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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.

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Motivation: ACEO & ICEO Advantages over DC Low voltage, portable (~1 – 10 volts) Good flow rates (~mm/s) Green et al PRE 2000, 2002 Ajdari PRE 2000 Brown PRE 2000 Bazant & Squires JFM 2004 Olesen et al PRE 2005 Positive Electrode Negative Electrode Soni, Squires, Meinhart, BC00004 Swaminathan, Hu FC00003 Yossifon, Frankel, Miloh, GC00007 ++++++++++++++++++++++++ ----------------------------------- Electric Field Negative Ions Positive Ions Flow

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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.

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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

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A simpler system to study body forces reactions at electrodes Binary, symmetric electrolyte R. F. Probstein. 1994. Physicochemical Hydrodynamics. Wiley. current

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Bulk equations (symmetric, binary, dilute electrolyte): Voltage scaled thermal voltage (25 mV) λ = 0.1 to0.0001 Pe = 100 to 1,000,000 Small device Large device Dilute High Concentration

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boundary conditions at electrodes: - fixed voltage difference - No slip - reactions periodic boundary conditions in x Butler-Volmer reaction kinetics: Boundary conditions

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K. T. Chu and M. Z. Bazant. 2005. SIAM J. Appl. Math. 65, 1485-1505. 1D Solutions λ=0.01

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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

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Fixed Debeye length 0.1 Stable unstable

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Streamlines for λ=.02, k=2.5, V=9.5 0 1 2 3

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Unsteady flow at high voltages

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Voltage-Current behavior

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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 averaged flow Electrode

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ACEO: Symmetric Electrodes (DC, λ=0.01, Pe=1000, V=10) Potential Charge Density Streamlines

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ACEO: Typical Streamlines (DC, λ=0.01, Pe=1000) V=1 V=5 V=10 V=20 Pos. Neg. Pos.

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

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Frequency response ( AC, λ=0.05 Pe=1000 ) Olesen et al. PRE 2005.

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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.

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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).

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