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)
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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)
Faculty: Todd Thorsen (ME), Martin Schmidt (EE)
Visitors: Armand Ajdari, Vincent Studer (ESPCI)
Collaborators: Todd Squires (UCSB),
Shankar Devasenathipathy (Stanford)
Howard Stone (Harvard)
Martin Z. Bazant
Department of Mathematics & Institute for Soldier Nanotechnologies, MIT
Funding: US Army Research Office
(Contract DAAD-19-02-002) and
ICEO in a microfluidic device.
Helmholtz-Smoluchowski fluid “slip” formula:
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?
Bazant, Thornton, Ajdari, Phys. Rev. E. (2004).
Analysis of the Poisson-Nernst-Planck equations
by time-dependent matched asymptotic expansions.
Classical “equivalent circuit” in
the thin-double-layer approximation
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”?
= nonlinear electro-osmotic slip at a polarizable surface
Bazant & Squires, Phys, Rev. Lett. 92, 0066101 (2004).
Example: An uncharged metal cylinder in a suddenly applied DC field
Same effect for metals & dielectrics, DC & AC fields…
A conducting cylinder in a suddenly applied uniform E field.
Electric field ICEO velocity
FEMLAB simulation by Yuxing Ben
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
of optical slice
velocimetry (mPIV) to
map the velocity profile
1. Prior examples of “ICEO”
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
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.
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
J. A. Levitan, Ph.D. Thesis (2005).
Fixed-potential ICEO “pump”
(u = 3 mm/sec)
ICEO “mixer” or “trap”
(u = 0.2 mm/sec)
E = 100V/cm (< 10 Volt), 300 Hz AC, 0.1 mM KCl, 0.5 mm fluorescent tracers
50-250 mm electroplated gold posts, PDMS polymer microchannels
A promising platform for portable microfluidics…
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!
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.
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)
Shilov & Simonova, Colloid J. USSR (1981, 2001). Metal sphere “dipolophoresis”
Squires & Bazant, J. Fluid Mech. (2006). General problem of DEP + ICEP
General solution for any 2d shape in any non-uniform E field bycomplex analysis…
Gamayunov et al. (1986); Ramos et al. (1998); Ajdari (2000); Squires & Bazant (2004).
1. Equivalent-circuit modelfor the induced zeta potential
Bulk resistor (Ohm’s law):
Double-layer circuit elements:
2. Stokes flow driven by ICEO slip
Dimensionless BC for AC forcing
Green et al, Phys Rev E (2002)
Levitan et al. Colloids & Surf. (2005)
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
Raw data from a slice
0-10 mm above the wire
Data collapse when scaled to
characteristic ICEO velocity
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.
Poisson-Nernst-Planck ion transport equations
Navier-Stokes fluid equations with electrostatic stresses
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, Ph.D. thesis (2005).
Nonlinear theory for large E, uncharged conductors
3. Diffusio-osmosis (= flow due to gradients
in bulk salt concentration)
Bulk diffusion around an
uncharged metal sphere
in a uniform E field.
Sabri Kilic, Bazant, Ajdari, in preparation.
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
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 ICEP
in a large uniform field, if the electrolyte is asymmetric.
JP Urbanski, Levitan, Bazant, Thorsen, in preparation
Bazant, Ben (2006)
The “conveyor belt principle”: Raised pumping surfaces, recess reverse rolls.
Apply to periodic array of electrodes in existing ACEO pumps
Raise half of each electrode to make a fast pump
Ramos et al (1999), Ajdari (2000)
Bazant, Yuxing Ben (2005)
Fastest existing ACEO pump
Green et al. (2003) theory;
Studer et al. (2004) expt.
10 times faster!
1. Battery-powered microfluidics
Example: on-field detection of exposure to biowarfare agents for the dismounted soldier by monitoring nanoliters of blood.
(T. Thorsen @ MIT Mech Eng)
From mathematical theory….
to scientific experiments and engineering applications.
Jeremy Levitan, Ph.D. thesis, Mechanical Engineering MIT (2005)
Deposit and pattern gold
on glass wafer
Strip resist; cap with PDMS
to form micro-channel
Deposit and pattern
thick resist mold
Similar ”ICEO flow” observed around mercury drops
(without any quantitative analysis):
Gamayunov, Mantrov, Murtsovkin, Colloid J. USSR (1992)
“Transient Dukhin number”
Bazant, Thornton & Ajdari, Phys. Rev. E 70, 021506 (2004).
1d model problem
V = 4 kT/e
potential charge density salt concentration
Neutral salt adsorption by the diffuse charge layer and bulk diffusion
1. Anolmalous “constant phase angle” double-layer impedance
Data suggests BC for power-law
Hypothesis: long waiting times
for Stern-layer adsorption
(not fractal surface roughness)
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)