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) 1 mm V High conductivity fluid Low conductivity fluid

Model comparison Experiment Computation 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 2004 Storey, Tilley, Lin. Santiago, Phys Fluids 2005 Lin, Storey, Santiago, JFM 2008

Hoburg and Melcher (1976)

Unstable EHD in microfluidics Posner, Santiago, JFM 2006 Chen, Lin, Lele, Santiago JFM 2005 Baygents, Baldessari PoF1998ElMochtar, Aubry, Batton, LoC 2003 Storey, PhysD 2005 Boy, Storey, PRE 2007

Field Amplified Sample Stacking (FASS) + t > Stacked Analyte - t = 0 High Conductivity buffer Low Conductivity SampleHigh Conductivity buffer UBUB USUS ESES EBEB E EBEB

Electrokinetic dispersion Electroosmotic velocity depends upon the electric field Electric field is high when conductivity is low Low conductivity = high EO velocity 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

Questions Can instability and dispersion interact in “stacking” applications? Does instability influence stacking efficiency? Lin, Storey, Santiago, JFM 2008

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

Electro-neutral bulk assumption Thin double layer approx.

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

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

Unstable flow E=25,000 V/m, Conductivity ratio=10 Posner, Santiago, JFM 2006

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.

Stability measure Maximum vertical V

Stability measure as function of applied field Unstable E field

Role of electric body force

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

Phase diagram

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.