“electrokinetic instability” 2003 experiments (mike oddy of j. santiago’s group)
DESCRIPTION
Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham MA. “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group). High conductivity fluid. 1 mm. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/1.jpg)
Instability of electro-osmotic channel flow with streamwise conductivity gradients
Brian StoreyJose Santos
Franklin W. Olin College of EngineeringNeedham MA
![Page 2: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/2.jpg)
“Electrokinetic instability”2003 Experiments (Mike Oddy of J. Santiago’s group)
1 mm
V
High conductivity fluid
Low conductivity fluid
![Page 3: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/3.jpg)
Model comparison
ExperimentComputation
t = 0.0 s
t = 0.5 s
t = 1.5 s
t = 2.0 s
t = 2.5 s
t = 3.0 s
t = 4.0 s
t = 5.0 s
t = 1.0 s
Lin, Storey, Oddy, Chen, Santiago, Phys Fluids 2004Storey, Tilley, Lin. Santiago, Phys Fluids 2005Lin, Storey, Santiago, JFM 2008
![Page 4: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/4.jpg)
Hoburg and Melcher (1976)
![Page 5: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/5.jpg)
Unstable EHD in microfluidics
Posner, Santiago, JFM 2006
Chen, Lin, Lele, Santiago JFM 2005
Baygents, Baldessari PoF1998 ElMochtar, Aubry, Batton, LoC 2003
Storey, PhysD 2005 Boy , Storey, PRE 2007
![Page 6: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/6.jpg)
Field Amplified Sample Stacking (FASS)
+t > 0-
-
---
--- -
Stacked Analyte
-
t = 0
High Conductivity bufferLow Conductivity SampleHigh Conductivity buffer
---- --
- - - -+
- -UB US Oi E
ESEB
EEB
![Page 7: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/7.jpg)
Electrokinetic dispersion
•Electroosmotic velocity depends upon the electric field•Electric field is high when conductivity is low•Low conductivity = high EO velocity
High conductivity, E1
ueof, 1 ueof, 2
High conductivity, E Low conductivity, E2
ueof, 1 ueof, 2
1
ueof, 1
High conductivity, E
Red; cond =10 Blue; cond =1
![Page 8: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/8.jpg)
Questions• Can instability and dispersion interact in “stacking”
applications? • Does instability influence stacking efficiency?
Lin, Storey, Santiago, JFM 2008
![Page 9: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/9.jpg)
Generalized governing equations two symmetric species, dilute
Convective diffusion (+) and (-)
0c
c v z Fc E D ct
Convection Electromigration Diffusion
( ) ~ ( )E F z c z c c c Charge Density and Gauss Law
0( )r EE
0v
2( ) E
vv v p v E
t
Navier-Stokes Equations
Note (c+-c-)/(c++c-)~10-5
![Page 10: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/10.jpg)
Electro-neutral bulk assumptionThin double layer approx.
0:Sub
0 :Add
0
0
utral)(Electrone
Ec
cDcvt
c
cDEFccvt
c
cDEFccvt
c
ccc
![Page 11: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/11.jpg)
Final eqns & mechanism for flow
( ) 0E
21,
eRv
t a
21( )
Re E
vv v p v E
t
0v
/EE
0 EE
HS electro-osmotic slip boundary conditions Euslip
![Page 12: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/12.jpg)
Dimensionless parameters
Re evU H
eve
U HRa
D
ev
eov U
UR
L
H
low
high
H
Lsample
Electric Rayleigh number
Reynolds number
Channel aspect ratio
Ratio of electro-osmotic to electroviscous velocity
Electrical conductivity ratio
Ratio of sample length to channel height
HE
U ev
2
![Page 13: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/13.jpg)
Unstable flowE=25,000 V/m, Conductivity ratio=10
Posner, Santiago, JFM 2006
![Page 14: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/14.jpg)
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.
![Page 15: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/15.jpg)
Stability measureMaximum vertical V
![Page 16: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/16.jpg)
Stability measure as function of applied field
Unstable E field
![Page 17: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/17.jpg)
Role of electric body force
![Page 18: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/18.jpg)
No electro-osmotic slip (zeta=0)E=10,000 V/m (much lower field than with EO)
![Page 19: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/19.jpg)
Phase diagram
![Page 20: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/20.jpg)
Phase diagram
DRaRv
22
D
HERa
22
lo
lohi
1
![Page 21: “Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)](https://reader035.vdocument.in/reader035/viewer/2022062718/56812e53550346895d93f7ae/html5/thumbnails/21.jpg)
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 doesn’t impact rate of dispersion that much.
• Preliminary – instability doesn’t seem to impact sample concentration as
much as you might think.