Steric effects on AC electroosmosis in dilute electrolytes

Brian D. Storey1, Lee R. Edwards1, Mustafa Sabri Kilic2, Martin Z. Bazant2

1Olin College of Engineering2MIT

Storey, Edwards, Kilic, Bazant PRE 2008Bazant, Kilic, Storey, Ajdari, arXiv, 2007

Motivation – ICEO microfluidics• For engineers, ICEO operates at low voltage (portable microfluidics). • For electrokinetic theorists, ICEO operates at high voltage ~100 kT/e.• Current simulations of ICEO microfluidic devices rely on classical

electrokinetic theory.• What’s complicated about ICEO? Large voltage, dynamics, long range

flow patterns, complex geometry.• Can we develop a simple theory that can be implemented as

boundary conditions in commercial finite element codes for predicting macro-scale flows?

Bazant & Squires PRL & JFM2004

Ramos, Morgan, Green, Castellenos 1998

AC Electroosmosis

ACEO PumpAjdari, PRE 2000

Exp. data from Urbanski et al, MIT

ln iiii eczckT

Near a wall, steady state, 1D:

Chemical potential of dilute point ions:

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

X

C

0 1 2 3 4 510

-20

10-10

100

1010

1020

X

C

Applied voltage =.025 V Applied voltage =0.75 V

kT

ez

i

i

ec

Would need ions to be 0.01 angstrom

Classical electrokinetics

Bikerman (1942)

Kilic, Bazant, Ajdari – PRE 2007

iii

i eczc

kT

1

ln kT

ze

ec

c

1 C, dimensionless, ν, volume fraction in bulk

@ equilibrium

Linearized, DH

Non-linear, GCS

Bikerman model

Model applied to ACEO

Flow contours – different ion size

Theory and experiment

Ion is 4 nm to best fit data.

Exp. from Studer, Pepin, Chen, Ajdari Analyst 2004

Better steric models

Carnahan Starling (2 nm)

“volume effects can be underestimated significantly” using Bikerman model.

We can reduce to ~1 nm if we assume ε changes in double layer

(Biesheuvel & van Soestbergen, JCIS 2007).

Concentration effects-ACEO experiments

Urbanski et al. 2007 Studer et al, 2004

Concentration effects - simple model

ts bEU

b

bdbD

0

cb

b

1

Electroosmotic mobility

Valid for any continuum model

Simplest model of a viscoelectric effect

(Bazant, Kilic, Storey, Ajdari 2007 arXiv)

Viscoelectric model applied to ACEO

10-1

100

101

102

-1

0

1

2

x 10-3

Frequency

Vel

ocit

y

Increasing concentration

Need an ion size of ~4 nm to fit forward flow dataLose the flow reversal when we combine models

What’s missing?

• Correlations effects.• Faradaic reactions (recall talk of Ramos et al on TWEO).• …..

What’s needed?• Experiments designed to study these effects.• Multi-scale modeling

Conclusions

• ICEO applications has opened new avenues for study in theoretical EK.

• Crowding of ions, increased viscosity, and decreased permittivity are not new ideas (Bikerman, 1970).

• Accounting for steric effects can effect qualitative and quantitative predictions in ACEO.

• Still more work is needed for a truly useful theory based on first principles.

Induced charge electroosmosis (ICEO)

Bazant & Squires PRL & JFM2004

Theory & experiment

Exp. from Studer, Pepin, Chen, Ajdari Analyst 2004

AC Electroosmosis

Ramos, Morgan, Green, Castellenos 1998*simulations account for EK through BC.