Electrokinetic flow in microfluidics: problems at high voltage

1. Electrokinetic flow in microfluidics:problems at high voltage Brian D. Storey Olin College of Engineering

2. People and funding • Collaborators • Martin Bazant (MIT) • Sabri Kilic (former PhD student MIT) • Armand Ajdari (ESPCI) • UG students • Jacqui Baca • Lee Edwards • Funding – NSF

3. Today • Classic linear electrokinetics • Induced charge and nonlinear electrokinetics • Classical theory and its breakdown • What can we do?

4. What’s electrokinetics? • Interaction of ion transport, fluid flow, and electric fields. • Electrophoresis • Electroosmosis • Sedimentation potential • Streaming potential • Discovered in 1809, theory is over 100 yrs old. • Today we are only concerned with transport in simple aqueous, dilute electrolytes.

5. What’s an electrolyte? A material in which the mobile species are ions and free movement of electrons is blocked. (Newman, Electrochemical Systems) Na+ Cl - Cl - Na+ Cl - Na+ Cl - Cl - Na+ Na+ Na+ 1 mM of salt water is a 3 mm salt cube in 1 liter 1 ion per 10,000 waters

6. The electric double layer Salt water Glass - + + - + + - + - + + - Glass + water + - + + + - + - - - - + + + + - + - + + - - + + + - + - - counter-ions co-ions

7. Electroosmosis (200th anniversary) + - + - - - + + + + + + + + + + + - - + + + - - - + + + + - - - + + + + - - + + + + + + - - + + - - - - + + + + + + + + + + + + - - + + + + + + - - + + + + + + - - - + + - - Electric field

8. Electroosmosis in a channel(the simplest pump?) Y Electric field Y Electroneutral in bulk Charge density Velocity

9. Double layers are typically thin ~10 nm Helmholtz-Smolochowski

10. Pressure-driven Electrokinetic Molho and Santiago, 2002 Electroosmosis-experiments

11. Classical electrokinetics double layer structure Chemical potential of dilute ions: Near a wall, steady state, 1D: Poisson’s eqn for electric potential: Wall voltage =.025 V n

12. “Classical” microfluidic application Sustarich, Storey, and Pennathur, 2010

13. Linear EK devices • 1 Problem: High voltage, restricted to the lab • 1 Solution: High fields can be generated at low voltage if electrodes are placed very close to each other.

14. Applied voltage via electrodes 1D transient problem Bazant, Thorton, Ajdari PRE 2004

15. Applied voltage via electrodes 1D problem Concentration C=1 Φ=+V Electric Potential Φ=-V Position

16. Applied voltage via electrodes 1D problem

17. Induced charge electromosis (ICEO) Flow is proportional to the square of the electric field, nonlinear. Bazant & Squires PRL & JFM2004

18. Flat electrodes and pumps Ramos, Morgan, Green, Castellenos 1998

19. ICEP Gangwal, Cayre, Bazant, Velev PRL 2008

20. And don’t think this is all new…

21. The “standard model” for ICEO Trivial to implement and solve in a commercial finite element package

22. Some problems with the standard model

23. Ajdari, PRE 2000 Flow reversal Storey, Edwards, Kilic, Bazant, PRE 2008

24. Unexplained freq response Huang, Bazant, Thorsen, LOC 2010

25. Universal flow decay with concentration Urbanski et al. 2007 Studer et al, 2004

26. Flow decay with concentration Bazant, Kilic, Storey, Ajdari ACIS 2009

27. ICEO microfluidics • For engineers, ICEO operates at low voltage. • For theory, ICEO operates at high voltage ~100 kT/e • Classical theory is great for some features, a number of phenomena have been predicted before observation. • Classical theory misses some important trends and cannot get quantitative agreement. • Would like a better theory, but one simple enough to be practical for device design.

28. The ICEO standard model Poisson-Nernst-Planck Navier Stokes Fundamental. Non-linear PDEs Flow and electrical problems are coupled. Very thin boundary layers. A bit nasty. Is this OK? Do some math (asymptotics) Is this OK? ICEO Standard model, Linear PDEs Flow and electrical problems are decoupled. Trivial.

29. Classical theory – one problem 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

30. Stern layer (1924) Bulk fluid Solid Diffuse layer Diffuse +Stern layer Zembala, 2004.

31. Steric effects – continuum theory Hard sphere Bare Hydrated • Borukhov and Andelman 1997 • Iglic and Kralj-Iglic 1994 • Strating and Wiegel 1993 • Wicke and Eigen 1951 • Dutta and Bagchi 1950 • Grimley and Mott 1947 • Bikerman 1942 • Stern 1924 Classic

32. Stern 1924 On the other hand, it is easy, instead of introducing the gas laws for osmotic pressure, to introduce the laws of the ideal concentrated solutions. Under this assumption, which simplifies to (2a) when the second addend in the square brackets is small compared to 1. (as translated by a German student in my class, Johannes Santen)

33. Bikerman model @ equilibrium n, dimensionless, ν, volume fraction in bulk ν Kilic, Bazant, Ajdari – PRE 2007

34. Bikerman model KPF6 on silver, no adsorption Potassium Hexafluorophosphate Bazant, Kilic, Storey, Ajdari ACIS 2009

35. Model applied to ICEO pump Linearized, DH Non-linear, GCS Bikerman model Storey, Edwards, Kilic, Bazant PRE 2008

36. Theory and experiment Bazant, Kilic, Storey, Ajdari, ACIS 2009 Exp. from Studer, Pepin, Chen, 2004 Ion is 4 nm to best fit data.

37. Carnahan-Starling - hard spheres “volume effects can be underestimated significantly” using Bikerman’s model. (Biesheuvel & van Soestbergen, JCIS 2007). 1-2 nm ion needed to fit the flow data – but capacitance data look more like Bikerman!

38. Flow halts at high concentrationWhy?

39. Continuum model of the slip plane Stern, 1924 (picture from Zembala, 2004)

40. A simple continuum model Electroosmotic mobility Valid for any continuum model Simplest model of thickening effect Other power laws explored Bazant, Kilic, Storey, Ajdari ACIS 2009

41. Charge induced thickening • Jamming against a surface (MD simulations, colloidal systems/granular ) • Electrostatic correlations (ion pulled back to correlation “hole”) • Dielectric saturation, permittivity thought to be ~5 near surface. • Alignment of solvent dipoles can increase viscosity (MD). • Viscosity in bulk known to increase with ion density (solubility limits usually don’t let us see this effect)

42. Charge induced thickening Helmholtz-Smolochowski Apparent induced voltage Applied voltage

43. Model applied to an ICEO pump 1 μM 10 mM Need an ion size of ~4 nm to fit flow data

44. What’s still missing? • Electrostatic correlations– initial work indicates this may help correct the ion size issue. • Faradaic reactions • Surface roughness • Ion-surface correlations • Specific adsorption • Perhaps a continuum model is just doomed from the start.

45. Conclusions • ICEO applications has opened new avenues for study in theoretical electrokinetics. • 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 ICEO. • More work is needed for a truly useful theory. • Goal: A simple continuum model that can be solved or implemented as simple boundary conditions in simulations. • “Surfaces are the work of the devil”

47. Some recent experiments, do work No dielectric assumed Thin dielectric coating 30-60 nm Thin dielectric coating and accounting for chemistry Pascall & Squire, PRL 2010

48. Carnahan Starling 1-2 nm ion needed to fit the data