1. Induced-Charge Electro-osmosis and Electrophoresis
Martin Z. Bazant
Department of Mathematics & Institute for Soldier Nanotechnologies, MIT
Nonlinear MIT
Students: 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)
Funding: US Army Research Office
(Contract DAAD ) and
MIT-France Program
ICEO in a microfluidic device.

2. The Electrochemical Double Layer+
neutral
bulk
electrolyte
solid
Electrostatic potential
Ion concentrations
continuum region

3. Electrokinetic Phenomena
Helmholtz-Smoluchowski fluid “slip” formula:
Electro-osmosis
Electrophoresis
The classical theory assumes that the “zeta potential” z (or charge density q) is a constant material property, but what happens at a polarizable (e.g. electrode) surface?

4. AC Electro-osmosis How general is this phenomenon?
Ramos et al., JCIS (1999); Ajdari, Phys. Rev. E (2000)
Steady flow for
AC period =
How general is this phenomenon?
Need electrode arrays? Need “AC”?

5. “Induced-Charge Electro-osmosis”
= nonlinear electro-osmotic slip at a polarizable surface
Bazant & Squires, Phys, Rev. Lett. 92, (2004).
Example: An uncharged metal cylinder in a suddenly applied DC field
Integral boundary conditions for surface charge -- Q = 0 --> phi not specified
Same effect for metals & dielectrics, DC & AC fields…

6. Double-layer polarization and ICEO flow
A conducting cylinder in a suddenly applied uniform E field.
Electric field ICEO velocity
FEMLAB simulation by Yuxing Ben
Poisson-Nernst-Planck/Navier-Stokes eqns
l/a=0.005

7. Experimental Observation of ICEO
J. A. Levitan, S. Devasenathipathy, V. Studer, Y. Ben, T. Thorsen, T. M. Squires, & M. Z. Bazant,
Colloids and Surfaces (2005)
100 mm Pt wire
on channel wall
Viewing plane
PDMS
polymer
microchannel
Bottom view
of optical slice
Inverted optics
microscope
Micro-particle image
velocimetry (mPIV) to
map the velocity profile

8. Movie: Optical slice sweeping through the 100 mm Pt wire

9. “Induced-Charge Electrokinetic Phenomena”
1. Prior examples of “ICEO”
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)
Simonova, Shilov, Colloid J. USSR (1981, 1998)
Ramos et al. (1998); Ajdari (2000); “EHD” Ristenpart, Saville (2004)…
Thamida & Chang (2002)
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).

10. “Fixed-Potential ICEO”
Squires & Bazant, J. Fluid Mech. (2004)
Idea: Vary the induced
total charge in phase
with the local field.
Generalizes “Flow FET” of
Ghowsi & Gale, J. Chromatogr. (1991)
Example: metal cylinder grounded to an electrode supplying an AC field.
Fixed-potential ICEO mixer

11. ICEO Microfluidic Elements
J. A. Levitan, Ph.D. Thesis (2005).
ICEO “mixer” or “trap”
(u = 0.2 mm/sec)
Fixed-potential ICEO “pump”
(u = 3 mm/sec)
E = 100V/cm (< 10 Volt), 300 Hz AC, 0.1 mM KCl, 0.5 mm fluorescent tracers
mm electroplated gold posts, PDMS polymer microchannels
A promising platform for portable microfluidics…

12. “Induced-Charge Electrophoresis” = ICEO swimming via broken symmetries
Bazant & Squires, Phys. Rev. Lett. (2004); Yariv, Phys. Fluids (2005).
I. Heterogeneous Surfaces
Squires & Bazant, J. Fluid Mech. (2006).
A metal sphere with a partial dielectric
coating swims toward its coated end,
which rotates to align perpendicular to E.
An “ICEO pinwheel” rotates to align and
spins continuously in a uniform AC field!
Stable
Unstable

13. ICEP II. Asymmetric Shapes
Squires & Bazant, J. Fluid Mech. (2006).
ICEP can separate polarizable colloids by shape
and size in a uniform DC or AC electric field,
while normal (linear) electrophoresis cannot.
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
Perturbation analysis
E u
An asymmetric metal post
can pump fluid in any direction
in a uniform DC or AC field, but
ICEO flow has quadrupolar rolls,
very different from normal EOF.
FEMLAB finite-element simulation (Yuxing Ben)

14. ICEP III. Non-uniform Fields
Shilov & Simonova, Colloid J. USSR (1981, 2001) Metal sphere “dipolophoresis”
Squires & Bazant, J. Fluid Mech. (2006) General problem of DEP + ICEP
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)
Electric Field
Fluid Streamlines

15. General solution for any 2d shape in any non-uniform E field by complex analysis…
Electric Field
Fluid Streamlines

16. “Weakly Nonlinear” Theory of ICEO
Gamayunov et al. (1986); Ramos et al. (1998); Ajdari (2000); Squires & Bazant (2004).
1. Equivalent-circuit model for the induced zeta potential
Bulk resistor (Ohm’s law):
Double-layer BC:
Double-layer circuit elements:
Gouy-Chapman capacitor
Stern model
Constant-phase-angle impedance
2. Stokes flow driven by ICEO slip b=
Dimensionless BC for AC forcing
Green et al, Phys Rev E (2002)
Levitan et al. Colloids & Surf. (2005)

17. FEMLAB simulation of our first experiment: ICEO around a 100 micron platinum wire in 0.1 mM KCl
Levitan, ... Y. Ben,… Colloids and Surfaces (2005).
Low frequency DC limit
At the “RC” frequency
Electric field lines:
Electric Field lines
Electric field lines
Electric field lines
Velocity fields
Velocity fields

18. Comparision of Simulation and PIV Data: Velocity Profiles
Raw data from a slice
0-10 mm above the wire
Data collapse when scaled to
characteristic ICEO velocity
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…

19. Theory of “strongly nonlinear” electrokinetics?
Use the basic methods of applied mathematics:
(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.

20. Classical Equations of “Dilute Solution Theory”
Poisson-Nernst-Planck ion transport equations
Singular perturbation
Navier-Stokes fluid equations with electrostatic stresses

21. Strongly Nonlinear Solutions to the Classical Equations
1. Breakdown of circuit models: Surface adsorption and bulk diffusion
Bazant, Thornton, Ajdari, PRE (2004).
2. Tangential transport of ions in the double layer
Bikerman (1933), SS Dukhin & Deryaguin (1969, 1974)
Linear theory for small E, highly charged surfaces
Kevin Chu & MZB (2006).
Nonlinear theory for large E, uncharged conductors,
Matched asymptotic expansions….
3. Diffusio-osmosis (= flow due to gradients
in bulk salt concentration)
Deryaguin (1964)
Bulk diffusion around an
uncharged metal sphere
in a uniform E field.

22. Modified Theory of Electrokinetics
Sabri Kilic, Bazant, Ajdari (2006).
Steric effects (ion size = a)
in an equilibrium double layer:
Borukhov et al. (1997).
2. Steric effects on dynamics:
Modified Nerst-Planck Eqns
Zeta
Steric & viscoelectric effects:
Modified Smoluchowski slip formula
DL Voltage (kT/ze)
New prediction: “Entropophoresis” of an
uncharged metal in asymmetric electrolyte.

23. Fast AC Electrokinetic Pumps
Bazant, 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

24. Optimization of ICEO/ACEO pumps
Bazant, Yuxing Ben (2005)
Fastest existing ACEO pump
Green et al. (2003) theory;
Bornw & Rennie (2001); Studer et al. (2004) expt.
New design:
10 times faster!

25. 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)

26. Experimental Results
Raised pumps are at least 3-5 times faster than existing planar pumps
10 micron electrodes can pump at mm/sec using only 1 Volt, kHz AC.
Demonstration of fast flows for
voltage steps 1,2,3,4 V (far from pump).
Tour of the 20mm microfluidic
loop in steady ACEO flow.

27. 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

28. Commercial Applications
Engineering Applications of ICEO
Commercial Applications
1. Battery-powered microfluidics
Portable/implantable devices for medical or chemical monitoring
Localized drug delivery
Pressure control (e.g. glaucoma)
Cooling portable electronics
Example: on-field detection of exposure to biowarfare agents for the dismounted soldier by monitoring nanoliters of blood.
(T. MIT Mech Eng)
2. Polarizable colloids
ICEO flows in dielectrophoresis
ICEO manipulation of nanobarcodes (Santiago, Stanford Mech Eng)

29. ICEO & ICEP From mathematical theory….
to scientific experiments and engineering applications.

30. Diffuse-Charge Dynamics
Bazant, Thornton, Ajdari, Phys. Rev. E. (2004).
Analysis of the Poisson-Nernst-Planck equations
by time-dependent matched asymptotic expansions.
Model Problem
Classical “equivalent circuit” in
the thin-double-layer approximation
Time scales

31. “Strongly Nonlinear” Solutions (as required by the experimental parameters)
Breakdown of circuit models at “large” voltages
when V > 2 kT/e = 0.05 V (z=V)
“Transient Dukhin number”
Bazant, Thornton & Ajdari, Phys. Rev. E 70, (2004).
1d model problem
(PNP equations)
BREAK INTO TWO SLIDES: 1d problem Kevin
V = 4 kT/e
potential charge density salt concentration
Neutral salt adsorption by the diffuse charge layer and bulk diffusion

32. Strip resist; cap with PDMS
ICEO microfluidic pumps without moving parts
Jeremy Levitan, Ph.D. thesis, Mechanical Engineering MIT (2005)
Experimental fabrication: soft lithography for micro-channels ( mm) and electroplating for gold structures ( mm wide, 5-50 mm tall) on glass
Deposit and pattern gold
on glass wafer
Electroplate gold
Deposit and pattern
thick resist mold
Strip resist; cap with PDMS
to form micro-channel

33. 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)

34. Towards a new mathematical model…
1. Anolmalous “constant phase angle” double-layer impedance
Data suggests BC for power-law
“fractional relaxation”:
Hypothesis: long waiting times
for Stern-layer adsorption
(not fractal surface roughness)
KCl/Au expt
By J. Levitan
2. Strong dependence on surface and solution chemistry
ICEO flow decreases with concentration
and depends on ion valence, size,…
Hypothesis: steric effects +
variable viscosity in the Stern layer
Borukhov et al
Phys Rev Lett (1997)