Concentration polarization and second-kind electrokinetic instability at an ion-selective surface admitting normal flow

Physics of Fluids

Volumn 23, Issue 7, 2011, Pages

  Khair, Aditya S ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; ASYMPTOTIC ANALYSIS; DIFFUSION IN LIQUIDS; ELECTRIC FIELDS; ELECTROLYTES; ELECTROOSMOSIS; IONS; LINEAR STABILITY ANALYSIS; MEMBRANES; POLARIZATION; SURFACE DIFFUSION;

CONCENTRATION POLARIZATION; ELECTRO-OSMOTIC INSTABILITY; ELECTROKINETIC INSTABILITIES; GENERALIZED MASTER EQUATIONS; ION-SELECTIVE SURFACES; MATCHED ASYMPTOTIC EXPANSION; NONLINEAR CONCENTRATION; OVER-LIMITING CURRENTS;

FLOW OF FLUIDS;

EID: 79960909521     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3605693     Document Type: Article

References (80)

1. Eijkel J.C. T. van den Berg A. Nanofluidics: what is it and what can we expect from it?. Microfluid. Nanofluid. 2005, 1:249. 10.1007/s10404-004-0012-9
2. Schoch R. Han J. Renaud P. Transport phenomena in nanofluidics. Rev. Mod. Phys. 2008, 80:839. 10.1103/RevModPhys.80.839
3. Bocquet L. Charlaix E. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 2010, 39:1073. 10.1039/b909366b
4. Napoli M. Eijkel J.C. T. Pennathur S. Nanofluidic technology for biomolecule applications: a critical review. Lab Chip 2010, 10:957. 10.1039/b917759k
5. Chang H.-C. Yeo L.Y. Electrokinetically-Driven Microfluidics and Nanofluidics 2010, and (Cambridge University Press, Cambridge, UK).
6. Stone H.A. Stroock A.D. Ajdari A. Engineering flows in small devices: microfluidics toward lab-on-a-chip. Annu. Rev. Fluid Mech. 2004, 36:381. 10.1146/annurev.fluid.36.050802.122124
7. Wang Y.-C. Stevens A.L. Han J. Million-fold preconcentration of proteins and peptides by nanofluidic filter. Anal. Chem. 2005, 77:4293. 10.1021/ac050321z
8. Kim S.J. Ko S.H. Kang K.H. Han J. Direct seawater desalination by ion concentration polarization. Nature Nanotechnol. 2010, 5:297. 10.1038/nnano.2010.34
9. van F.H. J. Bonthuis D.J. Stein D. Meyer C. Dekker C. Power generation by pressure-driven transport of ions in nanofluidic channels. Nano Lett. 2007, 7:1022. 10.1021/nl070194h, der Heyden
10. Vlassiouk I. Kozal T.R. Siwy Z.S. Biosensing with nanofluidic diodes. J. Am. Chem. Soc. 2009, 131:8211. 10.1021/ja901120f
11. Kim S.J. Wang Y.C. Lee J.H. Jang H. Han J. Concentration polarization and nonlinear electrokinetic flow near a nanofluidic channel. Phys. Rev. Lett. 2007, 99:044501. 10.1103/PhysRevLett.99.044501
12. Kim S.J. Li L.D. Han J. Amplified electrokinetic response by concentration polarization near nanofluidic channel. Langmuir 2009, 25:7759. 10.1021/la900332v
13. Siwy Z. Fuliński A. Fabrication of a synthetic nanopore ion pump. Phys. Rev. Lett. 89:198103. 10.1103/PhysRevLett.89.198103
14. Yossifon G. Chang H.-C. Selection of non-equilibrium overlimiting currents: universal depletion layer formation dynamics and vortex instability. Phys. Rev. Lett. 2008, 101:254501. 10.1103/PhysRevLett.101.254501
15. Yossifon G. Mushenheim P. Chang Y.-C. Chang H.-C. Nonlinear current-voltage characteristics of nanochannels. Phys. Rev. E 2009, 79:046305. 10.1103/PhysRevE.79.046305
16. Lyklema J. Fundamentals of Interface and Colloid Science. Volume II: Solid-Liquid Interfaces 1995, (Academic Press, San Diego CA).
17. Vlassiouk I. Siwy Z.S. Nanofluidic diode. Nano Lett. 2007, 7:552. 10.1021/nl062924b
18. Karnik R. Duan C. Castelino K. Daiguji H. Majumdar A. Rectification of ionic current in a nanofluidic diode. Nano Lett. 2007, 7:547. 10.1021/nl062806o
19. Jung J.-Y. Joshi P. Petrossian L. Thornton T.J. Posner J.D. Electromigration current rectification in a cylindrical nanopore due to asymmetric concentration polarization. Anal. Chem. 2009, 81:3128. 10.1021/ac900318j
20. Yossifon G. Chang Y.-C. Chang H.-C. Rectification, gating voltage, and interchannel communication of nanoslot arrays due to asymmetric entrance space charge polarization. Phys. Rev. Lett. 2009, 103:154502. 10.1103/PhysRevLett.103.154502
21. Mani A. Zangle T.A. Santiago J.G. On the propagation of concentration polarization from microchannel-nanochannel interfaces part I: Analytical model and characteristic analysis. Langmuir 2009, 25:3898. 10.1021/la803317p
22. Zangle T. Mani A. Santiago J.G. On the propagation of concentration polarization from microchannel-nanochannel interfaces part II: Numerical and experimental study. Langmuir 2009, 25:3909. 10.1021/la803318e
23. Tobias C.W. Einsenberg M. White C.R. Diffusion and convection in electrolysis-a theoretical review. J. Electrochem. Soc. 1952, 99:359C. 10.1149/1.2779636
24. Vogtländer P.H. Bakker C.A. P. An experimental study of mass transfer from a liquid flow to wires and gauzes. Chem. Eng. Sci. 1963, 18:583. 10.1016/0009-2509(63)85027-7
25. Rosso M. Electrodeposition from a binary electrolyte: new developments and applications. Electrochim. Acta 2007, 53:250. 10.1016/j.electacta.2007.02.026.
26. Rosenberg N.W. Tirrell C.E. Limiting currents in membrane cells. Ind. Eng. Chem. 1957, 49:780. 10.1021/ie50568a047
27. Cowan D. Brown J. Effect of turbulence on limiting current in electrodialysis cells. Ind. Eng. Chem. 1959, 51:1445. 10.1021/ie50600a026
28. Spiegler K.S. Polarization at ion exchange membrane-solution interfaces. Desalination 1971, 9:367. 10.1016/0011-9164(71)80005-X.
29. Rubinstein I. Shtilman L. Voltage against current curves of cation exchange membranes. J. Chem. Soc. Faraday Trans. II 1979, 75:231. 10.1039/f29797500231
30. Tanaka Y. Concentration polarization in ion exchange membrane electrodialysis. J. Membr. Sci. 1991, 57:217. 10.1016/S0376-7388(00)80680-8.
31. Tallarek U. Leinweber F.C. Nischang I. Perspective on concentration polarization effects in electrochromatographic separations. Electrophoresis 2005, 26:391. 10.1002/elps.v26:2
32. Nischang I. Höltzel A. Seidel-Morgenstern A. Tallarek U. Concentration polarization and non-equilibrium electroosmotic slip in hierarchical monolithic structures. Electrophoresis 2008, 29:1140. 10.1002/elps.v29:5
33. Weber H.F. Untersuchungen über das elementargesetz der hydrodiffusion. Ann. Phys. (Berlin) 1879, 243:536. 10.1002/andp.18792430803.
34. Nernst W. Theorie der reaktionsgeschwindigkeit in heterogenen systemen. Z. Phys. Chem. 1904, 47:52.
35. Brunner E. Reaktionsgeschwindigkeit in heterogenen systemen. Z. Phys. Chem. 1904, 47:56.
36. Brunner E. Die kathodische und anodische Stromspannungskurve bei der Elektrolyse von Jod-Jodkaliumlösungen. Z. Phys. Chem. 1908, 58:1.
37. Rubinstein I. Staude E. Kedem O. Role of the membrane surface in concentration polarization at ion-exchange membrane. Desalination 1988, 69:101. 10.1016/0011-9164(88)80013-4
38. Maletzki F. Rosler H.W. 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, 71:105. 10.1016/0376-7388(92)85010-G
39. Levich V.G. Physicochemical Hydrodynamics 1962, (Prentice-Hall, Inc., Englewood Cliffs, NJ).
40. Smyrl W.H. Newman J. Double layer structure at the limiting current. Trans. Faraday Soc. 1967, 63:207. 10.1039/tf9676300207
41. Chu K.T. Bazant M.Z. Electrochemical thin films at and above the classical limiting current. SIAM J Appl. Math. 2005, 65:1485. 10.1137/040609926
42. Rubinstein I. Zaltzmann B. Electrodiffusional free boundary problem in concentration polarization in electrodialysis. Math. Models Meth. Appl. Sci. 1996, 6:623. 10.1142/S0218202596000250
43. Rubinstein I. Zaltzman B. Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Models Meth. Appl. Sci. 2001, 11:263. 10.1142/S0218202501000866
44. Ben Y. Chang H.-C. Nonlinear Smoluchowski slip velocity and micro-vortex generation. J. Fluid Mech. 2002, 461:229. 10.1017/S0022112002008662
45. Yariv E. Asymptotic current-voltage relations for currents exceeding the diffusion limit. Phys. Rev. E 2009, 80:051201. 10.1103/PhysRevE.80.051201.
46. Rubinstein S.M. Manukyan G. Staicu A. Rubinstein I. Zaltzman B. Lammertink R.G. H. Mugele F. Wessling M. Direct observation of a non-equilibrium electro-osmotic instability. Phys. Rev. Lett. 2008, 101:236101. 10.1103/PhysRevLett.101.236101
47. Bruinsma R. Alexander S. Theory of electrohydrodynamic instabilities in electrolytic cells. J. Chem. Phys. 1990, 92:3075. 10.1063/1.457905
48. Baygents J.C. Baldessari F. Electrohydrodynamic instability in a thin fluid layer with an electrical conductivity gradient. Phys. Fluids 1998, 10:301. 10.1063/1.869567
49. Lin H. Storey B.D. Oddy M.H. Chen C.-H. Santiago J.G. Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 2004, 16:1922. 10.1063/1.1710898
50. Lerman I. Rubinstein I. Zaltzman B. Absence of bulk electroconvective instability in concentration polarization. Phys. Rev. E 2005, 71:011506. 10.1103/PhysRevE.71.011506
51. Dukhin S.S. Electrokinetic phenomena of the second kind and their applications. Adv. Colloid Interface Sci. 1991, 35:173. 10.1016/0001-8686(91)80022-C.
52. Zholkovskij E. Vorotyntsev M. Staude E. Electrokinetic instability of solution in a plane-parallel electrochemical cell. J. Colloid Interface Sci. 1996, 181:28. 10.1006/jcis.1996.0353
53. Mishchuk N.A. Takhistov P.V. Electroosmosis of the second kind. Colloids Surf. A 1995, 95:119. 10.1016/0927-7757(94)02988-5
54. Mishchuk N.A. Concentration polarization of interface and non-linear electrokinetic phenomena. Adv. Colloid Interface Sci. 2010, 160:16. 10.1016/j.cis.2010.07.001.
55. Rubinstein I. Zaltzman B. Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 2000, 62:2238. 10.1103/PhysRevE.62.2238
56. Rubinstein I. Zaltzman B. Wave number selection in a non-equilibrium electro-osmotic instability. Phys. Rev. E 2003, 68:032501. 10.1103/PhysRevE.68.032501
57. Takemoto N. The concentration distribution in the interfacial layer at the desalting side in ion exchange membrane electrodialysis. J. Chem. Soc. Jpn. 1972, 2053.
58. Ehlert S. Hlushkou D. Tallarek U. Electrohydrodynamics around single ion-permselective glass beads fixed in a microfluidic device. Microfluid. Nanofluid. 2008, 4:471. 10.1007/s10404-007-0200-5
59. Hsu J.P. Yang K.L. Ting K.C. Effect of convective boundary layer on the current efficiency of a membrane bearing nonuniformly distributed fixed charges. J. Phys. Chem. B 1997, 8984. 10.1021/jp962639o
60. Fíla V. Bouzek K. The effect of convection in the external diffusion layer on the results of a mathematical model of multiple ion transport across an ion-selective membrane. J. Appl. Electrochem. 2008, 38:1241. 10.1007/s10800-008-9545-z
61. Dukhin S.S. Churaev N.V. Shilov V.N. Starov V.M. Modelling reverse osmosis. Russ. Chem. Rev. 1988, 57:572. 10.1070/RC1988v057n06ABEH003374
62. Hoek E.M. V. Elimelech M. Cake-enhanced concentration polarization: a new fouling mechanism for salt-rejecting membranes. Environ. Sci. Technol. 2003, 37:5581. 10.1021/es0262636
63. Kim S. Hoek E.M. Modeling concentration polarization in reverse osmosis processes. Desalination 2005, 186:111. 10.1016/j.desal.2005.05.017
64. Bowen W.R. Welfoot J.S. Modelling the performance of membrane nanofiltration-critical assessment and model development. Chem. Eng. Sci. 2002, 57:1121. 10.1016/S0009-2509(01)00413-4
65. Nagy E. Kulcár E. Nagy A.N. Membrane mass transport by nanofiltration: Coupled effect of the polarization and membrane layers. J. Membr. Sci. 2011, 368:215. 10.1016/j.memsci.2010.11.046
66. Xie Y. Wang X. Xue J. Jin K. Chen L. Wang Y. Electric energy generation in single track etched nanopores. Appl. Phys. Lett. 2008, 93:163116. 10.1063/1.3001590
67. Bazant M.Z. Regulation of ramified electrochemical growth by a diffusive wave. Phys. Rev. E 1995, 52:1903. 10.1103/PhysRevE.52.1903.
68. Barkey D.P. LaPorte P.D. The dynamic diffusion layer in branched growth of a conductive polymer aggregate in a 2-D electrolysis cell. J. Electrochem. Soc. 1990, 137:1655. 10.1149/1.2086748
69. Leger C. Elezgaray J. Argoul F. Dynamical characterization of one-dimensional stationary growth regimes in diffusion-limited electrodeposition processes. Phys. Rev. E 1998, 58:7700. 10.1103/PhysRevE.58.7700
70. Chazalviel J.N. Electrochemical aspects of the generation of ramified metallic deposits. Phys. Rev. A 1990, 42:7355. 10.1103/PhysRevA.42.7355.
71. Huth J.M. Swinney H.L. McCormick W.D. Kuhn A. Argoul F. Role of convection in thin-layer electrodeposition. Phys. Rev. E 1995, 51:3444. 10.1103/PhysRevE.51.3444
72. Fleury V. Kaufman J. Hibbert B. Evolution of the space-charge layer during electrochemical deposition with convection. Phys. Rev. E 1993, 48:3831. 10.1103/PhysRevE.48.3831
73. Saville D.A. Electrokinetic effects with small particles. Ann. Rev. Fluid Mech. 1977, 9:321. 10.1146/annurev.fl.09.010177.001541.
74. Dukhin S.S. Non-equilibrium electric surface phenomena. Adv. Colloid Interface Sci. 1993, 44:1. 10.1016/0001-8686(93)80021-3.
75. Newman J. The polarized diffuse double layer. Trans. Faraday Soc. 1965, 61:2229. 10.1039/tf9656102229.
76. Newman J.S. Electrochemical systems 1991, (Prentice-Hall Inc., Englewood Cliffs, NJ).
77. Bazant M.Z. Chu K.T. Bayly B.J. Current-voltage relations for electrochemical thin films. SIAM J Appl. Math. 2005, 65:1463. 10.1137/040609938
78. Rubinstein I. Zaltzman B. Lerman I. Electroconvective instability in concentration polarization and non-equilibrium electro-osmotic slip. Phys. Rev. E 2005, 72:011505. 10.1103/PhysRevE.72.011505
79. Zaltzman B. Rubinstein I. Electro-osmotic slip and electroconvective instability. J. Fluid Mech. 2007, 579:173. 10.1017/S0022112007004880
80. Newman J. Current distribution on a rotating disk below the limiting current. J. Electrochem. Soc. 1966, 113:1235. 10.1149/1.2423795.