Induced-Charge Electrokinetic Phenomena

Martin Z. BazantDepartment of Mathematics, MIT

ESPCI-PCT & CNRS Gulliver

Paris-Sciences Chair Lecture Series, ESPCI

1. Introduction (7/1)

2. Induced-charge electrophoresis in colloids (10/1)

3. AC electro-osmosis in microfluidics (17/1)

4. Theory of electrokinetics at large voltages (14/2)

Research Interests

• Electrokinetics= Electrically driven motion of particles and fluids

• Microfluidics

• Electrochemical systems

• Granular flow

• Applied mathematics

Induced-charge electrokinetics

CURRENTStudents: 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)

FORMERPhD: Jeremy Levitan, Kevin Chu (2005),Postodoc: Yuxing Ben (2004-06)Interns: Kapil Subramanian, Andrew Jones, Brian Wheeler, Matt FishburnCollaborators: 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

Acknowledgments

Outline

1. Linear electrokinetics

2. Nonlinear “induced-charge” electrokinetics

3. Preview of upcoming lectures

Electrokinetic particle motion

Non-conducting viscous liquid,e.g. oil drops in air, Millikan 1900

Electrolyte (salt solution)e.g. clay particles in water, Reuss 1808

?

The Electric Double Layer

quasi-neutralbulk liquidelectrolyte

+

+

+

solid

Ion concentrations

0 continuum region

Electrostatic potential

Gouy 1910

Electrokinetics in electrolytes

- - -- -- - - - --- --

- -

(a) Electro-osmosis = fluid slip across the double layer, as an electric field pushes on the screening cloud

(b) Electrophoresis = particle motion due to electro-osmosis

-

Linear Electrokinetics: 1. Fluids

• Helmholtz: electro-osmotic flow• Onsager: streaming potential & current (inverse effects)• Ajdari: transverse couplings (anisotropic surfaces)

• uniform zeta, thin double layers: potential flow (no vortices)• No net response to AC forcing

LinearResponse

Application: DC EO pumps

• Small channels (porous media) lead to large pressure (>10atm)

• Disadvantages: – High voltage (kV)– Faradaic reactions – Gas management– Hard to miniaturize

Yau et al, JCIS (2003)

Porous Glass

Linear Electrokinetics: 2. Particles

• Smoluchowski: electrophoresis• Onsager: sedimentation potential, induced dipole• Dukhin, Deryaguin: surface conduction (large charge)• Anderson, Ajdari: transverse motion, rotation

• uniform zeta, thin double layers: cannot separate particles!

Applications in microfluidics

• Apply E across the chip

• Advantages:– EO plug flow has low hydrodynamic dispersion– Many uses of linear EP in

separation/detection

• Limitations: – High voltage (kV)– Often slow separations– No local flow control – “Table-top technology”

From Todd Thorsen

Outline

1. Linear electrokinetics

2. Nonlinear “induced-charge” electrokinetics

3. Preview of upcoming lectures

Nonlinear Electrokinetic PhenomenaSome early examples

• Dielectric liquids- dielectrophoresis (DEP): acts on induced dipole -Taylor (1966): deformation & flow in oil drops- Melcher (1960s): Traveling-wave AC pumping

• Electrolytes-Shilov (1976): double-layer effects in DEP-Murtsovkin (1986): flows around polarizable particles-Dukhin (1986): 2nd kind EP at large current-Saville (1997): AC colloidal self-assembly on electrodes-Ramos (1999): AC electro-osmosis-Ajdari (2000): ACEO pumping with electrode arrays

“Induced-Charge Electro-osmosis”

Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986) - flow around a metal sphereBazant & Squires, Phys, Rev. Lett. (2004) - general theory, broken symmetries, microfluidics

Example: An uncharged metal cylinder in a suddenly applied DC field

= nonlinear electro-osmotic slip at a polarizable surface

ICEO flow persists in an AC field (< charging frequency).

Double-layer polarization and ICEO flow

Electric field ICEO velocity

Movies from a finite-element simulation by Yuxing Ben (2005)Solving the Poisson-Nernst-Planck/Navier-Stokes eqns/a=0.005

A conducting cylinder in a suddenly applied uniform E field.

Experimental Observation of ICEO

PDMSpolymermicrochannel

100 m Pt wireon channel wall

Inverted opticsmicroscope

Viewing plane

Bottom viewof optical slice

Jeremy Levitan, PhD Thesis in Mechanical Engineering, MIT (2005)

Micro-particle imagevelocimetry (PIV) tomap the velocity profile

QuickTime™ and aH.263 decompressor

are needed to see this picture.

Movie: 5 m optical slice sweeping 100 m Pt cylinder (top view) 100 V/cm, 300 Hz, 0.1 mM KCl

J. A. Levitan, S. Devasenathipathy, V. Studer, Y. Ben, T. Thorsen, T. M. Squires & M. Z. Bazant, Colloids and Surfaces (2005)

ICEO Experiments

Collapse of experimental data

Simulated flow (side view)

Examples of ICEO in Microfluidics

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.

Flow around a metal post Fixed-potential ICEO

AC electro-osmosisDC jet at a dielectric cornerThamida & Chang (2002) Ramos et al (1999), Ajdari (2000)

A pioneer, ahead of his timeVladimir A. Murtsokvin (work from 1983 to 1996)

“ICEO” flow around an metal particle (courtesy of Andrei Dukhin)

Induced-Charge Electrophoresis= ICEO swimming by broken symmetry

Bazant & Squires, Phys. Rev. Lett. (2004); Yariv, Phys. Fluids (2005)Squires & Bazant, J. Fluid Mech (2006)

Stable Unstable

A metal/dielectric sphere in a uniform E field always movestoward its dielectric face, which rotates to perpendicular to E.

The particle swims sideways.

Example: Janus particle

Experimental observation of induced-charge electrophoresis

S. Gangwal, O. Cayre, MZB, O.Velev, Phys Rev. Lett. 100, 058302 (2008).

Outline

1. Linear electrokinetics

2. Nonlinear “induced-charge” electrokinetics

3. Preview of upcoming lectures

Lecture 2: ICEP in Colloids

• Theory

• Field-dependent EO mobility

• Shape-dependent ICEP motion

• Wall interactions

• ICEP & DEP in non-uniform fields

• Applications in separation, assembly

Thursday 10 Jan. 2pm

Some examples...

The ICEO pinwheeel

E

u

Non-uniform fields

Lecture 3: ACEO in Microfluidics

• Theory

• ICEO mixers

• ACEO flow over electrode arrays

• Fast (> mm/s), low-voltage (< 3V), high-pressure (10% atm) ACEO pumps

• Applications to portable/implantable labs-on-a-chip, drug delivery

Thursday 17 Jan. 2pm

Some examples...

The “Fluid Conveyor Belt”

Scientific American, Oct. 2007.

Lecture 4: Theory at large voltages

• Experimental puzzles

• Strongly nonlinear dynamics

• Breakdown of dilute-solution theory

• Modified theories for ion crowding

• New phenomena and open questions

Postponed…

Experimental puzzles in ACEO

• High-frequency flow reversal• Concentration dependence• Ion specificity• Classical theory breaks down…

V. Studer et al., Analyst (2004)

MZB et al., MicroTAS (2007)

Ion crowding at large voltagesCrucial new physics:

MZB, MS Kilic, B Storey, A Ajdari (2007)

Poisson-Boltzman/Dilute-solution theory

ICEO experiments,New theory needed

Conclusion

Induced-charge electrokinetics

provides many opportunities for

new science and new applications

Papers, slides… http://math.mit.edu/~bazant/ICEO