Paris-Sciences Chair Lecture Series 2008, ESPCI
Induced-Charge Electrokinetic Phenomena
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)
Acknowledgments
Induce-charge electrokinetics: Colloids
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
Outline
1. Linear electrophoresis
2. Induced-charge electrophoresis
3. Heterogeneous particles
Electrophoresis in a dielectric liquid
Lab frame
Size-dependent velocity
Particle frame
Long-range flow perturbation
Electrophoresis in an electrolyte
Smoluchowski (1907)
Electro-osmotic slip
Electrophoretic mobility
Zeta potential
force-free motion
Size-independent velocity
short-range flow perturbation
Electrophoresis of a colloid
Morrison (1970)
Solution for uniform
mobility: potential flow
No relative motion!
Non-uniform surface charge (1)
Anderson 1984
An inhomogeneous sphere rotates to align dipole with E
Force-free ICEP enhances forced dielectrophoresis (DEP)
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!
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
Outline
1. Linear electrophoresis
2. Induced-charge electrophoresis
3. Heterogeneous particles
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
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)
Ion-specific mobility
Bazant, Kilic, Storey, Ajdari, in preparation 2008
Dukhin effect in an asymmetric electrolyte
Mobility must depend on
ion charges, sizes,
U etc.
Eb
Even an uncharged sphereus
can move, if it is polarizable
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( b)
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
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
Thin-DL, low-voltage theory
Squires & Bazant, JFM 2004, 2006; Yariv 2005
Ohm’s law
Total charge constraint
“RC circuit” boundary condition
ICEO slip
Solve Stokes flow with
for particle
set by force=torque=0
Dielectrophoresis
Maxwell (1891), Pohl (1958)
Maxwell-Wagner induced dipole moment
Time-averaged force and torque
Velocity in Stokes flow
Dipolophoresis = DEP + ICEP
Shilov & Simonova, Colloid J. USSR (1981, 2001).
Squires & Bazant, J. Fluid Mech. (2006).
Metal sphere “dipolophoresis”
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
General solution for any 2d shape in any non-uniform E field by complex analysis…
Electric Field
Fluid Streamlines
Outline
1. Linear electrophoresis
2. Induced-charge electrophoresis
3. Heterogeneous particles
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
Field off
Field on
Saintillan, Darve & Shaqfeh,
J Fluid Mech (2006): theory
for spheroids + simulations
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).
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)
ICEP of Inhomogeneous Particles
Bazant & Squires, Phys. Rev. Lett. (2004); Squires & Bazant, J. Fluid Mech (2006)
Example: Janus particle
Stable
Unstable
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.
An even more surprising example (Squires & Bazant J Fluid Mech 2006):
An Electrophoretic Pinwheel
• Responds to any electric field by rotating (
)
• Could be used to apply torques to molecules or cells?
ICEP Experiments
S. Gangwal, O. Cayre, MZB, O.Velev, Phys Rev. Lett (2008).
Gold/latex Janus spheres in NaCl
Experimental data
0.1 mM
300 V/cm
Good fit to theory for
but particles move near the wall… why?
ICEO wall interactions
Zhao & Bau, Langmuir (2007)
We expect repulsion from non-polarizable walls, but
the Janus particles are attracted to the wall. Why?
ICEP of Janus particles near a wall
Kilic & Bazant, preprint, arXiv:0712.0453
Without tilting, the particle is indeed repelled, but it always
rotates to meet the wall and can translate with stable angle.
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).
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