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Electrokinetic flow in microfluidics: problems at high voltage

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Title: Electrokinetic flow in microfluidics: problems at high voltage


1
Electrokinetic flow in microfluidicsproblems 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
Whats 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
Whats an electrolyte?
A material in which the mobile species are ions
and free movement of electrons is blocked.
(Newman, Electrochemical Systems)
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
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Glass water
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7
Electroosmosis (200th anniversary)

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-
-
-
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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
Electroosmosis-experiments
11
Classical electrokinetics double layer structure
Chemical potential of dilute ions
Near a wall, steady state, 1D
Poissons 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
C1
FV
Electric Potential
F-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 dont 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
Flow reversal
Ajdari, PRE 2000
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
_at_ equilibrium
n, dimensionless, ?, volume fraction in bulk
?
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 Bikermans 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 dont 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
Whats 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

46
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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
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