Bulk%20electroconvective%20instability%20at%20high%20Peclet%20numbers

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) V1
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) limitD1, Pe8, low V
analysis
0
0
Purely imaginary spectrum
9
Modified Hoburg-Melcher (MHM) Pe8, low V
analysis
0

• Summary
• Dgt1, Real, S2lt0, Stable
• Dlt1, Real, S2gt0, Unstable
• D1, Imag, Oscillations

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Finite voltage, Pe8
MHM model (Pe8), low V limit
MHM model (Pe8)
Unstable
Stable
11
Bulk electroconvection (BE) model low V analysis
unstable
L-68
k4.74

• Summary
• Dgt1, Real, Stable
• Dlt1, Real, Unstable (threshold)
• D1, Stable

Current, Imax 4
12
BE at finite voltage, D0.1
Unstable
Pe9.9
13
BE at finite voltage Dgt1
Unstable
MHM model (Pe8)
14
BE model, Pe10000, V4
Real
Imag
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Conclusions

• Bulk instability can exist, in theory.
• New bulk instability mechanism found when D lt
  D-, that can occur at low V.
• Many previous studies only considered DD-, Pe
  1.
• Whether D gt 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) V20
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, Pe10000
Unstable
Unstable
Stable
BE
MHM model (Pe8)
BE, low V
18
Finite voltage, Pe10000
Unstable
V4
Unstable
Stable
BE, full
MHM model (Pe8)
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Bulk electroconvection (BE) modellow V, D1
HM
20
Low voltage limit, Pe10000
Unstable
Unstable
Stable
BE, low V limit