Transcript Induced-charge Electro-osmosis

Induced-Charge Electro-osmosis
and Electrophoresis
Martin Z. Bazant
Department of Mathematics & Institute for Soldier Nanotechnologies, MIT
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)
Funding: US Army Research Office
(Contract DAAD-19-02-002) and
MIT-France Program
ICEO in a microfluidic device.
The Electrochemical Double Layer
+
solid
neutral
bulk
electrolyte
+
+
Electrostatic potential
Ion concentrations
0
continuum region
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?
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
AC Electro-osmosis
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”?
“Induced-Charge Electro-osmosis”
= 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…
Double-layer polarization and ICEO flow
A conducting cylinder in a suddenly applied uniform E field.
Electric field
FEMLAB simulation by Yuxing Ben
Poisson-Nernst-Planck/Navier-Stokes eqns
l/a=0.005
ICEO velocity
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
Inverted optics
microscope
Micro-particle image
velocimetry (mPIV) to
map the velocity profile
Bottom view
of optical slice
Movie: Optical slice sweeping through the 100 mm Pt wire
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
“Induced-Charge Electrokinetic Phenomena”
1. Prior examples of “ICEO”
• Electro-osmotic flows around metal particles
Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986); Levich (1960)
• Dielectrophoresis of spheres in electrolytes (“dipolophoresis”)
Simonova, Shilov, Colloid J. USSR (1981, 1998)
• AC electro-osmosis & colloidal aggregation at electrodes
Ramos et al. (1998); Ajdari (2000); “EHD” Ristenpart, Saville (2004)…
• DC “electrokinetic jet” at a microchannel corner
Thamida & Chang (2002)
2. Some new examples - breaking symmetries
• ICEO pumps and mixers in microfluidics
Bazant & Squires, PRL (2004); Levitan et al. Colloids & Surfaces (2005).
• “Fixed-potential ICEO”
Squires & Bazant, JFM (2004); Levitan, PhD thesis MIT (2005).
• “Induced-charge electrophoresis” (ICEP) particle motion
Bazant & Squires, PRL (2004); Yariv, Phys. Fluids (2005);
Squires & Bazant, JFM (2006); Saintillon, Darve & Shaqfeh, preprint.
“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
ICEO Microfluidic Elements
J. A. Levitan, Ph.D. Thesis (2005).
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
ICEO “mixer” or “trap”
(u = 0.2 mm/sec)
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
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
50-250 mm electroplated gold posts, PDMS polymer microchannels
A promising platform for portable microfluidics…
“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
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)
ICEP III. Non-uniform Fields
Shilov & Simonova, Colloid J. USSR (1981, 2001).
Squires & Bazant, J. Fluid Mech. (2006).
Metal sphere “dipolophoresis”
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
General solution for any 2d shape in any non-uniform E field by complex analysis…
Electric Field
Fluid Streamlines
“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:
2. Stokes flow driven by ICEO slip
Double-layer circuit elements:
(a) Gouy-Chapman capacitor
(b) Stern model
(c) Constant-phase-angle impedance
Z DL 
Dimensionless BC for AC forcing
A
(i / 0 ) 
0.6-0.8
Green et al, Phys Rev E (2002)
Levitan et al. Colloids & Surf. (2005)
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
Electric field lines:
Electric field lines
Velocity fields
- Re()
- Im()
At the “RC” frequency
Electric Field lines
- Re()
Electric field lines - Im()
Velocity fields
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…
Theory of “strongly nonlinear” electrokinetics?
Use the basic methods of applied mathematics:
1.
(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!
2.
(Modeling) Postulate new equations, solve & compare to experiments.
This is now the only choice, and progress is underway.
Classical Equations of “Dilute Solution Theory”
Poisson-Nernst-Planck ion transport equations
Singular perturbation
Navier-Stokes fluid equations with electrostatic stresses
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, Ph.D. thesis (2005).
Nonlinear theory for large E, uncharged conductors
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.
Modified Equations for Electrokinetics
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
3.
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.
Engineering of Microfluidic Pumps
JP Urbanski, Levitan, Bazant, Thorsen, in preparation
• Exploit fixed-potential ICEO, and standard ACEO
• Electroplated interdigitated & recessed gold electrodes on glass
• PDMS soft lithography for microchannels
Fast AC Electrokinetic Pumps
Bazant, Ben (2006)
The “conveyor belt principle”: Raised pumping surfaces, recess reverse rolls.
Apply to periodic array of electrodes in existing ACEO pumps
Ramos et al (1999), Ajdari (2000)
Raise half of each electrode to make a fast pump
Optimization of ICEO/ACEO pumps
Bazant, Yuxing Ben (2005)
Fastest existing ACEO pump
Green et al. (2003) theory;
Studer et al. (2004) expt.
New design:
10 times faster!
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:
–
–
–
–
–
http://www.physics.ubc.ca/~chansen/
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
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. Thorsen @ MIT Mech Eng)
2. Polarizable colloids
• ICEO flows in dielectrophoresis
• ICEO manipulation of nanobarcodes
(Santiago, Shaqfeh @ Stanford Mech Eng)
www.studybusiness.com
ICEO & ICEP
From mathematical theory….
to scientific experiments and engineering applications.
http://math.mit.edu/~bazant/ICEO
ICEO microfluidic pumps without moving parts
Jeremy Levitan, Ph.D. thesis, Mechanical Engineering MIT (2005)
• Experimental fabrication: soft lithography for microchannels (50-200 mm) and electroplating for gold
structures (25-200 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
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)
“Strongly Nonlinear” Solutions
(as required by the experimental parameters)
1.
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, 021506 (2004).
1d model problem
(PNP equations)
V = 4 kT/e
potential
charge density
salt concentration
Neutral salt adsorption by the diffuse charge layer and bulk diffusion
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)