Download Slide 1

The role of Faradaic reactions
in microchannel flows
David A. Boy
Brian D. Storey
Franklin W. Olin College of Engineering
Needham, MA
Sponsor: NSF CTS, Research in Undergraduate Institutions.
Motivation: ACEO & ICEO
Electric Field
Positive Ions
Flow
++++++++++++++++++++++++
Negative Ions
-----------------------------------
Negative Electrode
Positive Electrode
Advantages over DC
• Low voltage, portable (~1 – 10 volts)
• Good flow rates (~mm/s)
Soni, Squires, Meinhart, BC00004
Swaminathan , Hu FC00003
Yossifon, Frankel, Miloh, GC00007
Green et al PRE 2000, 2002
Ajdari PRE 2000
Brown PRE 2000
Bazant & Squires JFM 2004
Olesen et al PRE 2005
Experimental observations
(reactions have been proposed as possible mechanism for each of these)
• Reversal of net pumping in ACEO is observed at high
frequency.
• Most flow stops at ~ 10 mM in ACEO & ICEO
• Typically, only qualitative flow is predicted.
Our goals
• Understand the general coupling between
reactions and flow.
• Account for non-linear effects
– Surface conduction
– Mass transfer: concentrations at electrodes
are not the same as the bulk.
– Body forces outside of EDL.
Olesen et al PRE 2005
A simpler system to study body forces
current
reactions at electrodes
Binary, symmetric
electrolyte
reactions at electrodes
R. F. Probstein. 1994. Physicochemical Hydrodynamics. Wiley.
Bulk equations
(symmetric, binary, dilute electrolyte):
v
1
 : electric potential
 v  v  p   2 v   E E
t
Re
 : electrical conductivi ty
 E : charge density
 v  0
 E
1
 v   E       E 
t
Pe

1
 v       E    
t
Pe
2  
1
E
2

E : electric field
 : dimensionl ess Debye length
Pe : Peclet number
Re : Reynolds number
V : Dimensionl ess applied voltage
K : Dimensionl ess reaction rates
Voltage scaled thermal voltage (25 mV)
λ = 0.1
to
0.0001
Pe = 100
to
1,000,000
Small device
Dilute
Large device
High Concentration
Boundary conditions
boundary conditions at electrodes:
- fixed voltage difference
- No slip
- reactions
periodic boundary conditions in x
f 0, y   f 2 , y 
y  1 :
v0
   S   n  V
   E    n  R
 E     n  R
Butler-Volmer
reaction kinetics:
R   C exp       C exp    

KH
D
 : voltage drop across Stern layer
1D Solutions λ=0.01
K. T. Chu and M. Z. Bazant. 2005. SIAM J. Appl. Math. 65, 1485-1505.
1D Voltage-Current Behavior
(fixed geometry & fluid properties)
unstable
Dilute
K. T. Chu and M. Z. Bazant. 2005. SIAM J. Appl. Math. 65, 1485-1505.
Rubinstein & Zaltzman PRE (2000, 2003, 2005 )
Fixed Debeye length 0.1
unstable
Stable
Streamlines for λ=.02, k=2.5, V=9.5
y
0
1
2

3
x
Unsteady flow at high voltages
Voltage-Current behavior
ACEO Pumping Geometry
Time averaged
flow
Electrode
Electrode
AC
When reactions occur:
•Flow occurs for all voltages
•Flow occurs in AC and DC case
•Flow is not symmetric even when electrodes are
ACEO: Symmetric Electrodes
(DC, λ=0.01, Pe=1000, V=10)
Potential
Charge
Density
Streamlines
ACEO: Typical Streamlines
(DC, λ=0.01, Pe=1000)
V=1
Neg.
V=5
Pos.
Neg.
V=20
V=10
Neg.
Pos.
Pos.
Neg.
Pos.
Reverse the sign on the electrodes
(DC, λ=0.01, Pe=1000, V=5)
Pos.
Neg.
Neg.
Pos.
Frequency response
(AC,
λ=0.05 Pe=1000)
Olesen et al. PRE 2005.
Future work
• Complete the parameter study of ACEO geometry. Can
body forces destabilize the flow?
• Compare ACEO flow computed with our “full” simulation
to simpler models (i.e. Olesen et al. PRE 2005).
• Use realistic reactions and electrolyte parameters as
opposed to model binary, symmetric electrolyte.
• Incorporate non-dilute effects. All applications well
exceed kT/e = 25 mV.
Conclusions
• Body force in extended charge region can induce
instability in parallel electrode geometry.
• Instability occurs in parameter range found in microfluidic
applications.
• Thus far, we have not flow instability due to body forces
in ACEO applications. Apparently, steady flow
overwhelms the instability. (Note: our study is currently
incomplete).