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“Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)

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.

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“Electrokinetic instability” 2003 Experiments (Mike Oddy of J. Santiago’s group)

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  1. Instability of electro-osmotic channel flow with streamwise conductivity gradients Brian StoreyJose SantosFranklin W. Olin College of EngineeringNeedham MA

  2. “Electrokinetic instability”2003 Experiments (Mike Oddy of J. Santiago’s group) High conductivity fluid 1 mm Low conductivity fluid V

  3. t = 0.0 s t = 0.5 s t = 1.0 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 Experiment Computation 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 Baygents, Baldessari PoF1998 Posner, Santiago, JFM 2006 ElMochtar, Aubry, Batton, LoC 2003 Storey, PhysD 2005 Chen, Lin, Lele, Santiago JFM 2005 Boy , Storey, PRE 2007

  6. t = 0 High Conductivity buffer Low Conductivity Sample High Conductivity buffer ES E UB EB US EB - - - - - - - - - - - - - - - - - - - t > 0 + + Stacked Analyte - - - Field Amplified Sample Stacking (FASS)

  7. u u eof , 1 eof , 2 Low conductivity, E High conductivity, E 2 Electrokinetic dispersion u u u eof , 1 eof , 1 eof , 2 High conductivity, E High conductivity, E 1 1 • 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. Convective diffusion (+) and (-) Convection Electromigration Diffusion • Charge Density and Gauss Law • Navier-Stokes Equations Generalized governing equations two symmetric species, dilute • Note (c+-c-)/(c++c-)~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 flowE=25,000 V/m, Conductivity ratio=10 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 (zeta=0)E=10,000 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 doesn’t impact rate of dispersion that much. • Preliminary – instability doesn’t seem to impact sample concentration as much as you might think.

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