Induced-Charge Electro-osmosis

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Induced-Charge Electro-osmosis

• Martin Z. Bazant
• Mathematics, MIT
• Supported by the Institute for Soldier
  Nanotechnologies

Todd M. Squires Applied Math, Caltech
Jeremy Levitan Todd Thorsen Mechanical
Engineering, MIT
Martin Schmidt Electrical Engineering, MIT
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AC Electro-osmosis
Ramos et. al (1998), Ajdari (2000)
Steady flow for AC period t
c
Sudden DC voltage
t 0
t t
t gtgt t
c
c
How general is this phenomenon? Need electrode
arrays? Need AC?
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Induced-Charge Electro-osmosis
Nonlinear electrokinetic slip at a polarizable
surface
Bazant Squires, Phys, Rev. Lett. 92, 0066101
(2004). Squires Bazant, J. Fluid. Mech. 509,
217 (2004).
Example An uncharged metal cylinder in a
suddenly applied DC field
E-field, t 0
E-field, t charging time
Steady ICEO flow
?induced E a
Same effect for metals and dielectrics, DC and AC
fields
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Nonlinear Electrokinetic Phenomena
1. Other examples of ICEO flows

• AC electro-osmosis ( colloidal aggregation?) at
  electrodes
• DC electrokinetic jet at a dielectric corner
• AC flows around metallic particles
• Dielectrophoresis in electrolytes

Ramos et al. (1998) Ajdari (2000) EHD
Ristenpart, Saville (2004)
Thamida Chang (2002)
Levich (1962) Simonov Shilov (1977)
Gamayunov, Murtsovkin, A. S. Dukhin (1984).
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)
(3. Bulk electrokinetic instability
)
Lin et al, Santiago (2001)
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ICEO in Microfluidics
Cross-channel Reversible pump
T pump
Post-array mixer
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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 Symmetry
Inspired by Ajdari (2000) AC EO pumping with
electrode arrays.
Symmetric metal wire
Asymmetric Stern layer
Asymmetric shape
Partial coating by an insulator
Misalignment with field also drives torques to
align.
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More ICEO in Microfluidics
Asymmetric posts
Pumping transverse to a AC or DC field
Patterned surfaces
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Non-uniform Applied Fields
Squires Bazant, in preparation.

• 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)
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Mathematical Theory of ICEO
I. Diffuse-Charge Dynamics
Bazant, Thornton, Ajdari, Phys. Rev. E (2004)
What is the time scale for charge screening?
2
Debye time, ? / D ? Diffusion time, L / D
? No! (and yes)
2
Model problem
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1. Weakly Nonlinear Dynamics
Equivalent circuit at leading order, ? ltlt L.
Intermediate RC time
Effective boundary condition
2. Strongly Nonlinear Dynamics
V 4 kT/e Transient bulk diffusion
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Weakly Nonlinear ICEO Flow
1. Electrochemical problem for the induced zeta
potential
Bazant, Thornton, Ajdari, Phys. Rev. E (2004)
J. Levitans experiment Platinum wire in a
polymer microchannel
BC
Electric field after double-layer charging
2. Stokes flow driven by ICEO slip
Steady ICEO flow
Green et al. (2000) ACEO Squires Bazant (2004)
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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 220pm

Papers http//math.mit.edu/bazant
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Example Dielectric-coated metal cylinder at
fixed potential in a suddenly applied DC field
Induced dipole moment
Surface capacitance ratio dielectric thickness
/ Debye length
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Experiments
Jeremy Levitan
Todd Thorsen, Martin Schmidt, Hongwei
Sun, Shankar Devasenathipathy (MIT), Vincent
Studer (ESPCI)
E
ltugt
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.
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Voltmeter
Function Generator
Viewing Resistor
Platinum Wire
Viewing Plane
KCl in PDMS Microchannel
Inverted Optics Microscope
Bottom View
200 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