Steric effects on AC electroosmosis in dilute electrolytes

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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
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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.
• Whats 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
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AC Electroosmosis
Ramos, Morgan, Green, Castellenos 1998
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ACEO Pump
Ajdari, PRE 2000
Exp. data from Urbanski et al, MIT
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Classical electrokinetics
Chemical potential of dilute point ions
Near a wall, steady state, 1D
Applied voltage .025 V
Applied voltage 0.75 V
Would need ions to be 0.01 angstrom
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Bikerman (1942)
_at_ equilibrium
C, dimensionless, ?, volume fraction in bulk
Kilic, Bazant, Ajdari PRE 2007
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Model applied to ACEO
Linearized, DH
Non-linear, GCS
Bikerman model
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Flow contours different ion size
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Theory and experiment
Ion is 4 nm to best fit data.
Exp. from Studer, Pepin, Chen, Ajdari Analyst 2004
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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 e changes in
double layer
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Concentration effects-ACEO experiments
Urbanski et al. 2007
Studer et al, 2004
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Concentration effects - simple model
Electroosmotic mobility
Valid for any continuum model
Simplest model of a viscoelectric effect
(Bazant, Kilic, Storey, Ajdari 2007 arXiv)
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Viscoelectric model applied to ACEO
Increasing concentration
Need an ion size of 4 nm to fit forward flow
data Lose the flow reversal when we combine models
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Whats missing?

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

Whats needed?

• Experiments designed to study these effects.
• Multi-scale modeling

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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.

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Induced charge electroosmosis (ICEO)
Bazant Squires PRL JFM2004
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Theory experiment
Exp. from Studer, Pepin, Chen, Ajdari Analyst 2004
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AC Electroosmosis
Ramos, Morgan, Green, Castellenos 1998
simulations account for EK through BC.