Induced-Charge Electro-osmosis
Martin Z. Bazant
Mathematics, MIT
Jeremy Levitan
Todd Thorsen
Mechanical Engineering, MIT
Todd M. Squires
Applied Math, Caltech
Martin Schmidt
Electrical Engineering, MIT
Supported by the Institute for Soldier Nanotechnologies
AC Electro-osmosis
Ramos et. al (1998), Ajdari (2000)
Steady flow for
AC period = t c
Sudden DC voltage
t=0
t = tc
How general is this phenomenon?
Need electrode arrays? Need “AC”?
t >> t c
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…
Nonlinear Electrokinetic Phenomena
1. Other examples of “ICEO” flows
• AC electro-osmosis (+ colloidal aggregation?) at electrodes
Ramos et al. (1998…); Ajdari (2000…); “EHD” Ristenpart, Saville (2004)…
• DC electrokinetic jet at a dielectric corner
Thamida & Chang (2002…)
• AC flows around metallic particles
Levich (1962); Simonov & Shilov (1977); Gamayunov, Murtsovkin, A. S. Dukhin (1984…).
• Dielectrophoresis in electrolytes
Simonova, Shilov, Shramko (2001…)
2. Other “Non-equilibrium Electro-surface Phenomena”
• Surface conduction, non-equilibrium diffusio-osmosis
S. S. Dukhin (1965); Deryaguin & S. S. Dukhin (1969…).
• Second-kind electro-osmosis, instability at limiting current
S. S. Dukhin (1989…); Ben & Chang (2002); Rubinstein & Zaltzman (2000…)
(3. Bulk “electrokinetic instability”
Lin et al, Santiago (2001…)
)
ICEO in Microfluidics
Cross-channel
Reversible pump
T pump
Post-array mixer
Fixed-Potential ICEO
Example: metal cylinder grounded to an electrode supplying an AC field.
Fixed-potential ICEO mixer
Pumping by Broken Symmetry
Inspired by Ajdari (2000): AC EO pumping with electrode arrays.
Symmetric
metal wire
Asymmetric
Stern layer
Partial coating
by an insulator
Asymmetric
shape
Misalignment with field also drives torques to align.
More ICEO in Microfluidics
Asymmetric posts
Pumping transverse
to a AC or DC field
Patterned surfaces
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)
Simonova, Shilov, Shramko, Colloid J. USSR (2001)
• All higher multipoles at infinity also pump in AC fields
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 ?
2
Diffusion time, L / D ?
No! (and yes…)
Model problem
1. Weakly Nonlinear Dynamics
Equivalent circuit at
leading order,  << L.
Intermediate “RC time”:
Effective boundary condition:
2. Strongly Nonlinear Dynamics
V = 4 kT/e
Transient bulk
diffusion
Weakly Nonlinear ICEO Flow
1. Electrochemical problem for the induced zeta potential
Bazant, Thornton, Ajdari, Phys. Rev. E (2004)
J. Levitan’s experiment:
Platinum wire in a polymer microchannel
BC:
Electric field after double-layer charging
2. Stokes flow driven by ICEO slip
Green et al. (2000) ACEO
Squires & Bazant (2004)
Steady ICEO flow
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
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
Example: Dielectric-coated metal cylinder at
fixed potential in a suddenly applied DC field
Induced dipole
moment
Surface capacitance ratio
= dielectric thickness / Debye length
Experiments
Jeremy Levitan
Todd Thorsen, Martin Schmidt, Hongwei Sun,
Shankar Devasenathipathy (MIT), Vincent Studer (ESPCI)
E
<u>
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.
Voltmeter
Function Generator
Viewing
Resistor
Platinum
Wire
Viewing Plane
KCl in
PDMS
Microchannel
Inverted Optics
Microscope
200 um X 1 mm X 1mm Channel
Bottom View
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)
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
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