todd squires aditya khair - american physical...
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The Francois Frenkiel Award Lecture:
Fundamental aspects of Concentration Polarization
Todd Squires
Aditya Khair
Chemical Engineering
University of California, Santa Barbara
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Diffuse ions
Electrokinetic effects
Electric
fields
fluid flow,
particle motion
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Diffuse ionsElectro-osmotic
flow
Field-driven motion
qE
Electrokinetic effects
Electricfields
fluid flow,particle motion
Paul et al. ‘99
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Electrokinetic effects
Diffuse ionsElectro-osmotic
flow
Field-driven motion
qE
Electricfields
(Wikipedia)
Electrophoresis
Paul et al. ‘99
E
Happy 200th Birthday!
“Notice sur un nouvel effet de l'électricité galvanique”
F.F. Reuss 1809
fluid flow,
particle motion
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Diffuse ionsElectro-osmotic
flow
Field-driven motion Flow-driven fieldsStreaming potential
Electrokinetic effects
qE
Electricfields
(Wikipedia)
Electrophoresis
Paul et al. ‘99
Happy 200th Birthday!
“Notice sur un nouvel effet de l'électricité galvanique”
F.F. Reuss 1809
E
fluid flow,particle motion
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Broader impacts of electrokinetics researchConvective charge separation in low-conductivity fluids
Streaming potential
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Convective charge separation in low-conductivity fluids
QuickTime™ and a decompressor
Broader impacts of electrokinetics research
Source: youtube
Potentially highly transformative, in the exothermic sense
My Outreach to you: please remember to ground your gas containers.
decompressorare needed to see this picture.
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A modern renaissance in electrokinetics
Microfabrication:Fields and flows provide many new ways to
control micro & nano-scale transport
DNA translocation Nanofluidic Diode Energy Harvesting
Yossifon & Chang 2008
Overlimiting Currentsin Electrochemical Systems
Concentration Polarizationat Micro/Nano Interfaces
Leinweber et al 2006
Salt “de-mixing”
Kim et al. 2005
Karnik et al. 2007Keyser et al. 2006 van der Heyden et al. 2007
QuickTime™ and a decompressor
are needed to see this picture.
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How most of you view water.
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Water dissolves ions...
OHHNa
+
+
-
NaCletc.
+
-
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Ions ‘screen’ charged surfaces
screening length λλλλD varies from ~1 – 103 nm
PotentialDrop
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Electric fields: body force on fluid
net force within screening cloud
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Electro-osmosis: field drives flow
‘slip’ velocity (conveyor belt)
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“Standard Model” for electrokinetics
(2) Electrostatics
(1) Fluid flow: low-Re flow
Coupled,
Nonlinear
PDE’s
…what lurks behind all the cartoons I’ll show.
diffusion advection electrostatic
(3) Ion conservation
(2) ElectrostaticsCommon Approach:
Matched asymptotics
With “thin” double-layers
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Stroock et al 00
Microfabrication: natural surface charge inhomogeneities
Green, Gonzales, Ramos … 00
QuickTime™ and a
Karnik et al. 07
Leinweber & Tallarek 2005
Andy Pascall & TMS
Theory: J. Anderson, Ajdari, Stone, Long, Ghosal, Yariv, TMS, many many others
QuickTime™ and a decompressor
are needed to see this picture.
Kim et al. 2005
QuickTime™ and a decompressor
are needed to see this picture.
Leinweber & Tallarek 2005
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Surface charge discontinuity
Electro-osmotic flow:Similarity solution
outside double-layerYariv (2004)
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Surface charge discontinuity
Violates ion conservation!
Electro-osmotic flow:Similarity solution
outside double-layerYariv (2004)
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Surface charge discontinuity
Violates ion conservation!
Electro-osmotic flow:Similarity solution
outside double-layerYariv (2004)
Ion conservation:•Field pulled in from bulk
•How far downstream (L) before
standard “parallel field”?
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Surface charge discontinuity
Violates ion conservation!
Electro-osmotic flow:Similarity solution
outside double-layerYariv (2004)
No geometric length scale: “Healing length” emerges
•Can be very long!
Ion conservation:•Field pulled in from bulk
•How far downstream (L) before
standard “parallel field”?
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Universal flow problem: scale by healing length
• Ion conservation alters electrostatic boundary condition
Electric Field
x = σs/σB
Field
Lines
FlowStream Lines
Field & flow “heal” over length scale λλλλH=σ=σ=σ=σs/σσσσBKhair & Squires, JFM 08
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Question: what happens to the ions…
Electric
Field Lines
At first:
Seems ok
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Question: what happens to the ions…
Electric
Field Lines
At first:
Seems ok
Reverse field: Ion accumulation
Steady state solution?
Copyright Aditya Khair and Todd Squires, 2009
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Simplest
model
system
Inhomogeneous surface transport:Ion conservation Khair & Squires, PoF (08)
Electro-osmosis over a periodically-varying charged surface
•Low-ζ:ζ:ζ:ζ: can be solved exactly•Steady-state concentration and fields•Oscillatory concentration and fields•Suddenly-applied field -- evolution of “concentration polarization”
•High-ζ ζ ζ ζ also amenable to analysis•Avoids field curvature effects •Convective transport due to EOF
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Concentration Polarization
E
Loss of (+) ions:
Need inward field
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Concentration Polarization
E
Loss of (+) ions:
Need inward field
Gain of (+) ions:
Need outward field
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Concentration Polarization
E
Loss of (+) ions:
Need inward field
Gain of (+) ions:
Need outward field
Gain of (-) ions:
Need inward field
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Concentration Polarization
E
Loss of (-) ions:
Need outward field
Loss of (+) ions:
Need inward field
Gain of (+) ions:
Need outward field
Gain of (-) ions:
Need inward field
This is a cartoon. All details emerge quantitatively from analysis
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Concentration polarizationsuddenly-applied field
Inhomogeneous double-layer: salt source/sink disribution
Outside DL: Salt transport via diffusion
Natural time scale: ττττD∼λ∼λ∼λ∼λ2/D
t = 10-3 ττττDt = 10-2 ττττD
E
t = ττττDt =10 ττττD
λλλλ
E
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Convection and diffusion of salt
PeE = 10-3
+_
E
Electro-osmoticPeclet number:
+_
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Convection and diffusion of salt
PeE = 10-3 PeE = 1
+_
E
Electro-osmoticPeclet number:
PeE = 10 PeE = 100
Flow asymmetry gives concentration asymmetry, form salt plumes
+_
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Convection-diffusion: salt plumes
E
Electro-osmoticPeclet number:
Leinweber & Tallarek 2005
Salt “de-mixing”
CP + Convection
EQuickTime™ and a
decompressorare needed to see this picture.
Salt “de-mixing”
Leinweber et al 2006
Yossifon & Chang 2008
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Surface charge discontinuities2D diffusion from line source/sink: ill-posed.
Regularization mechanisms:•Convective transport from EOF
•Convection-diffusion boundary layer, ‘upwind’ stabilizes•Downwind: salt gradually reduced
•Plate ends, providing a line source of salt
Time scale to reach steady state: •diffusion time L2/D•convection time L/UEOF
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Where we’ve since gone
Electrophoresis with slip & stericsUniversal EK mobility
Of highly-charged bodies
Surface conductiondetermines mobility
Steric ions
Roughness effects
Gating in ‘tunable’ nanochannels
Remarkable Collapse!
Partial Slip Khair & Squires, PoF 09, JFM 09
Voltage
Cu
rre
nt
QuickTime™ and a decompressor
are needed to see this picture.QuickTime™ and a
decompressorare needed to see this picture.
Squires, preprint
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Inhomogeneous surface transport
• Surface charge gradients:– Ion conservation necessitates bulk field perturbations
– At step changes: “healing length” ~ σS /σB can be long
– Field into/out of DL creates sources/sinks of salt– Field into/out of DL creates sources/sinks of salt
– Concentration Polarization• Established over ‘macro’ time and length scales
• Nontrivially influenced by convection with EOF
– Step Change:• ill defined without regularization
– Trailing edge - diffusive dipole
– Convection with EOF - boundary layer
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AcknowledgmentsThe Frenkiel Award Committee & DFD Community
Aditya Khair, Andy Pascall, Rob Messinger
Carl Meinhart
•Khair & Squires “Fundamental aspects of concentration polarization arising from non-uniform
surface transport”, Phys. Fluids 20, 087102 (2008)
•Khair & Squires, J. Fluid Mech. 615, 323-334 (2008)
References
UCSB nanofab
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Concentration polarizationElectrokinetic formation of salt concentration gradients
+E
Permiselective membrane
-Salt Source
+
-
+
-
+
-
+
-
+
-
E
Permiselective membrane
High Salt
QuickTime™ and a decompressor
are needed to see this picture.
Tallarek et al 2005
E +- Salt Sink+-
+- +- +-+- E Low salt
CP in porous granules
Kim, Han et al 2007
CP across nanochannels
See e.g. Rubinstein
•Induced-charge
electrokinetics
(e.g. Chu & Bazant)
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