Transcript Presentation

Steric effects on AC electroosmosis
in dilute electrolytes
Brian D. Storey1, Lee R. Edwards1, Mustafa Sabri
Kilic2, Martin Z. Bazant2
1Olin
College of Engineering
2MIT
Storey, Edwards, Kilic, Bazant PRE 2008
Bazant, 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
AC Electroosmosis
Ramos, Morgan, Green, Castellenos 1998
Ajdari, PRE 2000
ACEO Pump
Exp. data from Urbanski et al, MIT
Classical electrokinetics
i  kT ln ci  zi eci
Chemical potential of dilute point ions:
ci  e
Near a wall, steady state, 1D:
Applied voltage =.025 V
3
z i e
kT
Applied voltage =0.75 V
20
10
2.5
10
10
1.5
C
C
2
0
10
1
-10
10
0.5
0
0
Would need ions to be 0.01 angstrom
-20
1
2
3
X
4
5
10
0
1
2
3
X
4
5
Bikerman (1942)
ci
i  kT ln
 zi eci
1 
ze
@ equilibrium
c
 e kT
1  c
C, dimensionless,
ν, volume fraction in bulk
Kilic, Bazant, Ajdari – PRE 2007
Model applied to ACEO
Linearized, DH
Non-linear, GCS
Bikerman model
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.
(Biesheuvel & van Soestbergen, JCIS 2007).
We can reduce to ~1 nm if we assume ε changes in double layer
Concentration effects-ACEO experiments
Urbanski et al. 2007
Studer et al, 2004
Concentration effects - simple model
Electroosmotic mobility
U s  bE t
Valid for any continuum model
D
b

b   d 

b
0
Simplest model of a viscoelectric effect
 b
 1 c 
 b
(Bazant, Kilic, Storey, Ajdari 2007 arXiv)
Viscoelectric model applied to ACEO
x 10
-3
Velocity
2
1
0
Increasing concentration
-1 -1
10
10
0
10
Frequency
1
10
2
Need an ion size of ~4 nm to fit forward flow data
Lose 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
*simulations account for EK through BC.
Ramos, Morgan, Green, Castellenos 1998