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Bulk electroconvective instability at high Peclet numbers

Bulk electroconvective instability at high Peclet numbers. Brian D. Storey (Olin College) Boris Zaltzman & Isaak Rubinstein (Ben Gurion University of the Negev). Physical setup. Fixed potential Fixed concentration of C+ No flux of C-. Binary electrolyte (C+,C-) Equations

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Bulk electroconvective instability at high Peclet numbers

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  1. Bulk electroconvective instability at high Peclet numbers Brian D. Storey (Olin College) Boris Zaltzman & Isaak Rubinstein (Ben Gurion University of the Negev)

  2. Physical setup • Fixed potential • Fixed concentration of C+ • No flux of C- • Binary electrolyte (C+,C-) • Equations • Poisson-Nernst-Planck • Incompressible Navier-Stokes Solid surfaces are charge selective (electrode or ion exchange membrane). y x

  3. Steady state (no flow) V=1 Double layer, Debye =0.01 E, flux of C+ Double layer, Debye =0.01 Bulk is electro-neutral, linear conc. profile Typical dimensionless Debye =0.0001 or less

  4. Current-voltage relationship Resistor at low voltage

  5. Different views on bulk stability Microfluidic observations of bulk instability with imposed concentration gradients Conflicting reports of bulk instability in present geometry • Bulk instability. Grigin (1985, 1992) • Bulk instability, but not sufficient for mixing. Bruinsma & Alexander (1990) • Bulk instability. Rubinstein, Zaltzman, & Zaltzman (1995). • No bulk instability. Buchanan & Saville (1999) • No bulk instability. Highlighted problems with all earlier works reporting instability. Limited parameter space. Lerman, Zaltzman, Rubinstein (2005) Lin, Storey, Oddy, Chen & Santiago (2004) El Mochtar, Aubry, Batton (2003)

  6. Bulk electroconvective (BE) model Convection/Diffusion of concentration Current continuity Navier-Stokes Incompressibility First 2 equations are derived from Poisson-Nernst-Planck, assuming electro-neutrality.

  7. Parameters Peclet, approx. 1 for KCl in water Reynolds, approx .001 (so we disregard) 0 Ratio of applied voltage to thermal voltage (25 mv) Ratio of diffusivity of ions

  8. Hoburg-Melcher (HM) limitD=1, Pe=∞, low V analysis 0 0 Purely imaginary spectrum

  9. 0 Modified Hoburg-Melcher (MHM) Pe=∞, low V analysis • Summary • D>1, Real, S2<0, Stable • D<1, Real, S2>0, Unstable • D=1, Imag, Oscillations

  10. Finite voltage, Pe=∞ MHM model (Pe=∞), low V limit MHM model (Pe=∞) Unstable Stable

  11. Bulk electroconvection (BE) modellow V analysis unstable L=-68 k=4.74 • Summary • D>1, Real, Stable • D<1, Real, Unstable (threshold) • D=1, Stable Current, Imax =4

  12. BE at finite voltage, D=0.1 Unstable Pe=9.9

  13. BE at finite voltage D>1 Unstable MHM model (Pe=∞)

  14. BE model, Pe=10000, V=4 Real Imag

  15. Conclusions • Bulk instability can exist, in theory. • New bulk instability mechanism found when D+ < D-, that can occur at low V. • Many previous studies only considered D+=D-, Pe ~ 1. • Whether D+ > D- or vice versa can lead to different behaviors. • Unresolved questions: • Are there cases where this instability could be experimentally observed? • How does bulk instability relate to instability in extended space charge region? (Zaltzman and Rubinstein, 2006). • Does asymmetry in electrolyte matter in microfluidic applications? (Oddy and Santiago, 2005). • Does this instability matter in concentration polarization flows observed in nanochannel applications? Kim, Wang, Lee, Jang, Han (2007)

  16. Steady state (no flow) V=20 Double layer, Debye =0.01 Double layer, Debye =0.01 E, flux of C+ Extended space charge Bulk is electro-neutral, linear conc. profile

  17. Finite voltage, Pe=10000 Unstable Unstable Stable BE MHM model (Pe=∞) BE, low V

  18. Finite voltage, Pe=10000 Unstable V=4 Unstable Stable BE, full MHM model (Pe=∞)

  19. Bulk electroconvection (BE) modellow V, D=1 HM

  20. Low voltage limit, Pe=10000 Unstable Unstable Stable BE, low V limit

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