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Instability of electroosmotic channel flow with streamwise conductivity gradients J. Jobim Santos Br

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Instability of electro-osmotic channel flow with streamwise conductivity gradients ... No electro-osmotic slip (zeta=0) E=10,000 V/m (much lower field than with EO) ... – PowerPoint PPT presentation

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Title: Instability of electroosmotic channel flow with streamwise conductivity gradients J. Jobim Santos Br


1
Instability of electro-osmotic channel flow
with streamwise conductivity gradients J.
Jobim Santos Brian D. StoreyFranklin W. Olin
College of EngineeringNeedham MA
PHYSICAL REVIEW E 78, 046316 2008 NSF CTS-0521845
(RUI)
2
EHD instability in microfluidicsbuilding on
Hoburg and Melcher (JFM 1976)
Lin, Storey, Oddy, Chen Santaigo PoF2004
Baygents, Baldessari PoF1998
ElMochtar, Aubry, Batton, LoC 2003
Posner, Santiago, JFM 2006
Chen, Lin, Lele, Santiago JFM 2005
Lin, Storey, Santaigo JFM 2008
3
Problem statement
Electric field
50 micron channel

-
V
Question Is this flow stable?
4
Example of axial conductivity gradients in
EKField Amplified Sample Stacking (FASS)
Burgi Chein 1991, Analytical Chem.
5
Electrokinetic dispersion
  • Electroosmotic velocity depends upon the electric
    field
  • Electric field is high when conductivity is low
  • Low conductivity high electroosmotic velocity
  • No applied pressure gradient pressure is
    generatedEO mismatch

E

Red cond 10
Blue cond 1
Ghosal, EP 2004 Baradawaj Santiago JFM 2005 Ren
Li JCIS 2006 Sounart Baygents JFM 2007
6
Model summary
  • Incompressible Navier-Stokes plus electric body
    force
  • Ion transport based on Nernst-Planck for binary,
    symmetric electrolyte simplified by assuming
    fluid bulk is electro-neutral.

Ls/L
H/L
Hoburg Melcher, JFM 1976 Lin, Storey, Oddy,
Chen Santaigo PoF2004
7
Unstable flowE25,000 V/m, Conductivity ratio10
8
Observations
  • Shock at the leading edge of the sample.
  • Vertical velocity at the channel walls pumps
    fluid toward the centerline.
  • Unstable flow only inside the sample region.

9
Stability measure
E10000 V/m
Maximum vertical vel. along the centerline
E25000 V/m
10
Stability measure as function of applied field
Unstable E field
11
Phase diagram
E
Typical exp. range
12
Conclusions
  • Instability can occur in FASS geometry.
  • Simple stability map can be used to predict
    stability within reason.
  • Phenomena seems generic when you drive low
    conductivity into high conductivity.
  • Future work could include role of instability on
    stacking efficiency, role of analyte on
    stability, single interface FASS, and
    experimental validation.

13
(No Transcript)
14
Dimensionless parameters
Electric Rayleigh number
Reynolds number
Electrical conductivity ratio
Ratio of electro-osmotic to electroviscous
velocity
Channel aspect ratio
Ratio of sample length to channel height
15
Role of electric body force
16
Phase diagram
Baygents, Baldessari PoF1998
17
Generalized governing equations two symmetric
species, dilute
  • Note (c-c-)/(cc-)10-5

18
Electro-neutral bulk assumptionThin double layer
approx.
19
Final eqns mechanism for flow
HS electro-osmotic slip boundary conditions
20
No electro-osmotic slip (zeta0)E10,000 V/m
(much lower field than with EO)
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