The role of Faradaic reactions in microchannel

flows

David A. BoyBrian D. Storey

Franklin W. Olin College of EngineeringNeedham, MA

Sponsor: NSF CTS, Research in Undergraduate Institutions.

Motivation: ACEO & ICEO

Advantages over DC• Low voltage, portable (~1 – 10 volts)• Good flow rates (~mm/s)

Green et al PRE 2000, 2002Ajdari PRE 2000Brown PRE 2000Bazant & Squires JFM 2004Olesen et al PRE 2005

Positive ElectrodeNegative Electrode

Soni, Squires, Meinhart, BC00004Swaminathan , Hu FC00003Yossifon, Frankel, Miloh, GC00007

++++++++++++++++++++++++-----------------------------------

Electric Field

Negative IonsPositive Ions Flow

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

reactions at electrodes

reactions at electrodes

Binary, symmetricelectrolyte

R. F. Probstein. 1994. Physicochemical Hydrodynamics. Wiley.

current

ratesreaction essDimensionl :K voltageapplied essDimensionl :V

number Reynolds:numberPeclet :

length Debye essdimensionl:

field electric:

density charge:tyconductivi electrical:

potential electric:

RePe

EE

Bulk equations (symmetric, binary, dilute electrolyte):

Voltage scaled thermal voltage (25 mV)λ = 0.1 to 0.0001Pe = 100 to 1,000,000 Small device Large device Dilute High Concentration

E2

2 1

EEE

Pet

1v

EPet1v

EvvvvERe

pt

21

0 v

0vVS n

RE n

boundary conditions at electrodes: - fixed voltage difference - No slip - reactions

RE n expexp CCR

DKH

periodic boundary conditions in x

yfyf ,2,0

Butler-Volmerreaction kinetics:

layer Stern across drop voltage:

:1y

Boundary conditions

K. T. Chu and M. Z. Bazant. 2005. SIAM J. Appl. Math. 65, 1485-1505.

1D Solutions λ=0.01

K. T. Chu and M. Z. Bazant. 2005. SIAM J. Appl. Math. 65, 1485-1505.Rubinstein & Zaltzman PRE (2000, 2003, 2005 )

1D Voltage-Current Behavior (fixed geometry & fluid properties)

Dilute

unstable

Fixed Debeye length 0.1

Stable

unstable

Streamlines for λ=.02, k=2.5, V=9.5

x

y

0 1 2 3

Unsteady flow at high voltages

Voltage-Current behavior

ACEO Pumping Geometry

When reactions occur:•Flow occurs for all voltages•Flow occurs in AC and DC case•Flow is not symmetric even when electrodes are

AC

Time averagedflow

ElectrodeElectrode

ACEO: Symmetric Electrodes (DC, λ=0.01, Pe=1000, V=10)

Potential

ChargeDensity

Streamlines

ACEO: Typical Streamlines (DC, λ=0.01, Pe=1000)

V=1 V=5

V=10 V=20Pos.Neg.

Neg.

Neg.

Neg.Pos.

Pos.

Pos.

Reverse the sign on the electrodes (DC, λ=0.01, Pe=1000, V=5)

Pos.

Pos.

Neg.

Neg.

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).