Induced-Charge Electro-osmosis and Electrophoresis

1
Induced-Charge Electro-osmosis and
Electrophoresis

• Martin Z. Bazant
• Department of Mathematics Institute for
  Soldier Nanotechnologies, MIT

Nonlinear Electrokinetics _at_ MIT Students Jeremy
Levitan (ME PhD05), Kevin Chu (Math
PhD05), 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-19-02-002) and MIT-France Program
ICEO in a microfluidic device.
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The Electrochemical Double Layer

neutral bulk electrolyte
solid
Electrostatic potential
Ion concentrations
0
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?
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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?
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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
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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/Nav
ier-Stokes eqns l/a0.005
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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
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Movie Optical slice sweeping through the 100 mm
Pt wire
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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).
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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

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ICEO Microfluidic Elements
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 (lt 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
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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
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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)
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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
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General solution for any 2d shape in any
non-uniform E field by complex analysis
Electric Field
Fluid Streamlines
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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 (Ohms law)
Double-layer BC

• Double-layer circuit elements
• Gouy-Chapman capacitor
• Stern model
• Constant-phase-angle impedance

2. Stokes flow driven by ICEO slip
b0.6-0.8
Dimensionless BC for AC forcing
Green et al, Phys Rev E (2002) Levitan et al.
Colloids Surf. (2005)
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FEMLAB simulation of our first experimentICEO
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
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Comparision of Simulation and PIV DataVelocity
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

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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 gt 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.

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

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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.
http//web.mit.edu/urbanski/Public/Microfluidics/
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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 (lt 10 Volt), low power (lt 1 mW)
• AC (lt 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 (lt 10 mM)
• Sensitive to solution chemistry, surface
  contamination

our micro experiment
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Commercial Applications
Engineering Applications of ICEO

• 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 _at_ MIT
Mech Eng)

• 2. Polarizable colloids
• ICEO flows in dielectrophoresis
• ICEO manipulation of nanobarcodes (Santiago,
  Shaqfeh _at_ Stanford Mech Eng)

www.studybusiness.com
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ICEO ICEP
From mathematical theory.
to scientific experiments and engineering
applications.
http//math.mit.edu/bazant/ICEO
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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
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Strongly Nonlinear Solutions(as required by
the experimental parameters)

• Breakdown of circuit models at large voltages
• when V gt 2 kT/e 0.05 V (zV)

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
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ICEO microfluidic pumps without moving parts
Jeremy Levitan, Ph.D. thesis, Mechanical
Engineering MIT (2005)

• Experimental fabrication soft lithography for
  micro-channels (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
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Comparision of Simulation and PIV DataScaling
with Voltage and Frequency
Similar ICEO flow observed around mercury
drops (without any quantitative analysis)
Gamayunov, Mantrov, Murtsovkin, Colloid J. USSR
(1992)
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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)