Micro-fluidic Applications of Induced-Charge Electro-osmosis Jeremy Levitan Mechanical Engineering, MIT Martin Bazant Applied Mathematics, MIT Todd Squires Applied Mathematics, CalTech Martin Schmidt Electrical Engineering, MIT Todd Thorsen Mechanical Engineering, MIT

Pumping in Micro-Fluidics Mechanical pumping Robust Poor scaling: U ~ h2 P/  Bulky external pressure source Shear dispersion Capillary electro-osmosis Material sensitive Plug flow: U = 100 um/sec in E = 100 V/cm Linear: <U> = 0 in AC DC requires Faradaic reactions => hydrolysis Need large V for large E along channel

Mixing in Micro-Fluidics Diffusion down a channel: with EO Jacobson, McKnight, Ramsey (1999) Serpentine channels Mengeaud et al (2002) Geometric splitting Schonfeld, Hessel, and Hofmann (2004), Wang et al (2002) Passive recirculation Chung et al (2004) Pressure-driven flow with chaotic streamlines: Johnson et al (2002), Stroock et al (2002) AC Electro-osmosis Studer, Pepin, Chen, Ajdari (2002) Electrohydrodynamic Mixing Oddy, Santiago and Mikkelsen (2001), Lin et al, Santiago (2001) Micro peristaltic pumps (moving walls) (Schilling 2001) (Stroock 2002)

Induced-Charge Electro-Osmosis Nonlinear slip at a polarizable surface Example: An uncharged metal cylinder in a suddenly applied DC field Metal sphere: V. Levich (1962); N. Gamayunov, V. Murtsovkin, A. Dukhin, Colloid J. USSR (1984). E-field, t = 0 E-field, t » charging time Steady ICEO flow induced ~ E a MZB & TMS, Phys, Rev. Lett. 92, 0066101 (2004); TMS & MZB, J. Fluid. Mech. 509, 217 (2004).

A Simple Model System 100um dia. platinum wire transverse to PDMS polymer microchannel (200um tall, 1mm wide); 0.1 - 1mM KCl with 0.01% by volume 0.5um fluorescent latex particles; Sinusoidal voltage (10 - 100V) excitation, 0 DC offset; Applied 0.5cm away from center wire via gold and/or platinum wires; V Cross-section of experiment

Simple Mathematical Model 1. Electrochemical problem for the induced zeta potential Bazant, Thornton, Ajdari, Phys. Rev. E (2004) Steady-state potential, electric field after double layer charging 2. Stokes flow driven by ICEO slip Steady-state Stokes flow Simulation is of actual experimental geometry

Voltmeter Function Generator Viewing Resistor Platinum Wire Viewing Plane KCl in PDMS Microchannel Inverted Optics Microscope Bottom View 200 um X 1 mm X 1mm Channel

ICEO Around A 100 µm Pt Wire

Particle Image Velocimetry 500 nm seed particles Slide used with permission of S. Devasenathipathy

PIV Mean Velocity Data PIV measurement with 0.01% volume dielectric (fluorescent) tracer particles Correct scaling, but inferred surface slip smaller from simple theory by 10 Metal colloids: Gamayunov, Mantrov, Murtsovkin (1992)

Frequency Dependence At “fast” frequencies, double layer not fully charged; Consistent with “RC” charging U ~ U0/(1 + (/c)2) c = 2  d a/D = 1/c = 3 ms Experiments in 1 mM KCl at 75 V

Extensions to Model Surface Capacitance/Contamination: All reduce predicted velocities Surface Capacitance/Contamination: multi-step cleaning for metal surfaces; Surface Conductance: Visco-electric effect

Current Work Fixed potential posts; Post-array mixers; Asymmetric objects; Integration with microfluidic devices -- microchannels and valves; DNA hybridization arrays;

Induced-Charge Electro-osmosis Demonstrated non-linear electro-osmosis at polarizable (metal) surfaces Sensitive to frequency, voltage, etc. At low concentration (<1mM), no concentration dependence, but U decreases at higher c Advantages in microfluidics: Time-dependent local control of streamlines Requires small AC voltages, transverse to channels Compatible with silicon fabrication technology Disadvantages: Sensitive to surface contamination, solution chemistry Relatively weak for long-range pumping Additional movies/data: http://media.mit.edu/~jlevitan/iceo.html Papers: http://math.mit.edu/~bazant