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Paris-Sciences Chair Lecture Series 2008, ESPCI. Induced-Charge Electrokinetic Phenomena. Introduction ( 7/1) Induced-charge electrophoresis in colloids (10/1) AC electro-osmosis in microfluidics (17/1) Theory at large applied voltages ( 14/2 ). Martin Z. Bazant

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Induced charge electrokinetic phenomena

Paris-Sciences Chair Lecture Series 2008, ESPCI

Induced-Charge Electrokinetic Phenomena

Introduction (7/1)

Induced-charge electrophoresis in colloids (10/1)

AC electro-osmosis in microfluidics (17/1)

Theory at large applied voltages (14/2)

Martin Z. Bazant

Department of Mathematics, MIT


Induced charge electrokinetics theory


Induced-charge electrokinetics: Theory


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)

Maarten Biesheuvel (Twente),

Antonio Ramos (Sevilla)


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


  • Experimental puzzles

  • Strongly nonlinear dynamics

  • Beyond dilute solution theory

Induced charge electro osmosis
Induced-Charge Electro-osmosis

= nonlinear electro-osmotic slip at a polarizable surface

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

Gamayunov, Murtsovkin, Dukhin, Colloid J. USSR (1986) - flow around a metal sphere

Bazant & Squires, Phys, Rev. Lett. (2004) - theory, broken symmetries, microfluidics

Low voltage weakly nonlinear theory
Low-voltage “weakly nonlinear” theory

Gamayunov et al. (1986); Ramos et al. (1999); Ajdari (2000); Squires & Bazant (2004).

1. Equivalent-circuit modelfor the induced zeta potential

Bulk resistor (Ohm’s law):

Double-layer BC:


Stern model

Constant-phase-angle impedance

2. Stokes flow driven by ICEO slip


AC linear response

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
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

At the “RC” frequency

In-phase E field (insulator)

Normal current

Out-of-phase E (negligible)

Induced dipole

Time-averaged velocity

Induced charge electrokinetic phenomena

Theory vs experiment at low salt concentration

Levitan et al (2005)

Horiz. velocity from a slice

10 mm above the wire

Data collapse when scaled to

characteristic ICEO velocity

  • Scaling and flow profile consistent with theory

  • Velocity is 3 times smaller than expected (no fitting)

  • BUT this is only for dilute 0.1 mM KCl…

Flow depends on solution chemistry
Flow depends on solution chemistry

J. A. Levitan, Ph.D. Thesis (2005).

  • ICEO flow around a gold post

  • in “large fields” (Ea = 1 Volt)

  • Flow vanishes around10 mM

  • Decreases with ion size, a

  • Decreases with ion valence, z

Not predicted by the theory

Induced charge electrophoresis of metallo dielectric janus particles
Induced-charge electrophoresisof metallo-dielectric Janus particles

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

Similar concentration dependence for velocity of janus particles in nacl
Similar concentration dependence for velocity of Janus particles in NaCl

Apparent scaling for C > 0.1 mM

(or perhaps power-law decay;

need more experiments…)

Ac electro osmotic pumps theory
AC electro-osmotic pumps: Theory particles in NaCl

Bazant & Ben (2006)

Planar electrode array. Brown, Smith & Rennie (2001).

Same geometry with raised steps

Low-voltage theory always predicts

a single peak of “forward” pumping

Stepped electrodes, symmetric footprint

Low voltage experimental data
Low-voltage experimental data particles in NaCl

  • Brown et al (2001), water

  • straight channel

  • planar electrode array

  • similar to theory (0.2-1.2 Vrms)

Reproduced in < 1 mM KCl

Studer 2004

Urbanski et al 2006

High voltage data
High-voltage data particles in NaCl

V. Studer et al. Analyst (2004)

  • Dilute KCl

  • Planar electrodes, unequal sizes & gaps

  • Flow reverses at high frequency

  • Flow effectively vanishes > 10 mM.

C = 10 mM

C = 1 mM

C = 0.1 mM

More puzzling high voltage data
More puzzling high-voltage data particles in NaCl

Bazant et al, MicroTAS (2007) Urbanski et al, Appl Phys Lett (2006)

KCl, 3 Vpp, planar pump

De-ionized water (pH = 6)

Reversal at high frequency?

Concentration decay?

Double peaks?

Faradaic reactions
Faradaic reactions particles in NaCl

  • Ajdari (2000) predicted weak low-frequency flow reversal

    in planar ACEO pumps due to Faradaic (redox) reactions

  • Observed by Gregersen et al (2007)

  • Lastochkin et al (2004) attributed high frequency ACEO reversal

    to reactions, but gave no theory

  • Olesen, Bruus, Ajdari (2006) could not predict realistic

    ACEO flows with linearized Butler-Volmer model of reactions

  • Wu et al (2005) used DC bias + AC to reverse ACEO flow

  • Still no mathematical theory

Wu (2006) ACEO trapping e Coli bacteria with DC bias

Outline particles in NaCl

  • Experimental puzzles

  • Strongly nonlinear dynamics

  • Beyond dilute solution theory

The simplest problem of diffuse charge dynamics
The simplest problem of particles in NaCldiffuse-charge dynamics

Bazant, Thornton, Ajdari, Phys. Rev. E (2004)

A sudden voltage across parallel-plate blocking electrodes.

What is the time

to charge thin double

layers of width

 = 1-100nm << L?



Debye time,  / D ?

Diffusion time, L / D ?


Equivalent circuit approximation
Equivalent Circuit Approximation particles in NaCl


What about nonlinear response? Few models…

Electrokinetics in a dilute electrolyte
Electrokinetics in a dilute electrolyte particles in NaCl

point-like ions

Poisson-Nernst-Planck equations

Singular perturbation

Navier-Stokes equations with electrostatic stress

Weakly nonlinear charging dynamics
“Weakly Nonlinear” Charging Dynamics particles in NaCl

Bazant, Thornton, Ajdari, Phys. Rev. E (2004)

Derive by boundary-layer analysis

(matched asymptotic expansions)

Ohm’s Law in the neutral bulk

Effective “RC” boundary condition

Weakly nonlinear ac electro osmosis
Weakly nonlinear AC electro-osmosis particles in NaCl

Olesen, Bruus, Ajdari, Phys. Rev. E (2006). Simulations of U vs log(V) and log(freq):

Faradaic reactions

“short circuit” the flow

Nonlinear DL capacitance

shifts flow to low frequency

Classical models fail…

Strongly nonlinear charging dynamics
“Strongly Nonlinear” Charging Dynamics particles in NaCl

Bazant, Thornton, Ajdari, Phys. Rev. E (2004)

New effect: neutral salt adsorption by the double layers

depletes the nearby bulk solution and couples double-layer charging to slow bulk diffusion

The simplest problem in d 1
The simplest problem in d>1 particles in NaCl

Chu & Bazant, Phys Rev E (2006).

A metal cylinder/sphere in a sudden uniform E field

  • Surface conduction through

    double layers sets in at same

    time as bulk salt adsorption

  • yields recirculating current

Dukhin (Bikerman) number

Strongly nonlinear electrokinetics
Strongly nonlinear electrokinetics particles in NaCl

Laurits Olesen, PhD Thesis, DTU (2006)

Some new effects

  • Surface conduction “short circuits” double-layer charging

  • Diffusio-osmosis & bulk electroconvection oppose ACEO

  • Space-charge and “2nd kind” electro-osmotic flow

  • BUT

  • Even fully nonlinear Poisson-Nernst-Planck-Smoluchowski

    theory does not agree with experiment

  • No high-frequency flow reversal & concentration effects

    It seems time to modify the fundamental equations…

Outline particles in NaCl

  • Experimental puzzles

  • Strongly nonlinear dynamics

  • Beyond dilute solution theory

Breakdown of poisson boltzmann theory
Breakdown of Poisson-Boltzmann theory particles in NaCl

  • Stern (1924) introduced a cutoff distance for closest approach of ions to a charged surface, but this does not fix the problem or describe crowding dynamics.

  • At high voltage, Boltzmann statistics predict unphysical

    surface concentrations, even in very dilute bulk solutions:

Packing limit


Ion crowding at large voltages

Crucial new physics: particles in NaCl

Ion crowding at large voltages

Steric effects in equilibrium
Steric effects in equilibrium particles in NaCl

Bikerman (1942); Dutta, Indian J Chem (1949);

Wicke & Eigen, Z. Elektrochem. (1952)

Iglic & Kral-Iglic, Electrotech. Rev. (Slovenia) (1994).

Borukhov, Andelman & Orland, Phys. Rev. Lett. (1997)

Modified Poisson-Boltzmann equation

a = minimum ion spacing

  • Minimize free energy, F = E-TS

  • Mean-field electrostatics

  • Continuum approx. of lattice entropy

  • Ignore ion correlations, specific forces, etc.

Borukhov et al. (1997)

Large ions, high concentration



Steric effects on electrolyte dynamics
Steric effects on electrolyte dynamics particles in NaCl

Kilic, Bazant, Ajdari, Phys. Rev. E (2007). Sudden DC voltage

Olesen, Bazant, Bruus, in preparation (2008). Large AC voltage (steady response)

Chemical potentials, e.g. from a lattice model (or liquid state theory)

dilute solution theory + entropy of solvent (excluded volume)

Modified Poisson-Nernst-Planck equations

1d blocking cell, sudden V

Steric effects on diffuse layer relaxation
Steric effects on diffuse-layer relaxation particles in NaCl

Kilic, Bazant, Ajdari, Phys. Rev. E (2007).

Exact formulae for Bikerman’s MPB model (red) and simpler Condensed Layer Model (blue) are in the paper.

All nonlinear effects are suppressed by steric constraints:

  • Capacitance is bounded, and decreases at large potential.

  • Salt adsorption (Dukhin number) cannot be as large for thin diffuse layers.

Example 1 field dependent mobility of charged metal particles
Example 1: particles in NaClField-dependent mobility of charged metal particles

Bazant, Kilic, Storey, Ajdari,

in preparation (2008)

AS Dukhin (1993) predicted the

effect for small E.

PB predicts no motion in large E:

Opposite trend

for steric models

Example 2 reversal of planar aceo pumps

steric effects particles in NaCl

Example 2:Reversal of planar ACEO pumps

log V

Storey, Edwards, Kilic, Bazant

Phys. Rev. E to appear (2008)


Large electrode wins

(since it has time to charge)

B. Small electrode wins

(since it charges faster at high V)

Towards better models
Towards better models particles in NaCl

  • Bikerman’s lattice-based

    MPB model under-estimates

    steric effects in a liquid

  • Can use better models

    for ion chemical potentials

  • Still need a>1nm to fit

    experimental flow reversal

  • Steric effects alone cannot

    predict strong decay of

    flow at high concentration…

Bazant, Kilic, Storey, Ajdari (2007, 2008)

Biesheuvel, van Soestbergen (2007)

Storey, Edwards, Kilic, Bazant (2008)

Model using Carnahan-Starling

entropy for hard-sphere liquid

Induced charge electrokinetic phenomena
Crowding effects on electro-osmotic slip particles in NaClBazant, Kilic, Storey, Ajdari (2007, 2008), arXiv:cond-mat/0703035v2

Electro-osmotic mobility for variable viscosity and/or permittivity:

1. Lyklema, Overbeek (1961): viscoelectric effect

2. Instead, assume viscosity diverges at close packing (jamming)

Modified slip formula depends on polarity and composition

Can use with any MPB model;

Easy to integrate for Bikerman

Example ion specific electrophoretic mobility
Example: Ion-specific electrophoretic mobility particles in NaCl

ICEP of a polarizable uncharged sphere in asymmetric electrolyte





Mobility in large DC fields:

Also may explain double peaks in water ACEO (H+, OH-)

Electrokinetics at large voltages
Electrokinetics at large voltages particles in NaCl

  • Steric effects (more accurate models, mixtures)

  • Induced viscosity increase

  • Electrostatic correlations (beyond the mean-field approximation)

  • Solvent structure, surface roughness (effect on ion crowding?)

  • Faradaic reactions, specific adsorption of ions

  • Dielectric breakdown?

  • Strongly nonlinear dynamics with modified equations


Conclusion particles in NaCl

Nonlinear electrokinetics is a frontier of

theoretical physics and applied mathematics

with many possible applications in engineering.

Related physics: Carbon nanotube

ultracapacitor (Schindall/Signorelli, MIT)

Induced-charge electro-osmosis

Papers, slides: