instability of electro-osmotic channel flow with streamwise conductivity gradients brian storey jose...
Post on 22-Dec-2015
218 views
TRANSCRIPT
![Page 1: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/4.jpg)
Hoburg and Melcher (1976)
![Page 5: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/13.jpg)
Unstable flowE=25,000 V/m, Conductivity ratio=10
Posner, Santiago, JFM 2006
![Page 14: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/15.jpg)
Stability measureMaximum vertical V
![Page 16: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/16.jpg)
Stability measure as function of applied field
Unstable E field
![Page 17: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/17.jpg)
Role of electric body force
![Page 18: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/18.jpg)
No electro-osmotic slip (zeta=0)E=10,000 V/m (much lower field than with EO)
![Page 19: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/19.jpg)
Phase diagram
![Page 20: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/html5/thumbnails/20.jpg)
Phase diagram
DRaRv
22
D
HERa
22
lo
lohi
1
![Page 21: Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian Storey Jose Santos Franklin W. Olin College of Engineering Needham](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d775503460f94a598b5/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.