Direct numerical simulation of electrokinetic instability and transition to chaotic motion

Physics of Fluids

Volumn 25, Issue 12, 2013, Pages

  Demekhin, E A ^a,b   Nikitin, N V ^a   Shelistov, V S ^a,b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b KUBAN STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CHANNEL FLOW; COMPUTATIONAL FLUID DYNAMICS; ELECTRODYNAMICS; HOPF BIFURCATION; INTEGRATION; NONLINEAR ANALYSIS; NUMERICAL MODELS; PHASE SPACE METHODS; RUNGE KUTTA METHODS; STABILITY; VORTEX FLOW; WHITE NOISE;

CONCENTRATION POLARIZATION; CURRENT CHARACTERISTIC; ELECTROKINETIC INSTABILITIES; HYDRODYNAMIC STABILITY; NERNST-PLANCK-POISSON; NUMERICAL INTEGRATIONS; NUMERICAL INVESTIGATIONS; THRESHOLD OF INSTABILITY;

FINITE DIFFERENCE METHOD;

EID: 84891616497     PISSN: 10706631     EISSN: 10897666     Source Type: Journal    
DOI: 10.1063/1.4843095     Document Type: Article

References (44)

1. Levich L.G. Physicochemical Hydrodynamics 1962, (Prentice-Hall, New York).
2. Grafov B.M. Chernenko A.A. The theory of the passage of a constant current through a solution of a binary electrolyte. Dokl. Akad. Nauk SSSR 1962, 146:135. (in Russian).
3. Bass L. Electrical structures of interfaces in steady electrolysis. Trans. Faraday Soc. 1964, 60:1656. 10.1039/tf9646001656
4. Smyrl W.H. Newman J. Double layer structure at the limiting current. Trans. Faraday Soc. 1967, 63:207. 10.1039/tf9676300207.
5. Buck R.P. Steady state space charge effects in symmetric cells with concentration polarized electrodes. J. Electroanal. Chem. Interfacial Electrochem. 1973, 46:1. 10.1016/S0022-0728(73)80173-1.
6. Dukhin S.S. Derjagin B.V. Electrophoresis 1976, and 2nd ed. (Nauka, Moscow) (in Russian).
7. Rubinstein I. Shtilman L. Voltage against current curves of cation exchange membranes. J. Chem. Soc. Faraday Trans. 2 1979, 75:231. 10.1039/f29797500231
8. Nikonenko V.V. Zabolotsky V.I. Gnusin N.P. Electric transport of ions through diffusion layers with impaired electroneutrality. Sov. Electrochem. 1989, 25:301.
9. Listovnichy A.V. Passage of currents higher than the limiting one through the electrode-electrolyte solution system. Sov. Electrochem. 1989, 51:1651.
10. Manzanares J.A. Murphy W.D. Mafe S. Reiss H. Numerical simulation of the nonequilibrium diffuse double layer in ion-exchange membranes. J. Phys. Chem. 1993, 97:8524. 10.1021/j100134a023
11. Babeshko V.A. Zabolotsky V.I. Korzhenko N.M. Seidov R.R. Urtenov M.K. The theory of steady-state transport of a binary electrolyte in the one-dimensional case. Dokl. Akad. Nauk 1998, 361:41. (in Russian).
12. 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
13. Zaltzman B. Rubinstein I. Electroosmotic slip and electroconvective instability. J. Fluid Mech. 2007, 579:173. 10.1017/S0022112007004880
14. Belova E.I. Lopatkova G.Y. Pismenskaya N.D. Nikonenko V.V. Larchet C. Pourcelly G. Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer. J. Phys. Chem. B 2006, 110:13458. 10.1021/jp062433f
15. Pismenskaya N.D. Nikonenko V.V. Belova E.I. Lopatkova G. Sistat P. Pourcelly G. Larchet K. Coupled convection of solution near the surface of ion-exchange membranes in intensive current regimes. Russ. J. Electrochem. 2007, 43:307. 10.1134/S102319350703010X
16. 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
17. Maletzki F. Rossler 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 condition of free convection. J. Membr. Sci. 1992, 71:105. 10.1016/0376-7388(92)85010-G
18. Rubinshtein I. Zaltzman B. Pretz J. Linder C. Experimental verification of the electroosmotic mechanism of overlimiting conductance through a cation exchange electrodialysis membrane. Russ. J. Electrochem. 2002, 38:853. 10.1023/A:1016861711744
19. Rubinstein S.M. Manukyan G. Staicu A. Rubinstein I. Zaltzman B. Lammertink R.G. H. Mugele F. Wessling M. Direct observation of nonequilibrium electroosmotic instability. Phys. Rev. Lett. 2008, 101:236101. 10.1103/PhysRevLett.101.236101
20. Yossifon G. Chang H.-C. Selection of nonequilibrium overlimiting currents: Universal depletion layer formation dynamics and vortex instability. Phys. Rev. Lett. 2008, 101:254501. 10.1103/PhysRevLett.101.254501
21. 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
22. Rubinstein I. Zaltzman B. Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 2000, 62:2238. 10.1103/PhysRevE.62.2238
23. 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
24. Demekhin E.A. Shelistov V.S. Polyanskikh S.V. Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability. Phys. Rev. E 2011, 84:036318. 10.1103/PhysRevE.84.036318
25. Shelistov V.S. Nikitin N.V. Ganchenko G.S. Demekhin E.A. Numerical modeling of electrokinetic instability in semipermeable membranes. Dokl. Phys. 2011, 56:538. 10.1134/S1028335811100107
26. Chang H.-C. Yossifon G. Demekhin E.A. Nanoscale electrokinetics and microvortices: How microhydrodynamics affects nanofluidic ion flux. Annu. Rev. Fluid Mech. 2012, 44:401. 10.1146/annurev-fluid-120710-101046
27. Kalaidin E.N. Polyanskikh S.V. Demekhin E.A. Self-similar solutions in ion-exchange membranes and their stability. Dokl. Phys. 2010, 55:502. 10.1134/S1028335810100071
28. Demekhin E.A. Polyanskikh S.V. Shtemler Y.M. Electroconvective instability of self-similar equilibria. e-print arXiv:1001.4502.
29. Demekhin E.A. Shapar E.M. Lapchenko V.V. Initiation of electroconvection in semipermeable electric membranes. Dokl. Phys. 2008, 53:450. 10.1134/S1028335808080119
30. 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 permselective membrane. Phys. Rev. E 2012, 86:046310. 10.1103/PhysRevE.86.046310
31. Druzgalski C.L. Andersen M.B. Mani A. Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface. Phys. Fluids 2013, 25:110804. 10.1063/1.4818995
32. Nikonenko V. Pismenskaya N. Belova E. Sistat P. Huguet P. Pourcelly G. Larchet C. Intensive current transfer in membrane systems: Modelling, mechanisms and application in electrodialysis. Adv. Colloid Interface Sci. 2010, 160:101. 10.1016/j.cis.2010.08.001
33. Rubinstein I. Zaltzman B. Wave number selection in a nonequilibrium electroosmotic instability. Phys. Rev. E 2003, 68:032501. 10.1103/PhysRevE.68.032501
34. Pundik T. Rubinstein I. Zaltzman B. Bulk electroconvection in electrolyte. Phys. Rev. E 2005, 72:061502. 10.1103/PhysRevE.72.061502
35. Chang H.-C. Demekhin E.A. Shelistov V.S. Competition between Dukhin's and Rubinstein's electrokinetic modes. Phys. Rev. E 2012, 86:046319. 10.1103/PhysRevE.86.046319
36. Nikitin N.V. Third-order-accurate semi-implicit Runge-Kutta scheme for incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 2006, 51(2):221. 10.1002/fld.1122.
37. Nikitin N.V. Finite-difference method for incompressible Navier-Stokes equations in arbitrary orthogonal curvilinear coordinates. J. Comput. Phys. 2006, 217(2):759. 10.1016/j.jcp.2006.01.036.
38. Nikitin N.V. On the rate of spatial predictability in near-wall flows. J. Fluid Mech. 2008, 614:495. 10.1017/S0022112008003741.
39. Nikitin N.V. A spectral finite-difference method of calculating turbulent flows of an incompressible fluid in pipes and channels. Comput. Math. Math. Phys. 1994, 34:785. available online at:.
40. Nikitin N.V. Statistical characteristics of wall turbulence. Fluid Dyn. 1996, 31:361. 10.1007/BF02030217.
41. Cross M.C. Hohenberg P.G. Pattern formation outside of equilibrium. Rev. Mod. Phys. 1993, 65(3):851. 10.1103/RevModPhys.65.851
42. Eckhaus W. Studies in Nonlinear Stability Theory 1965, (Springer-Verlag, New York).
43. Chang H.-C. Demekhin E.A. Kopevevich D.I. Nonlinear evolution of waves on a vertically falling film. J. Fluid Mech. 1993, 250:433. 10.1017/S0022112093001521
44. Guckenheimer J. Holmes P. Nonlinear Oscillations. Dynamical System and Bifurcations of Vector Fields 1983, xvi + 453. and (Springer-Verlag, New York)