Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham MA

1
Instability of electro-osmotic channel flow
with streamwise conductivity gradients Brian
StoreyJose SantosFranklin W. Olin College of
EngineeringNeedham MA
2
Electrokinetic instability2003 Experiments
(Mike Oddy of J. Santiagos group)
High conductivity fluid
1 mm
Low conductivity fluid
V
3
Model comparison
Lin, Storey, Oddy, Chen, Santiago, Phys Fluids
2004 Storey, Tilley, Lin. Santiago, Phys Fluids
2005 Lin, Storey, Santiago, JFM 2008
4
Hoburg and Melcher (1976)
5
Unstable EHD in microfluidics
Posner, Santiago, JFM 2006
Baygents, Baldessari PoF1998
ElMochtar, Aubry, Batton, LoC 2003
Storey, PhysD 2005
Chen, Lin, Lele, Santiago JFM 2005
Boy , Storey, PRE 2007
6
Field Amplified Sample Stacking (FASS)
7
Electrokinetic dispersion

• Electroosmotic velocity depends upon the electric
  field
• Electric field is high when conductivity is low
• Low conductivity high EO velocity

Red cond 10
Blue cond 1
8
Questions

• Can instability and dispersion interact in
  stacking applications?
• Does instability influence stacking efficiency?

Lin, Storey, Santiago, JFM 2008
9
Generalized governing equations two symmetric
species, dilute

• Note (c-c-)/(cc-)10-5

10
Electro-neutral bulk assumptionThin double layer
approx.
11
Final eqns mechanism for flow
HS electro-osmotic slip boundary conditions
12
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
13
Unstable flowE25,000 V/m, Conductivity ratio10
Posner, Santiago, JFM 2006
14
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.

15
Stability measure
Maximum vertical V
16
Stability measure as function of applied field
Unstable E field
17
Role of electric body force
18
No electro-osmotic slip (zeta0)E10,000 V/m
(much lower field than with EO)
19
Phase diagram
20
Phase diagram
21
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.
• Instability doesnt impact rate of dispersion
  that much.
• Preliminary instability doesnt seem to impact
  sample concentration as much as you might think.