1 / 20

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

thurston-love
Télécharger la présentation

Bulk electroconvective instability at high Peclet numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related