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IMECE, November 15 th , 2004, Anaheim, CA

IMECE, November 15 th , 2004, Anaheim, CA. A D EPTH -A VERAGED M ODEL F OR E LECTROKINETIC F LOWS I N A T HIN M ICROCHANNEL G EOMETRY Hao Lin, 1 Brian D. Storey 2 and Juan G. Santiago 1 Mechanical Engineering Department, Stanford University

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IMECE, November 15 th , 2004, Anaheim, CA

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  1. IMECE, November 15th, 2004, Anaheim, CA A DEPTH-AVERAGED MODEL FOR ELECTROKINETIC FLOWS IN A THIN MICROCHANNEL GEOMETRY Hao Lin,1 Brian D. Storey2 and Juan G. Santiago1 • Mechanical Engineering Department, Stanford University • Franklin W. Olin College of Engineering

  2. Motivation: Generalized EK flow with conductivity gradients • Field amplified sample stacking (FASS) • Electrokinetic instability (EKI) Rajiv Bharadwaj Michael H. Oddy

  3. Previous Work • Lin, Storey, Oddy, Chen & Santiago 2004, Phys. Fluids.16(6): 1922-1935 • Instability mechanism: induced by bulk charge accumulation; stabilized by diffusion (Taylor-Melcher-Baygents) • 2D and 3D linear analyses • 2D nonlinear computations • Storey, Tilley, Lin & Santiago 2004 Phys. Fluids, in press. • Depth-averaged Hele-Shaw analysis (zeroth-order) • Chen, Lin, Lele & Santiago 2004 J. Fluid Mech., in press • Instability mechanism: induced by bulk charge accumulation; stabilized by diffusion (Taylor-Melcher-Baygents) • Depth-averaged linear analyses • Convective and absolute instability Experiment 2D Computation

  4. Thin-Channel Model z y H x d s2 E s1 • Practicality Consideration • 2D depth-averaged model significantly reduces the cost of 3D computation • Model well captures the full 3D physics • Develop flow model for generalized electrokinetic channel flows • Eletrokinetic instability and mixing • Sample stacking • Other EK flows which involves conductivity gradients

  5. Full 3D Formulation (Lin et al.) H. Lin, Storey, B., M. Oddy, Chen, C.-H., and J.G. Santiago, “Instability of Electrokinetic Microchannel Flows with Conductivity Gradients,” Phys. Fluids16(6), 1922-1935, 2004. C.-H. Chen, H. Lin, S.K. Lele, and J.G. Santiago, “Convective and Absolute Electrokinetic Instabilities with Conductivity Gradients,” J. Fluid Mech., in press, 2004.

  6. Depth Averaged Model • Equations are depth-averaged to obtain in-plane (x,y) governing equations z u x • Asymptotic Expansion based on the aspect ratio d = d/H which is similar to lubrication/Hele-Shaw theory • Flows in the z-direction are integrated and modeled

  7. Depth Averaged Equations • Convective dispersion: Taylor-Aris type • Momentum: Darcy-Brinkman-Forchheimer H. Lin, Storey, B., and J.G. Santiago, “A depth-averaged model for electrokinetic flows in a thin microchannel geometry,” to be submitted, 2004.

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

  9. 1D Simplification (y-invariant) E y x • Dispersion effects include: • EOF variation in x • Vertical circulation in z z x u u eo , 1 eo , 2 w High Conductivity Low Conductivity

  10. FASS: Model vs DNS Model DNS DNS Model w/o Dispersion Model Model DNS Model w/o Dispersion

  11. FASS: Model vs DNS DNS Model Model w/o Dispersion Model w/o Dispersion sRMS DNS Time (s) Model

  12. Motivation: Electrokinetic Instability (EKI) 1 mm 50 mm g= 10 No gradient (Michael H. Oddy) (Rajiv Bharadwaj) (C.-H. Chen)

  13. Linear Analysis: 2D vs 3D 2D Linear Analysis 3D Linear Analysis Stable Stable Ecr,experiment ~ 0.3 kv/cm, Ecr,2D ~ 0.04 kv/cm, Ecr,3D ~ 0.18 kv/cm H. Lin, Storey, B., M. Oddy, Chen, C.-H., and J.G. Santiago, “Instability of Electrokinetic Microchannel Flows with Conductivity Gradients,” Phys. Fluids16(6), 1922-1935, 2004.

  14. EKI: Linear Analysis zeroth-order momentum 3D Linear Model

  15. EKI: Nonlinear Simulation 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 Model

  16. Conclusions and Future Work • Developed depth-averaged model for general EK flows in microchannels • Model validated with DNS and experiments • Future work: • Modeling and optimization of realistic FASS applications • Modeling and optimization of EKI mixing

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