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Induced-Charge Electro-osmosis and Electrophoresis

Induced-Charge Electro-osmosis and Electrophoresis. Nonlinear Electrokinetics @ MIT Students: Jeremy Levitan (ME PhD’05), Kevin Chu (Math PhD’05), JP Urbanski (ME), Mustafa Sabri Kilic (Math) Postdocs : Yuxing Ben , Hongwei Sun (Math) Faculty : Todd Thorsen (ME), Martin Schmidt (EE)

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Induced-Charge Electro-osmosis and Electrophoresis

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  1. Induced-Charge Electro-osmosis and Electrophoresis Nonlinear Electrokinetics @ MIT Students:Jeremy Levitan (ME PhD’05), Kevin Chu (Math PhD’05), JP Urbanski (ME), Mustafa Sabri Kilic (Math) Postdocs: Yuxing Ben, Hongwei Sun (Math) Faculty: Todd Thorsen (ME), Martin Schmidt (EE) Visitors: Armand Ajdari, Vincent Studer (ESPCI) Collaborators: Todd Squires (UCSB), Shankar Devasenathipathy (Stanford) Howard Stone (Harvard) Martin Z. Bazant Department of Mathematics & Institute for Soldier Nanotechnologies, MIT Funding: US Army Research Office (Contract DAAD-19-02-002) and MIT-France Program ICEO in a microfluidic device.

  2. The Electrochemical Double Layer + + + neutral bulk electrolyte solid Electrostatic potential Ion concentrations 0 continuum region

  3. Electrokinetic Phenomena Helmholtz-Smoluchowski fluid “slip” formula: Electro-osmosis Electrophoresis The classical theory assumes that the “zeta potential” z (or charge density q) is a constant material property, but what happens at a polarizable (e.g. electrode) surface?

  4. AC Electro-osmosis Ramos et al., JCIS (1999); Ajdari, Phys. Rev. E (2000) Steady flow for AC period = How general is this phenomenon? Need electrode arrays? Need “AC”?

  5. “Induced-Charge Electro-osmosis” = nonlinear electro-osmotic slip at a polarizable surface Bazant & Squires, Phys, Rev. Lett. 92, 0066101 (2004). Example: An uncharged metal cylinder in a suddenly applied DC field Same effect for metals & dielectrics, DC & AC fields…

  6. Double-layer polarization and ICEO flow A conducting cylinder in a suddenly applied uniform E field. Electric field ICEO velocity FEMLAB simulation by Yuxing Ben Poisson-Nernst-Planck/Navier-Stokes eqns l/a=0.005

  7. Experimental Observation of ICEO J. A. Levitan, S. Devasenathipathy, V. Studer, Y. Ben, T. Thorsen, T. M. Squires, & M. Z. Bazant, Colloids and Surfaces (2005) 100 mm Pt wire on channel wall Viewing plane PDMS polymer microchannel Bottom view of optical slice Inverted optics microscope Micro-particle image velocimetry (mPIV) to map the velocity profile

  8. Movie: Optical slice sweeping through the 100 mm Pt wire

  9. “Induced-Charge Electrokinetic Phenomena” 1. Prior examples of “ICEO” • Electro-osmotic flows around metal particles • Dielectrophoresis of spheres in electrolytes (“dipolophoresis”) • AC electro-osmosis & colloidal aggregation at electrodes • DC “electrokinetic jet” at a microchannel corner Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986); Levich (1960) Simonova, Shilov, Colloid J. USSR (1981, 1998) Ramos et al. (1998); Ajdari (2000); “EHD” Ristenpart, Saville (2004)… Thamida & Chang (2002) 2. Some new examples - breaking symmetries • ICEO pumps and mixers in microfluidics • “Fixed-potential ICEO” • “Induced-charge electrophoresis” (ICEP) particle motion Bazant & Squires, PRL (2004); Levitan et al. Colloids & Surfaces (2005). Squires & Bazant, JFM (2004); Levitan, PhD thesis MIT (2005). Bazant & Squires, PRL (2004); Yariv, Phys. Fluids (2005); Squires & Bazant, JFM (2006); Saintillon, Darve & Shaqfeh JFM (2006); Rose & Santiago (2006).

  10. “Fixed-Potential ICEO” Squires & Bazant, J. Fluid Mech. (2004) Idea: Vary the induced total charge in phase with the local field. Generalizes “Flow FET” of Ghowsi & Gale, J. Chromatogr. (1991) Example: metal cylinder grounded to an electrode supplying an AC field. Fixed-potential ICEO mixer

  11. ICEO Microfluidic Elements J. A. Levitan, Ph.D. Thesis (2005). Fixed-potential ICEO “pump” (u = 3 mm/sec) ICEO “mixer” or “trap” (u = 0.2 mm/sec) E = 100V/cm (< 10 Volt), 300 Hz AC, 0.1 mM KCl, 0.5 mm fluorescent tracers 50-250 mm electroplated gold posts, PDMS polymer microchannels A promising platform for portable microfluidics…

  12. “Induced-Charge Electrophoresis”= ICEO swimming via broken symmetries Bazant & Squires, Phys. Rev. Lett. (2004); Yariv, Phys. Fluids (2005). I. Heterogeneous Surfaces Squires & Bazant, J. Fluid Mech. (2006). A metal sphere with a partial dielectric coating swims toward its coated end, which rotates to align perpendicular to E. An “ICEO pinwheel” rotates to align and spins continuously in a uniform AC field! Stable Unstable

  13. ICEP II. Asymmetric Shapes Squires & Bazant, J. Fluid Mech. (2006). ICEP can separate polarizable colloids by shape and size in a uniform DC or AC electric field, while normal (linear) electrophoresis cannot. • long axis rotates to align with E • a “thin arrow” swims parallel to E, • towards its “blunt” end • a “fat arrow” swims transverse to E • towards its “pointed” end Perturbation analysis E u An asymmetric metal post can pump fluid in any direction in a uniform DC or AC field, but ICEO flow has quadrupolar rolls, very different from normal EOF. FEMLAB finite-element simulation (Yuxing Ben)

  14. ICEP III. Non-uniform Fields Shilov & Simonova, Colloid J. USSR (1981, 2001). Metal sphere “dipolophoresis” Squires & Bazant, J. Fluid Mech. (2006). General problem of DEP + ICEP • Must include electrostatic force and torque (Maxwell stress tensor) • Dielectrophoresis (DEP) + ICEP • For metals, ICEP points up, and DEP down, an electric field gradient • ICEP cancels DEP for a metal sphere (but not a cylinder or other shapes) Electric Field Fluid Streamlines

  15. General solution for any 2d shape in any non-uniform E field bycomplex analysis… Electric Field Fluid Streamlines

  16. “Weakly Nonlinear” Theory of ICEO Gamayunov et al. (1986); Ramos et al. (1998); Ajdari (2000); Squires & Bazant (2004). 1. Equivalent-circuit modelfor the induced zeta potential Bulk resistor (Ohm’s law): Double-layer BC: Double-layer circuit elements: Gouy-Chapman capacitor Stern model Constant-phase-angle impedance 2. Stokes flow driven by ICEO slip b=0.6-0.8 Dimensionless BC for AC forcing Green et al, Phys Rev E (2002) Levitan et al. Colloids & Surf. (2005)

  17. FEMLAB simulation of our first experiment:ICEO around a 100 micron platinum wire in 0.1 mM KCl Levitan, ... Y. Ben,… Colloids and Surfaces (2005). Low frequency DC limit At the “RC” frequency Electric field lines: Electric Field lines Electric field lines Electric field lines Velocity fields Velocity fields

  18. Comparision of Simulation and PIV Data:Velocity Profiles Raw data from a slice 0-10 mm above the wire Data collapse when scaled to characteristic ICEO velocity • Scaling and flow profile consistent with ICEO theory • Flow magnitude roughly 2 times smaller than in simple theory • Need better theories for large voltages and varying solution chemistry…

  19. Theory of “strongly nonlinear” electrokinetics? Use the basic methods of applied mathematics: (Analysis) Solve the existing equations in a new regime. This leads to some interesting new effects, but does not explain all the experimental data (e.g. decrease in ICEO flow for C > 10 mM). More importantly, the solutions contain physical nonsense! (Modeling) Postulate new equations, solve & compare to experiments. This is now the only choice, and progress is underway.

  20. Classical Equations of “Dilute Solution Theory” Poisson-Nernst-Planck ion transport equations Singular perturbation Navier-Stokes fluid equations with electrostatic stresses

  21. Strongly Nonlinear Solutions to the Classical Equations 1. Breakdown of circuit models: Surface adsorption and bulk diffusion Bazant, Thornton, Ajdari, PRE (2004). 2. Tangential transport of ions in the double layer Bikerman (1933), SS Dukhin & Deryaguin (1969, 1974) Linear theory for small E, highly charged surfaces Kevin Chu & MZB (2006). Nonlinear theory for large E, uncharged conductors, Matched asymptotic expansions…. 3. Diffusio-osmosis (= flow due to gradients in bulk salt concentration) Deryaguin (1964) Bulk diffusion around an uncharged metal sphere in a uniform E field.

  22. Modified Theory of Electrokinetics Sabri Kilic, Bazant, Ajdari (2006). Steric effects (ion size = a) in an equilibrium double layer: Borukhov et al. (1997). 2. Steric effects on dynamics: Modified Nerst-Planck Eqns Zeta Steric & viscoelectric effects: Modified Smoluchowski slip formula DL Voltage (kT/ze) New prediction: “Entropophoresis” of an uncharged metal in asymmetric electrolyte.

  23. Fast AC Electrokinetic Pumps Bazant, Ben (2005) The “conveyor belt principle”: Raised pumping surfaces, recess reverse rolls. Apply to symmetric array of electrodes in existing ACEO pumps Raise half of each electrode to make a fast pump Ramos et al (1999), Ajdari (2000)

  24. Optimization of ICEO/ACEO pumps Bazant, Yuxing Ben (2005) Fastest existing ACEO pump Green et al. (2003) theory; Bornw & Rennie (2001); Studer et al. (2004) expt. New design: 10 times faster!

  25. Engineering of Electrokinetic Pumps JP Urbanski, Levitan, Bazant, Thorsen (2006) • Exploit fixed-potential ICEO, and standard ACEO • Electroplated interdigitated & recessed gold electrodes on glass • PDMS soft lithography for microchannels • Microfluidic loop for testing pumps (Studer et al. 2004)

  26. Experimental Results Raised pumps are at least 3-5 times faster than existing planar pumps 10 micron electrodes can pump at mm/sec using only 1 Volt, kHz AC. Demonstration of fast flows for voltage steps 1,2,3,4 V (far from pump). Tour of the 20mm microfluidic loop in steady ACEO flow. http://web.mit.edu/urbanski/Public/Microfluidics/

  27. ICEO: a platform for portable microfluidics? • State-of-the-art “table-top microfluidics” • Pressure-driven microfluidics (e.g. K. Jensen) • Capillary electro-osmosis (e.g. J. Santiago) • Soft microfluidic networks (e.g S. Quake) • Possible advantages of ICEO: • Low voltage (< 10 Volt), low power (< 1 mW) • AC (< kHz) reduces unwanted reactions / bubbles in linear EOF • Time-dependent local flow control for mixing, trapping, switching,… • Excellent scaling with miniaturization • Standard “hard” microfabrication methods • Possible disadvantages: • Requires low ionic strength (< 10 mM) • Sensitive to solution chemistry, surface contamination our “micro” experiment

  28. Engineering Applications of ICEO Commercial Applications 1. Battery-powered microfluidics • Portable/implantable devices for medical or chemical monitoring • Localized drug delivery • Pressure control (e.g. glaucoma) • Cooling portable electronics Example: on-field detection of exposure to biowarfare agents for the dismounted soldier by monitoring nanoliters of blood. (T. Thorsen @ MIT Mech Eng) • 2. Polarizable colloids • ICEO flows in dielectrophoresis • ICEO manipulation of nanobarcodes(Santiago, Shaqfeh @ Stanford Mech Eng) www.studybusiness.com

  29. ICEO & ICEP From mathematical theory…. to scientific experiments and engineering applications. http://math.mit.edu/~bazant/ICEO

  30. Diffuse-Charge Dynamics Bazant, Thornton, Ajdari, Phys. Rev. E. (2004). Analysis of the Poisson-Nernst-Planck equations by time-dependent matched asymptotic expansions. Model Problem Classical “equivalent circuit” in the thin-double-layer approximation Time scales

  31. “Strongly Nonlinear” Solutions(as required by the experimental parameters) • Breakdown of circuit models at “large” voltages • when V > 2 kT/e = 0.05 V (z=V) “Transient Dukhin number” Bazant, Thornton & Ajdari, Phys. Rev. E 70, 021506 (2004). 1d model problem (PNP equations) V = 4 kT/e potential charge density salt concentration Neutral salt adsorption by the diffuse charge layer and bulk diffusion

  32. ICEO microfluidic pumps without moving parts Jeremy Levitan, Ph.D. thesis, Mechanical Engineering MIT (2005) • Experimental fabrication: soft lithography for micro-channels (50-200 mm) and electroplating for gold structures (25-200 mm wide, 5-50 mm tall) on glass Deposit and pattern gold on glass wafer Electroplate gold Strip resist; cap with PDMS to form micro-channel Deposit and pattern thick resist mold

  33. Comparision of Simulation and PIV Data:Scaling with Voltage and Frequency Similar ”ICEO flow” observed around mercury drops (without any quantitative analysis): Gamayunov, Mantrov, Murtsovkin, Colloid J. USSR (1992)

  34. Towards a new mathematical model… 1. Anolmalous “constant phase angle” double-layer impedance Data suggests BC for power-law “fractional relaxation”: Hypothesis: long waiting times for Stern-layer adsorption (not fractal surface roughness) KCl/Au expt By J. Levitan 2. Strong dependence on surface and solution chemistry ICEO flow decreases with concentration and depends on ion valence, size,… Hypothesis: steric effects + variable viscosity in the Stern layer Borukhov et al Phys Rev Lett (1997)

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