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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) - PowerPoint PPT Presentation
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Induced-Charge Electro-osmosis and Electrophoresis
Martin Z. BazantDepartment 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, 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-19-02-002) andMIT-France Program
The Electrochemical Double Layer
neutralbulkelectrolyte
+
+
+
solid
Ion concentrations
0 continuum region
Electrostatic potential
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?
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
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”?
“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…
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.
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
Movie: Optical slice sweeping through the 100 m Pt wire
QuickTime™ and aDV/DVCPRO - NTSC decompressor
are needed to see this picture.
“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” ofGhowsi & Gale, J. Chromatogr. (1991)
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
are needed to see this picture.
QuickTime™ and aDV/DVCPRO - NTSC decompressor
are needed to see this picture.
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).
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 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 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)
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
General solution for any 2d shape in any non-uniform E field by complex analysis…
Electric Field Fluid Streamlines
“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
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).
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
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.
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 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).
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 ICEPin a large uniform field, if the electrolyte is asymmetric.
Engineering of Microfluidic PumpsJP 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 PumpsBazant, 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 pumpGreen 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
http://www.physics.ubc.ca/~chansen/
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
ICEO & ICEPFrom mathematical theory….
to scientific experiments and engineering applications.
http://math.mit.edu/~bazant/ICEO
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
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, 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
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