Induced-Charge Electrokinetic Phenomena

1
Induced-Charge Electrokinetic Phenomena
Paris-Sciences Chair Lecture Series 2008, ESPCI

• Martin Z. Bazant
• Department of Mathematics, MIT
• ESPCI-PCT CNRS Gulliver

1. Introduction (7/1)
2. Induced-charge electrophoresis in colloids (10/1)
3. AC electro-osmosis in microfluidics (17/1)
4. Theory at large applied voltages (14/2)

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Induce-charge electrokinetics Colloids
Acknowledgments
CURRENT Students Sabri Kilic, Damian Burch,
JP Urbanski (Thorsen) Postdoc Chien-Chih
Huang Faculty Todd Thorsen (Mech
Eng) Collaborators Armand Ajdari (St. Gobain)
Brian Storey (Olin College) Orlin
Velev (NC State), Henrik Bruus (DTU)
Antonio Ramos (Sevilla) FORMER PhD Jeremy
Levitan, Kevin Chu (2005), Postodocs Yuxing Ben,
Hongwei Sun (2004-06) Interns Kapil Subramanian,
Andrew Jones, Brian Wheeler, Matt
Fishburn Collaborators Todd Squires (UCSB),
Vincent Studer (ESPCI), Martin Schmidt
(MIT), Shankar Devasenathipathy (Stanford)

• Funding
• Army Research Office
• National Science Foundation
• MIT-France Program
• MIT-Spain Program

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Outline

1. Linear electrophoresis
2. Induced-charge electrophoresis
3. Heterogeneous particles

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Electrophoresis in a dielectric liquid
Lab frame
Particle frame
Long-range flow perturbation
Size-dependent velocity
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Electrophoresis in an electrolyte
Smoluchowski (1907)
Electro-osmotic slip
Electrophoretic mobility
Zeta potential
force-free motion
Size-independent velocity
short-range flow perturbation
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Electrophoresis of a colloid
Morrison (1970)
Solution for uniform mobility potential flow
No relative motion!
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Non-uniform surface charge (1)
Anderson 1984
An inhomogeneous sphere rotates to align dipole
with E
Force-free ICEP enhances forced dielectrophoresis
(DEP)
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Non-uniform surface charge (2)
Anderson 1984
Transverse EP is possible, but only for certain
orientations
EP mobility is not related to total or average
charge!
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Non-spherical non-uniform particles
Ajdari 1995, Long Ajdari 1998
A particle can exhibit transverse EP for any
orientation
Continuous rotation is also possible, but
only around a special axis, with chiral, charged
grooves
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Outline

1. Linear electrophoresis
2. Induced-charge electrophoresis
3. Heterogeneous particles

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Electrophoresis of Polarizable Particles
Classical result, e.g. Levich (1956)
Electrophoretic mobility depends on the total
charge, but not on the induced dipole moment
BUT this only holds for linear response to
small E
Induced dipole
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Stotz-Wien-Dukhin Effect
For nonlinear double-layer capacitance, the
mobility depends on E, since induced charge must
redistribute to maintain the same the total
charge (AS Dukhin 1992)
Can exploit for separation in unbalanced AC
fields
(SS Dukhin et al 1986, R Chimenti, patent 1986)
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Ion-specific mobility
Bazant, Kilic, Storey, Ajdari, in preparation 2008
Dukhin effect in an asymmetric electrolyte
Mobility must depend on ion charges, sizes, etc.
Even an uncharged sphere can move, if it is
polarizable
Its apparent charge is that of ions which screen
at higher density
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Induced-Charge Electro-osmosis
Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR
(1986) - flow around a metal sphere Bazant
Squires, Phys, Rev. Lett. (2004) - general
theory, broken symmetries, microfluidics
Example An uncharged metal particle in a DC (or
AC) field
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First studies of ICEO flow
Vladimir A. Murtsokvin (work from 1983 to
1996) with Andrei Dukhin, Mantrov, Gamayunov
Nonlinear flow induced around a tin
particle (albeit in the wrong direction at
large sizes)
Also studied interactions between particles
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Thin-DL, low-voltage theory
Squires Bazant, JFM 2004, 2006 Yariv 2005
Ohms law
Total charge constraint
RC circuit boundary condition
ICEO slip
Solve Stokes flow with for
particle set by forcetorque0
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Dielectrophoresis
Maxwell (1891), Pohl (1958)
Maxwell-Wagner induced dipole moment
Time-averaged force and torque
Velocity in Stokes flow
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Dipolophoresis DEP ICEP
Shilov Simonova, Colloid J. USSR (1981, 2001).
Metal sphere dipolophoresis Squires
Bazant, J. Fluid Mech. (2006).
General problem of DEP ICEP

• In an electrolyte, ICEP opposes DEP for highly
  polarizable particles
• Both effects have the same scaling

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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Outline

1. Linear electrophoresis
2. Induced-charge electrophoresis
3. Heterogeneous particles

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Electrokinetic motion of rod-like metal particles
Perturbation theory Squires Bazant, JFM (2006)
Rose Santiago, Phys Rev E (2006) Experiments
on alignment of nano-barcode particles
Saintillan, Darve Shaqfeh, J Fluid Mech
(2006) theory for spheroids simulations
Field off
Field on
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ICEP of Irregular Shapes
ICEP can separate particles of the same material
and same size by shape alone. Any direction is
possible.
Expts on quartz particles Gamayunov Murtsovkin
(1992). Theory Bazant Squires (2004) Tensor
relations Yariv (2005) Perturbation analysis
Squires Bazant (2006).
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ICEP of 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 of Inhomogeneous Particles
Bazant Squires, Phys. Rev. Lett. (2004)
Squires Bazant, J. Fluid Mech (2006)
Example Janus particle
A metal/dielectric sphere in a uniform E field
always moves toward its dielectric face, which
rotates to perpendicular to E. The particle
swims sideways.
Stable
Unstable
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An Electrophoretic Pinwheel
An even more surprising example (Squires Bazant
J Fluid Mech 2006)

• Responds to any electric field by rotating (
  )
• Could be used to apply torques to molecules or
  cells?

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ICEP Experiments
S. Gangwal, O. Cayre, MZB, O.Velev, Phys Rev.
Lett (2008).
Gold/latex Janus spheres in NaCl
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Experimental data
0.1 mM 300 V/cm
Good fit to theory for
but particles move near the wall why?
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ICEO wall interactions
Zhao Bau, Langmuir (2007)
We expect repulsion from non-polarizable walls,
but the Janus particles are attracted to the
wall. Why?
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ICEP of Janus particles near a wall
Kilic Bazant, preprint, arXiv0712.0453
Without tilting, the particle is indeed repelled,
but it always rotates to meet the wall and can
translate with stable angle.
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Simulations of Janus-Wall interaction
Strong ICEO flows make particle face the wall
and get stuck.
Weaker ICEO flows produce tilted translation as
observed (due to DEP).
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Conclusion
Induced-charge electrophoresis leads to many
new phenomena in colloids with applications to
separation, manipulation, self-assembly. Better
theories needed.
ACEO pumps in Lecture 3
Papers, slides http//math.mit.edu/bazant/ICEO