Induced-Charge Electro-osmosis and Electrophoresis
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Induced-Charge Electro-osmosis
and ElectrophoresisMartin Z. Bazant
Department of Mathematics & Institute for Soldier Nanotechnologies, MIT
Nonlinear Electrokinetics @ MITStudents: 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)
ICEO in a microfluidic device. Funding: US Army Research Office(Contract DAAD-19-02-002) andMIT-France Program
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The Electrochemical Double Layer
neutralbulkelectrolyte
+
+
+
solid
Ion concentrations
0 continuum region
Electrostatic potential
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Electrokinetic Phenomena
Helmholtz-Smoluchowski fluid “slip” formula:
Electro-osmosis Electrophoresis
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?
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AC Electro-osmosisRamos et al., JCIS (1999); Ajdari, Phys. Rev. E (2000)
Steady flow forAC period =
How general is this phenomenon? Need electrode arrays? Need “AC”?
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“Induced-Charge Electro-osmosis”
Bazant & Squires, Phys, Rev. Lett. 92, 0066101 (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…
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Double-layer polarization and ICEO flow
Electric field ICEO velocity
FEMLAB simulation by Yuxing BenPoisson-Nernst-Planck/Navier-Stokes eqns/a=0.005
A conducting cylinder in a suddenly applied uniform E field.
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Experimental Observation of ICEO
PDMSpolymermicrochannel
100 m Pt wireon channel wall
Inverted opticsmicroscope
Viewing plane
Bottom viewof 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 imagevelocimetry (PIV) tomap the velocity profile
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Movie: Optical slice sweeping through the 100 m Pt wire
QuickTime™ and aDV/DVCPRO - NTSC decompressor
are needed to see this picture.
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“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 JFM (2006); Rose & Santiago (2006).
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“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” ofGhowsi & Gale, J. Chromatogr. (1991)
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ICEO Microfluidic Elements
E = 100V/cm (< 10 Volt), 300 Hz AC, 0.1 mM KCl, 0.5 m fluorescent tracers50-250 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…
QuickTime™ and aDV/DVCPRO - NTSC decompressor
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J. A. Levitan, Ph.D. Thesis (2005).
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“Induced-Charge Electrophoresis”= ICEO swimming via broken symmetries
Bazant & Squires, Phys. Rev. Lett. (2004); Yariv, Phys. Fluids (2005).
Stable Unstable
A metal sphere with a partial dielectriccoating swims toward its coated end,which rotates to align perpendicular to E.
An “ICEO pinwheel” rotates to align andspins continuously in a uniform AC field!
I. Heterogeneous SurfacesSquires & Bazant, J. Fluid Mech. (2006).
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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 shapeand size in a uniform DC or AC electric field,while normal (linear) electrophoresis cannot.
An asymmetric metal postcan pump fluid in any directionin a uniform DC or AC field, but ICEO flow has quadrupolar rolls,very different from normal EOF.
Perturbation analysisE u
FEMLAB finite-element simulation (Yuxing Ben)
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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 Field Fluid Streamlines
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General solution for any 2d shape in any non-uniform E field by complex analysis…
Electric Field Fluid Streamlines
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“Weakly Nonlinear” Theory of ICEO
1. Equivalent-circuit model for the induced zeta potential
2. Stokes flow driven by ICEO slip
βωω )/( 0i
AZDL =
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)
β
Gamayunov et al. (1986); Ramos et al. (1998); Ajdari (2000); Squires & Bazant (2004).
Dimensionless BC for AC forcing
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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” frequencyElectric field lines:
Velocity fields
Electric Field lines
Velocity fields
Electric field lines Electric field lines
)Re( Φ∇−
)Im( Φ∇−
)Re( Φ∇−
)Im( Φ∇−
Levitan, ... Y. Ben,… Colloids and Surfaces (2005).
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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 slice0-10 m above the wire
Data collapse when scaled tocharacteristic ICEO velocity
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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!
• (Modeling) Postulate new equations, solve & compare to experiments.
This is now the only choice, and progress is underway.
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Classical Equations of “Dilute Solution Theory”
Poisson-Nernst-Planck ion transport equations
Navier-Stokes fluid equations with electrostatic stresses
Singular perturbation
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Strongly Nonlinear Solutions to the Classical Equations
2. Tangential transport of ions in the double layer
Kevin Chu & MZB (2006).Nonlinear theory for large E, uncharged conductors,Matched asymptotic expansions….
Bikerman (1933), SS Dukhin & Deryaguin (1969, 1974)Linear theory for small E, highly charged surfaces
Bulk diffusion around an uncharged metal spherein 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 diffusionBazant, Thornton, Ajdari, PRE (2004).
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Modified Theory of Electrokinetics
1. Steric effects (ion size = a) in an equilibrium double layer:
Borukhov et al. (1997).
2. Steric effects on dynamics: Modified Nerst-Planck Eqns
Sabri Kilic, Bazant, Ajdari (2006).
3. Steric & viscoelectric effects: Modified Smoluchowski slip formula
New prediction: “Entropophoresis” of an uncharged metal in asymmetric electrolyte.
Zeta
DL Voltage (kT/ze)
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Fast AC Electrokinetic PumpsBazant, Ben (2005)
The “conveyor belt principle”: Raised pumping surfaces, recess reverse rolls.
Apply to symmetric array of electrodes in existing ACEO pumps
Ramos et al (1999), Ajdari (2000) Raise half of each electrode to make a fast pump
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Optimization of ICEO/ACEO pumps
Fastest existing ACEO pumpGreen et al. (2003) theory; Bornw & Rennie (2001); Studer et al. (2004) expt.
Bazant, Yuxing Ben (2005)
New design:10 times faster!
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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)
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Experimental ResultsRaised pumps are at least 3-5 times faster than existing planar pumps10 micron electrodes can pump at mm/sec using only 1 Volt, kHz AC.
http://web.mit.edu/urbanski/Public/Microfluidics/
QuickTime™ and aMPEG-4 Video decompressor
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QuickTime™ and aMPEG-4 Video decompressor
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Tour of the 20mm microfluidic loop in steady ACEO flow.
Demonstration of fast flows for voltage steps 1,2,3,4 V (far from pump).
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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
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Commercial Applications1. 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. Thorsen @ MIT Mech Eng)
2. Polarizable colloids• ICEO flows in dielectrophoresis• ICEO manipulation of nanobarcodes (Santiago, Shaqfeh @ Stanford Mech Eng)
www.studybusiness.com
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ICEO & ICEPFrom mathematical theory….
to scientific experiments and engineering applications.
http://math.mit.edu/~bazant/ICEO
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Diffuse-Charge DynamicsBazant, Thornton, Ajdari, Phys. Rev. E. (2004).Analysis of the Poisson-Nernst-Planck equations by time-dependent matched asymptotic expansions.
Model Problem
Classical “equivalent circuit” inthe thin-double-layer approximation
Time scales
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“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, 021506 (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
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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 partsJeremy Levitan, Ph.D. thesis, Mechanical Engineering MIT (2005)
• Experimental fabrication: soft lithography for micro-channels (50-200 m) and electroplating for gold structures (25-200 m wide, 5-50 m tall) on glass
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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)
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Towards a new mathematical model…
1. Anolmalous “constant phase angle” double-layer impedance
Data suggests BC for power-law“fractional relaxation”:
Hypothesis: long waiting timesfor Stern-layer adsorption(not fractal surface roughness)
2. Strong dependence on surface and solution chemistry
ICEO flow decreases with concentrationand depends on ion valence, size,…
Hypothesis: steric effects + variable viscosity in the Stern layer
Borukhov et al Phys Rev Lett (1997)
KCl/Au exptBy J. Levitan