1. Induced-Charge Electrokinetic Phenomena Martin Z. Bazant Department of Mathematics, MIT ESPCI-PCT & CNRS Gulliver Paris-Sciences Chair Lecture Series 2008, ESPCI 1.Introduction (7/1) 2.Induced-charge electrophoresis in colloids (10/1) 3.AC electro-osmosis in microfluidics (17/1) 4.Theory at large applied voltages (14/2)

2. Induced-charge electrokinetics: Microfluidics CURRENT Students: Sabri Kilic, Damian Burch, JP Urbanski (Thorsen) Postdoc: Chien-Chih Huang Faculty: Todd Thorsen (Mech Eng) Collaborators: Armand Ajdari (St. Gobain) Brian Storey (Olin College) Orlin Velev (NC State), Henrik Bruus (DTU) Antonio Ramos (Sevilla) FORMER PhD: Jeremy Levitan, Kevin Chu (2005), Postodocs: Yuxing Ben (2004-06) Interns: Kapil Subramanian, Andrew Jones, Brian Wheeler, Matt Fishburn, Jacub Kominiarczuk Collaborators: Todd Squires (UCSB), Vincent Studer (ESPCI), Martin Schmidt (MIT), Shankar Devasenathipathy (Stanford) Funding: Army Research Office National Science Foundation MIT-France Program MIT-Spain Program Acknowledgments

3. Outline 1.Electrokinetic microfluidics 2.ICEO mixers 3.AC electro-osmotic pumps

4. Electro-osmosis Slip: Potential / plug flow for uniformly charged walls:

5. Electro-osmotic Labs-on-a-Chip Apply E across chip Advantages –EO plug flow has low hydrodynamic dispersion –Standard uses of in separation/detection Limitations: –High voltage (kV) –No local flow control –“Table-top technology”

6. Pressure generation by slip Use small channels!

7. DC Electro-osmotic Pumps Nanochannels or porous media can produce large pressures (0.1-50 atm) Disadvantages: –High voltage (kV) –Faradaic reactions –Gas management –Hard to miniaturize Yau et al, JCIS (2003) Juan Santiago’s group at Stanford Porous Glass

8. Electro-osmotic mixing Non-uniform zeta produces vorticity Patterned charge + grooves can also drive transverse flows (Ajdari 2001) which allow lower voltage across a channel BUT –Must sustain direct current –Flow is set by geometry, not “tunable”

9. Outline 1.Electrokinetic microfluidics 2.ICEO mixers 3.AC electro-osmotic pumps

10. Induced-Charge Electro-osmosis Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986) - flow around a metal sphere Bazant & Squires, Phys, Rev. Lett. (2004) - general theory, broken symmetries, microfluidics Example: An uncharged metal cylinder in a DC (or AC) field Can generate vorticity and pressure with AC fields

11. ICEO Mixers, Switches, Pumps… Advantages tunable flow control 0.1 mm/sec slip low voltage (few V) Disadvantages small pressure (<< Pa) low salt concentration

12. ICEO-based microfluidic mixing (C. K. Harnett, University of Louisville/M.P. Kanouff, Sandia National Laboratories) (a) Simulation of dye loading in the mixing channel by pressure- driven flow. Some slow diffusional mixing is seen. (b) Simulation of fast mixing after loading, when sidewall electrodes are energized. (c) Simulated velocity field surrounding the triangular posts when sidewall electrodes are energized. (d) Microfabricated device consisting of vertical gold-coated silicon posts and sidewall electrodes in an insulating channel. (Channel width 200 um, depth 300 um)

13. Features in flow images (top row) are replicated in the model (bottom row) without electric field (a) (b) and with electric field applied between channel sidewalls (c), (d). ICEO-based microfluidic mixing (C. K. Harnett, University of Louisville/M.P. Kanouff, Sandia National Laboratories)

14. Comparison of experimental (a,c) and calculated (b,d) results during steady flow of dyed and un-dyed solutions (2  l/min combined flow rate) without power (a,b) and with power (c,d). Flow is from left to right. 10 V pp, 37 Hz square wave applied across 200 um wide channel. Left-right transit time ~2 s. ICEO-based microfluidic mixing (C. K. Harnett, University of Louisville/M.P. Kanouff, Sandia National Laboratories) Power Off: Incomplete diffusional mixing Power On: Complete ICEO-based mixing experimental calculated

15. “ Fixed-Potential ICEO ” Example: metal cylinder grounded to an electrode supplying an AC field. Fixed-potential ICEO mixer Idea: Vary the induced total charge in phase with the local field. Squires & Bazant, J. Fluid Mech. (2004) Generalizes “Flow FET” of Ghowsi & Gale, J. Chromatogr. (1991) Flow past a 20 micron electroplated gold post (J. Levitan, PhD Thesis 2005)

16. Outline 1.Electrokinetic microfluidics 2.Induced-charge mixers 3.AC electro-osmotic pumps

17. AC electro-osmosis A. Ramos, A. Gonzalez, A. Castellanos (Sevilla), N. Green, H. Morgan (Southampton), 1999.

18. Circuit model Ramos et al. (1999) Debye time: “RC time”

19. ICEO flow over electrodes Example: response to a sudden DC voltage ACEO flow peaks if period = charging time Maximizes flow/voltage due to large field

20. AC electro-osmotic pumps Ajdari (2000) “Ratchet” concept inspired by molecular motors: Broken local symmetry in a periodic structure with “shaking” causes pumping without a global gradient. Brown, Smith, Rennie (2001): asymmetric planar electrodes

21. Experimental data Brown et al (2001), water - straight channel - planar electrode array - similar to theory (0.2-1.2 Vrms) Vincent Studer et al (2004), KCl - microfluidic loop, same array - flow reversal at large V, freq - no flow for C > 10mM

22. More data for planar pumps Urbanski et Appl Phys Lett (2006); Bazant et al, MicroTAS (2007) KCl, 3 Vpp, loop chip 5x load Puzzling features - flow reversal - decay with salt concentration - ion specific Can we improve performance?

23. Fast, robust “3D” pump designs Fastest planar ACEO pump Brown, Smith & Rennie (2001). Studer (2004) New design: electrode steps create a “fluid conveyor belt” Theory: “3D” design is 20x faster (>mm/sec at 3 Volts) and should not reverse Bazant & Ben, Lab on a Chip (2006)

24. The Fluid Conveyor Belt CQ Choi, “Big Lab on a Tiny Chip”, Scientific American, Oct. 2007.

25. 3D ACEO pumping of water Movie of fast flows for voltage steps 1,2,3,4 V (far from pump). Max velocity 5x larger (+suboptimal design) JP Urbanski, JA Levitan, MZB & T Thorsen, Appl. Phys. Lett. (2006)

26. Optimization of non-planar ACEO pumps JP Urbanski, JA Levitan, D Burch, T Thorsen & MZB, J Colloid Interface Science (2007) Electroplated Au steps on Au/Cr/glass Robust mm/sec max flow in 3  m KCl

27. Even faster, more robust pumps Damian Burch & MZB, preprint arXiv:0709.1304 “plated” “grooved” grooved plated Grooved design amplifies the fluid conveyor belt * 2x faster flow * less unlikely to reverse * wide operating conditions Experiments coming soon…

28. AC vs. DC Electro-osmotic Pumps

29. Conclusion * Induced-charge electro-osmotic flows driven by AC voltages offer new opportunities for mixers, switches, pumps, droplet manipulation, etc. in microfluidics * Better theories needed…. (Lecture 4 14/2/08) Papers, slides… http://math.mit.edu/~bazant/ICEO