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![Page 1: Induced-Charge Electro-osmosis Martin Z. Bazant Mathematics, MIT Supported by the Institute for Soldier Nanotechnologies Jeremy Levitan Todd Thorsen Mechanical.](https://reader033.fdocuments.us/reader033/viewer/2022051516/56649e9e5503460f94b9f75f/html5/thumbnails/1.jpg)
Induced-Charge Electro-osmosis
Martin Z. BazantMathematics, MIT
Supported by the Institute for Soldier Nanotechnologies
Jeremy Levitan
Todd ThorsenMechanical Engineering, MIT Martin Schmidt
Electrical Engineering, MIT
Todd M. SquiresApplied Math, Caltech
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AC Electro-osmosisRamos et. al (1998), Ajdari (2000)
t = 0 t = t t >> t
Steady flow forAC period = t
c
c
c
How general is this phenomenon? Need electrode arrays? Need “AC”?
Sudden DC voltage
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Induced-Charge Electro-osmosis
Bazant & Squires, Phys, Rev. Lett. 92, 0066101 (2004).Squires & Bazant, J. Fluid. Mech. 509, 217 (2004).
E-field, t = 0 E-field, t » charging time Steady ICEO flow
Example: An uncharged metal cylinder in a suddenly applied DC field
Nonlinear electrokinetic slip at a polarizable surface
induced ~ E a
Same effect for metals and dielectrics, DC and AC fields…
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Nonlinear Electrokinetic Phenomena
• AC electro-osmosis (+ colloidal aggregation?) at electrodes • DC electrokinetic jet at a dielectric corner
• AC flows around metallic particles
• Dielectrophoresis in electrolytes
Levich (1962); Simonov & Shilov (1977); Gamayunov, Murtsovkin, A. S. Dukhin (1984…).
1. Other examples of “ICEO” flows
Thamida & Chang (2002…)
Simonova, Shilov, Shramko (2001…)
2. Other “Non-equilibrium Electro-surface Phenomena”• Surface conduction, non-equilibrium diffusio-osmosis
• Second-kind electro-osmosis, instability at limiting current
S. S. Dukhin (1965); Deryaguin & S. S. Dukhin (1969…).
S. S. Dukhin (1989…); Ben & Chang (2002); Rubinstein & Zaltzman (2000…)
Ramos et al. (1998…); Ajdari (2000…); “EHD” Ristenpart, Saville (2004)…
(3. Bulk “electrokinetic instability” )Lin et al, Santiago (2001…)
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ICEO in Microfluidics
Cross-channel Reversible pump
Post-array mixer
T pump
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Fixed-Potential ICEO
Example: metal cylinder grounded to an electrode supplying an AC field.
Fixed-potential ICEO mixer
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Pumping by Broken SymmetryInspired by Ajdari (2000): AC EO pumping with electrode arrays.
Symmetricmetal wire
Asymmetric Stern layer
Partial coatingby an insulator
Asymmetric shape
Misalignment with field also drives torques to align.
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More ICEO in Microfluidics
Patterned surfaces
Asymmetric postsPumping transverseto a AC or DC field
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Non-uniform Applied Fields
• ICEO pumps in a non-uniform AC or DC field
• Very sensitive to size, shape, and time-dependence
• Cancels DEP for a metal sphere (but not other shapes)
• All higher multipoles at infinity also pump in AC fields
Simonova, Shilov, Shramko, Colloid J. USSR (2001)
Squires & Bazant, in preparation.
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Mathematical Theory of ICEO
I. Diffuse-Charge Dynamics
What is the time scale for charge screening?
Bazant, Thornton, Ajdari, Phys. Rev. E (2004)
Debye time, / D ?
Diffusion time, L / D ?
No! (and yes…)
2
2
Model problem
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1. Weakly Nonlinear Dynamics
Intermediate “RC time”:
Effective boundary condition:
Equivalent circuit at leading order, << L.
2. Strongly Nonlinear Dynamics
V = 4 kT/eTransient bulk diffusion
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Weakly Nonlinear ICEO Flow
BC:
1. Electrochemical problem for the induced zeta potential
2. Stokes flow driven by ICEO slip
Bazant, Thornton, Ajdari, Phys. Rev. E (2004)
Green et al. (2000) ACEOSquires & Bazant (2004)
J. Levitan’s experiment:Platinum wire in a polymer microchannel
Electric field after double-layer charging
Steady ICEO flow
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Strongly Nonlinear ICEO/NESP
• Nernst-Planck Equations
• Deryaguin/Dukhin BC for double-layer ion adsorption
Adsorption rate = bulk flux + surface flux + reactions
Dukhin number:
• Stokes flow due to “first-kind” electro/diffusio-osmosis
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Induced-Charge Electro-osmosis
• Nonlinear electro-osmosis at a polarizable surface• Sensitive to size, shape, voltage, time-dependence,…• Builds on ACEO, Russian colloid literature, etc.• Open theoretical questions
– “Strongly nonlinear” ICEO with large induced zeta– Effect of Faradaic reactions (e.g. Butler-Volmer)– Why theory over-predicts experimental velocities– Optimization of geometry & forcing for mixing & pumping
• Experiments & microfluidic applications – See talk by Jeremy Levitan at 2:20pm…
Papers: http://math.mit.edu/~bazant
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Example: Dielectric-coated metal cylinder at fixed potential in a suddenly applied DC field
Surface capacitance ratio= dielectric thickness / Debye length
Induced dipolemoment
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ExperimentsJeremy Levitan
Todd Thorsen, Martin Schmidt, Hongwei Sun,Shankar Devasenathipathy (MIT), Vincent Studer (ESPCI)
First model system: Isolated 100 micron platinum wire in KCl in a 0.2 x 1 x 1 mm PDMS microchannel with electrode ends.
Next generation: electroplated gold posts.
E
<u>
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Voltmeter Function Generator
ViewingResistor
KCl inPDMSMicrochannel
PlatinumWire
Inverted OpticsMicroscope
Viewing Plane
Bottom View200 um X 1 mm X 1mm Channel
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PIV Mean Velocity Data• PIV measurement with 0.01% volume dielectric (fluorescent) tracer particles• Fit velocity profile to ICEO simulation 25 microns from wire• Correct scaling, but smaller magnitude by factor of 30, perhaps due to surface impurity
Metal colloids: Gamayunov, Mantrov, Murtsovkin (1992)
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Frequency Scaling
• Decay above the “RC time”
• Consistent with ICEO theory U ~ U0/(1 + (/c)2) c = 2 d a/D = 1/c = 3 ms
Experiments in 1 mM KCl at 75 V
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Induced-Charge Electro-osmosis
• Nonlinear electro-osmosis at a polarizable surface• Sensitive to size, shape, voltage, time-dependence,…• Unifies & extends ACEO, Russian colloid literature, ...• Open theoretical questions
– “Strongly nonlinear” ICEO with large induced zeta– Effect of Faradaic reactions (e.g. Butler-Volmer)– Why theory under-predicts experimental velocities– Optimization of geometry & forcing for mixing & pumping
• Experiments & microfluidic applications underway
Papers: http://math.mit.edu/~bazant