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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 , Sergiy Sidenko (Math) Postdocs : Yuxing Ben , Hongwei Sun (Math)

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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, Sergiy Sidenko (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. 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

  5. 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”?

  6. “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…

  7. 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

  8. 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

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

  10. “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, preprint.

  11. “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

  12. 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…

  13. “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

  14. 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)

  15. 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

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

  17. “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)

  18. 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

  19. 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…

  20. 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.

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

  22. 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, Ph.D. thesis (2005). Nonlinear theory for large E, uncharged conductors 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.

  23. Modified Equations for Electrokinetics Sabri Kilic, Bazant, Ajdari, in preparation. 1. Steric effects (finite ion size) on equilibrium: Modified Poisson-Boltzmann equation PB = Poisson-Boltzmann theory Borukhov et al. Phys. Rev. Lett. (1997). 2. Steric effects on dynamics: Modified Nerst-Planck equations Steric & viscoelectric effects on electro-osmosis: Modified Helmholtz-Smoluchowski slip formula 4. Steric & viscoelectric effects on ICEO… New prediction: An uncharged metal sphere will move by ICEP in a large uniform field, if the electrolyte is asymmetric.

  24. Engineering of Microfluidic Pumps JP Urbanski, Levitan, Bazant, Thorsen, in preparation • Exploit fixed-potential ICEO, and standard ACEO • Electroplated interdigitated & recessed gold electrodes on glass • PDMS soft lithography for microchannels

  25. Fast AC Electrokinetic Pumps Bazant, Ben (2006) The “conveyor belt principle”: Raised pumping surfaces, recess reverse rolls. Apply to periodic array of electrodes in existing ACEO pumps Raise half of each electrode to make a fast pump Ramos et al (1999), Ajdari (2000)

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

  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 http://www.physics.ubc.ca/~chansen/

  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. 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

  31. 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)

  32. “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

  33. 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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