charge diffusion in finite amplitude electroconvection. Phys. Rev. A 40, 5844–5855.CrossRefGoogle ScholarPubMed
Posner, J. D. & Santiago, J. G. 2006 Convective instability of electrokinetic flows in a cross-shaped microchannel. J. Fluid. Mech 555, 1–42.CrossRefGoogle Scholar
Rehberg, I., Horner, F. & Hartung, G. 1991 The measurement of subcritical electroconvection. J. Stat. Phys. 64, 1017–1023.CrossRefGoogle Scholar
Reich, S., Gavish, B. & Lifson, S. 1978 Visualization of hydrodynamic phenomena in the vicinity of a semipermeable membranes. Desalination 24, 295–296.CrossRefGoogle Scholar
Reuss, F. F. 1809 Charge-induced flow. Proc. Imp. Soc. Nat. Moscow 3, 327–336.Google Scholar
Rubinstein, I. 1990 Electrodiffusion of Ions, 1st edn. SIAM.CrossRefGoogle Scholar
Rubinstein, I. 1991 Electroconvection at an electrically inhomogeneous permselective interface. Phys. Fluids A 3, 2301–2309.CrossRefGoogle Scholar
Rubinstein, I. & Shtilman, L. 1979 Voltage against current curves of cation exchange membranes. J. Chem. Soc. Faraday Trans. II 75, 231–246.CrossRefGoogle Scholar
Rubinstein, I. & Zaltzman, B. 2000 Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 62, 2238–2251.Google Scholar
Rubinstein, I. & Zaltzman, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Mod. Meth. Appl. Sci. 11, 263–300.CrossRefGoogle Scholar
Rubinstein, I. & Zaltzman, B. 2003 Wave number selection in a nonequilibrium electro-osmotic instability. Phys. Rev. E 68, 032501.Google Scholar
Rubinstein, I., Warshawsky, A., Schechtman, L. & Kedem, O. 1984 Elimination of acid-base generation (‘water splitting’) in electrodialysis. Desalination 51, 55–60.CrossRefGoogle Scholar
Rubinstein, I., Shtaude, E. & Kedem, O. 1988 Role of the membrane surface in concentration polarization at ion-exchange membrane. Desalination 62, 101–114.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, T. & Zaltzman, B. 1995 Electroconvection in a layer and in a loop. Phys. Fluids 7, 1467–1482.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, B. & Kedem, O. 1997 Electric fields in and around ion-exchange membranes. J. Membrane Sci. 125, 17–23.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, B., Pretz, J. & Linder, C. 2002 Experimental verification of the electroosmotic mechanism of overlimiting conductance through a cation exchange electrodialysis membrane. Russ. Electrochem. 38, 853–864.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, B. & Lerman, I. 2005 Electroconvective instability in concentration polarization and nonequilibrium electro-osmotic slip. Phys. Rev. E 72, 011505.Google ScholarPubMed
Saville, D. A. 1997 Electrohydrodynamics: The Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.CrossRefGoogle Scholar
Schneider, M. & Watson, P. K. 1970 Electrohydrodynamic stability of space-charge-limited currents in dielectric liquids: I. theoretical study. Phys. Fluids 19, 1948–1954.CrossRefGoogle Scholar
Simons, R. 1979 a The origin and elimination of water splitting in ion-exchange membranes s during water demineralization by electrodialysis. Desalination 29, 41–42.CrossRefGoogle Scholar
Simons, R. 1979 b Strong electric field effects on proton transfer between membrane-bound amines and water. Nature 280, 824–826.CrossRefGoogle Scholar
Smoluchowski, M. 1914 Elektrische Endosmose und Strömungsstr. J. A. Barth, Leipzig.Google Scholar
Smyrl, W. H. & Newman, J. 1967 Double layer structure at the limiting current. Trans. Farday Soc. 63, 207–216.CrossRefGoogle Scholar
Taylor, G. I. 1966 Studies in electrohydrodynamics. i. Circulation produced in a drop byan electric field. Proc. R. Soc. Lond. A 291, 159–166.Google Scholar
Trau, M., Saville, D. A. & Aksay, I. A. 1996 Field-induced layering of colloidal crystals. Science 272, 706–709.CrossRefGoogle ScholarPubMed
Trau, M., Saville, D.A. & Aksay, I. A. 1997 Assembly of colloidal crystals at electrode interfaces. Langmuir 13, 6375–6381.CrossRefGoogle Scholar
Winkler, B. L., Richter, H., Rehberg, I., Zimmermann, W., Kramer, L. & Buka, A. 1991 Nonequilibrium patterns in the electric-field-induced splay fréedericksz transition. Phys. Rev. A 43, 1940–1951.CrossRefGoogle ScholarPubMed
Zholkovskij, E. K., Vorotyntsev, M. A. & Staude, E. 1996 Electrokinetic instability of solution in a plane-parallel electrochemical cell. J. Colloid Interface Sci. 181, 28–331.CrossRefGoogle Scholar