Induced-Charge Electro-osmosis

Martin Z. BazantMathematics, MIT

Supported by the Institute for Soldier Nanotechnologies

Jeremy Levitan

Todd ThorsenMechanical Engineering, MIT Martin Schmidt

Electrical Engineering, MIT

Todd M. SquiresApplied Math, Caltech

AC Electro-osmosisRamos et. al (1998), Ajdari (2000)

t = 0 t = t t >> t

Steady flow forAC period = t

c

c

c

How general is this phenomenon? Need electrode arrays? Need “AC”?

Sudden DC voltage

Induced-Charge Electro-osmosis

Bazant & Squires, Phys, Rev. Lett. 92, 0066101 (2004).Squires & Bazant, J. Fluid. Mech. 509, 217 (2004).

E-field, t = 0 E-field, t » charging time Steady ICEO flow

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

Nonlinear electrokinetic slip at a polarizable surface

induced ~ E a

Same effect for metals and dielectrics, DC and AC fields…

Nonlinear Electrokinetic Phenomena

• AC electro-osmosis (+ colloidal aggregation?) at electrodes • DC electrokinetic jet at a dielectric corner

• AC flows around metallic particles

• Dielectrophoresis in electrolytes

Levich (1962); Simonov & Shilov (1977); Gamayunov, Murtsovkin, A. S. Dukhin (1984…).

1. Other examples of “ICEO” flows

Thamida & Chang (2002…)

Simonova, Shilov, Shramko (2001…)

2. Other “Non-equilibrium Electro-surface Phenomena”• Surface conduction, non-equilibrium diffusio-osmosis

• Second-kind electro-osmosis, instability at limiting current

S. S. Dukhin (1965); Deryaguin & S. S. Dukhin (1969…).

S. S. Dukhin (1989…); Ben & Chang (2002); Rubinstein & Zaltzman (2000…)

Ramos et al. (1998…); Ajdari (2000…); “EHD” Ristenpart, Saville (2004)…

(3. Bulk “electrokinetic instability” )Lin et al, Santiago (2001…)

ICEO in Microfluidics

Cross-channel Reversible pump

Post-array mixer

T pump

Fixed-Potential ICEO

Example: metal cylinder grounded to an electrode supplying an AC field.

Fixed-potential ICEO mixer

Pumping by Broken SymmetryInspired by Ajdari (2000): AC EO pumping with electrode arrays.

Symmetricmetal wire

Asymmetric Stern layer

Partial coatingby an insulator

Asymmetric shape

Misalignment with field also drives torques to align.

More ICEO in Microfluidics

Patterned surfaces

Asymmetric postsPumping transverseto a AC or DC field

Non-uniform Applied Fields

• ICEO pumps in a non-uniform AC or DC field

• Very sensitive to size, shape, and time-dependence

• Cancels DEP for a metal sphere (but not other shapes)

• All higher multipoles at infinity also pump in AC fields

Simonova, Shilov, Shramko, Colloid J. USSR (2001)

Squires & Bazant, in preparation.

Mathematical Theory of ICEO

I. Diffuse-Charge Dynamics

What is the time scale for charge screening?

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

Debye time, / D ?

Diffusion time, L / D ?

No! (and yes…)

2

2

Model problem

1. Weakly Nonlinear Dynamics

Intermediate “RC time”:

Effective boundary condition:

Equivalent circuit at leading order, << L.

2. Strongly Nonlinear Dynamics

V = 4 kT/eTransient bulk diffusion

Weakly Nonlinear ICEO Flow

BC:

1. Electrochemical problem for the induced zeta potential

2. Stokes flow driven by ICEO slip

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

Green et al. (2000) ACEOSquires & Bazant (2004)

J. Levitan’s experiment:Platinum wire in a polymer microchannel

Electric field after double-layer charging

Steady ICEO flow

Strongly Nonlinear ICEO/NESP

• Nernst-Planck Equations

• Deryaguin/Dukhin BC for double-layer ion adsorption

Adsorption rate = bulk flux + surface flux + reactions

Dukhin number:

• Stokes flow due to “first-kind” electro/diffusio-osmosis

Induced-Charge Electro-osmosis

• Nonlinear electro-osmosis at a polarizable surface• Sensitive to size, shape, voltage, time-dependence,…• Builds on ACEO, Russian colloid literature, etc.• Open theoretical questions

– “Strongly nonlinear” ICEO with large induced zeta– Effect of Faradaic reactions (e.g. Butler-Volmer)– Why theory over-predicts experimental velocities– Optimization of geometry & forcing for mixing & pumping

• Experiments & microfluidic applications – See talk by Jeremy Levitan at 2:20pm…

Papers: http://math.mit.edu/~bazant

Example: Dielectric-coated metal cylinder at fixed potential in a suddenly applied DC field

Surface capacitance ratio= dielectric thickness / Debye length

Induced dipolemoment

ExperimentsJeremy Levitan

Todd Thorsen, Martin Schmidt, Hongwei Sun,Shankar Devasenathipathy (MIT), Vincent Studer (ESPCI)

First model system: Isolated 100 micron platinum wire in KCl in a 0.2 x 1 x 1 mm PDMS microchannel with electrode ends.

Next generation: electroplated gold posts.

E

<u>

Voltmeter Function Generator

ViewingResistor

KCl inPDMSMicrochannel

PlatinumWire

Inverted OpticsMicroscope

Viewing Plane

Bottom View200 um X 1 mm X 1mm Channel

PIV Mean Velocity Data• PIV measurement with 0.01% volume dielectric (fluorescent) tracer particles• Fit velocity profile to ICEO simulation 25 microns from wire• Correct scaling, but smaller magnitude by factor of 30, perhaps due to surface impurity

Metal colloids: Gamayunov, Mantrov, Murtsovkin (1992)

Frequency Scaling

• Decay above the “RC time”

• Consistent with ICEO theory U ~ U0/(1 + (/c)2) c = 2 d a/D = 1/c = 3 ms

Experiments in 1 mM KCl at 75 V

Induced-Charge Electro-osmosis

• Nonlinear electro-osmosis at a polarizable surface• Sensitive to size, shape, voltage, time-dependence,…• Unifies & extends ACEO, Russian colloid literature, ...• Open theoretical questions

– “Strongly nonlinear” ICEO with large induced zeta– Effect of Faradaic reactions (e.g. Butler-Volmer)– Why theory under-predicts experimental velocities– Optimization of geometry & forcing for mixing & pumping

• Experiments & microfluidic applications underway

Papers: http://math.mit.edu/~bazant