1. Steric effects on AC electroosmosis in dilute electrolytes Brian D. Storey 1, Lee R. Edwards 1, Mustafa Sabri Kilic 2, Martin Z. Bazant 2 1 Olin College of Engineering 2 MIT Storey, Edwards, Kilic, Bazant PRE 2008 Bazant, Kilic, Storey, Ajdari, arXiv, 2007

2. 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

3. Ramos, Morgan, Green, Castellenos 1998 AC Electroosmosis

4. ACEO Pump Ajdari, PRE 2000 Exp. data from Urbanski et al, MIT

5. Near a wall, steady state, 1D: Chemical potential of dilute point ions: Applied voltage =.025 V Applied voltage =0.75 V Would need ions to be 0.01 angstrom Classical electrokinetics

6. Bikerman (1942) Kilic, Bazant, Ajdari – PRE 2007 C, dimensionless, ν, volume fraction in bulk @ equilibrium

7. Linearized, DH Non-linear, GCS Bikerman model Model applied to ACEO

8. Flow contours – different ion size

9. Theory and experiment Ion is 4 nm to best fit data. Exp. from Studer, Pepin, Chen, Ajdari Analyst 2004

10. 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).

11. Concentration effects-ACEO experiments Urbanski et al. 2007 Studer et al, 2004

12. Concentration effects - simple model Electroosmotic mobility Valid for any continuum model Simplest model of a viscoelectric effect (Bazant, Kilic, Storey, Ajdari 2007 arXiv)

13. 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

14. 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

15. 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.

17. Induced charge electroosmosis (ICEO) Bazant & Squires PRL & JFM2004

18. Theory & experiment Exp. from Studer, Pepin, Chen, Ajdari Analyst 2004

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