Induced-Charge Electro-osmosis and Electrophoresis Martin Z. Bazant Department of Mathematics & Institute for Soldier Nanotechnologies, MIT Nonlinear 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) ICEO in a microfluidic device. Funding: US Army Research Office (Contract DAAD ) and MIT-France Program

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

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

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

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”?

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

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

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

Movie: Optical slice sweeping through the 100  m Pt wire

“Induced-Charge Electrokinetic Phenomena” 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) 1. Prior examples of “ICEO” Thamida & Chang (2002) Simonova, Shilov, Colloid J. USSR (1981, 1998) Ramos et al. (1998); Ajdari (2000); “EHD” Ristenpart, Saville (2004)… 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.

“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)

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

“Induced-Charge Electrophoresis” = ICEO swimming via broken symmetries Bazant & Squires, Phys. Rev. Lett. (2004); Yariv, Phys. Fluids (2005). StableUnstable 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! I. Heterogeneous Surfaces Squires & Bazant, J. Fluid Mech. (2006).

ICEP II. Asymmetric Shapes - 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 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. 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. Perturbation analysis E u FEMLAB finite-element simulation (Yuxing Ben)

ICEP III. Non-uniform Fields 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) Shilov & Simonova, Colloid J. USSR (1981, 2001). Metal sphere “dipolophoresis” Squires & Bazant, J. Fluid Mech. (2006). General problem of DEP + ICEP Electric FieldFluid Streamlines

General solution for any 2d shape in any non-uniform E field by complex analysis… Electric FieldFluid Streamlines

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

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

Comparision of Simulation and PIV Data: Velocity Profiles 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… Raw data from a slice 0-10  m above the wire Data collapse when scaled to characteristic ICEO velocity

Theory of “strongly nonlinear” electrokinetics? Use the basic methods of applied mathematics: 1.(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! 2.(Modeling) Postulate new equations, solve & compare to experiments. This is now the only choice, and progress is underway.

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

Strongly Nonlinear Solutions to the Classical Equations 2. Tangential transport of ions in the double layer Kevin Chu, Ph.D. thesis (2005). Nonlinear theory for large E, uncharged conductors Bikerman (1933), SS Dukhin & Deryaguin (1969, 1974) Linear theory for small E, highly charged surfaces Bulk diffusion around an uncharged metal sphere in a uniform E field. 3. Diffusio-osmosis (= flow due to gradients in bulk salt concentration) Deryaguin (1964) 1. Breakdown of circuit models: Surface adsorption and bulk diffusion Bazant, Thornton, Ajdari, PRE (2004).

Modified Equations for Electrokinetics 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 Sabri Kilic, Bazant, Ajdari, in preparation. 3.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.

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

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 Ramos et al (1999), Ajdari (2000) Raise half of each electrode to make a fast pump

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

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

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 Engineering Applications of ICEO Example: on-field detection of exposure to biowarfare agents for the dismounted soldier by monitoring nanoliters of blood. (T. MIT Mech Eng) 2. Polarizable colloids ICEO flows in dielectrophoresis ICEO manipulation of nanobarcodes (Santiago, Stanford Mech Eng)

ICEO & ICEP From mathematical theory…. to scientific experiments and engineering applications.

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

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)

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

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) 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) KCl/Au expt By J. Levitan