1. Instability of electro-osmotic channel flow with streamwise conductivity gradients J. Jobim Santos Brian D. Storey Franklin W. Olin College of Engineering Needham MA PHYSICAL REVIEW E 78, 046316 2008 NSF CTS-0521845 (RUI)

2. EHD instability in microfluidics …building on Hoburg and Melcher (JFM 1976) Posner, Santiago, JFM 2006 Chen, Lin, Lele, Santiago JFM 2005 Baygents, Baldessari PoF1998ElMochtar, Aubry, Batton, LoC 2003 Lin, Storey, Oddy, Chen Santaigo PoF2004 Lin, Storey, Santaigo JFM 2008 Computation Experiment

3. Problem statement Electric field Question: Is this flow stable? ~50 micron channel V + -

4. Example of axial conductivity gradients in EK Field Amplified Sample Stacking (FASS) + t > 0 - - - - - - - -- Stacked Analyte - t = 0 High Conductivity buffer Low Conductivity SampleHigh Conductivity buffer -- - - - - --- -+ - - UBUB USUS ESES EBEB E EBEB 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 High conductivity, E 1 u eof, 1 u eof, 2 High conductivity, E Low conductivity, E 2 u eof, 1 u eof, 2 1 u eof, 1 High conductivity, E Red; cond =10Blue; cond =1 Ghosal, EP 2004 Baradawaj & Santiago JFM 2005 Ren & Li JCIS 2006 Sounart & Baygents JFM 2007 E

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. Hoburg & Melcher, JFM 1976 Lin, Storey, Oddy, Chen Santaigo PoF2004 H/L L s /L

7. Unstable flow E=25,000 V/m, Conductivity ratio=10

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 Maximum vertical vel. along the centerline E=10000 V/m E=25000 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.

14. Dimensionless parameters 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

15. Role of electric body force

16. Phase diagram Baygents, Baldessari PoF1998

17. Generalized governing equations two symmetric species, dilute Convective diffusion (+) and (-) ConvectionElectromigrationDiffusion Charge Density and Gauss Law Navier-Stokes Equations Note (c + -c - )/(c + +c - )~10 -5

18. Electro-neutral bulk assumption Thin double layer approx.

19. Final eqns & mechanism for flow HS electro-osmotic slip boundary conditions

20. No electro-osmotic slip (zeta=0) E=10,000 V/m (much lower field than with EO)