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TECHNICAL PAPERS

Streaming Electric Potential in Pressure-Driven Flows Through Reservoir-Connected Microchannels

[+] Author and Article Information
S. A. Mirbozorgi

Mechanical Engineering Department, University of Birjand, Birjand 97175–376, Iran

H. Niazmand

Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad 91775–1111, Iran

M. Renksizbulut1

Mechanical and Mechatronics Engineering Department, University of Waterloo, Waterloo, ON, N2L 3G1, Canadametin@uwaterloo.ca

1

Corresponding author.

J. Fluids Eng. 129(10), 1346-1357 (May 16, 2007) (12 pages) doi:10.1115/1.2776967 History: Received August 28, 2006; Revised May 16, 2007

Electrical power generation employing pressure-driven flows is a fundamental problem in microfluidics. In the present work, analytical and numerical analyses are performed to study the interplaying effects of electrolyte motion with the associated electrical current in a flat microchannel with and without fluid reservoirs. The modified Navier–Stokes equations as well as a Poisson equation for the distribution of electric potential and the Nernst–Planck equations for the distribution of charge densities are solved for the steady flow of a Newtonian liquid. The results show that for a pressure-driven flow, an electric potential is induced due to the motion of charged particles, which increases linearly along the microchannel. This streaming potential generates an opposing conduction current in the core region of the channel as well as in the immediate vicinity of the walls, where the streaming current is negligible. The streaming potential varies in a nonlinear manner with the zeta potential at the walls such that a maximum potential exists at a certain zeta potential. The maximum potential is also observed to increase with both the applied pressure difference and the electric double layer thickness in the range studied. The presence of reservoirs adds significant complexity to this electrokinetic flow.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow geometry and coordinates

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Figure 2

Typical numerical mesh and grid expansion ratios. For clarity, a coarse grid is shown with smaller reservoirs.

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Figure 3

Velocity profiles at midchannel (x=L∕2) for different grid sizes and expansion ratios for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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Figure 4

Distribution of midplane (y=H∕2) electric potential along the channel for Re=1, k=20, ΔP=80, and L=10

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Figure 5

Velocity profiles at midchannel (x=L∕2) for Re=1, k=20, ΔP=80, L=10, and ζ*=0, −50, −100mV

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Figure 6

Cross-sectional variation of electric current components at midchannel (x=L∕2) for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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Figure 7

Nondimensional induced electric field strength as a function of zeta potential for Re=1, ΔP=80, L=10, and k=10,20,40

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Figure 8

Cross-section averaged electrical conductivity and streaming current density as a function of zeta potential for Re=1, k=20, ΔP=80, and L=10

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Figure 9

Induced electric potential as a function of zeta potential for k=20, ΔP=80, L=10, and Re=0.5,0.7,1,1.5

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Figure 10

Induced electric potential as a function of applied pressure difference for k=20, L=10, and ζ*=−25, −50, −75, −100mV

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Figure 11

Numerical results for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10: (a) pressure contours and (b) streamlines

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Figure 12

Comparison of midplane (y=H∕2) pressure distributions along the channel for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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Figure 13

Comparison of axial velocity profiles at midchannel (x=L∕2) for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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Figure 14

Numerical results for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10: (a) electric current lines, (b) induced electric potential contours, (c) magnified view of current lines at the channel inlet region, and (d) magnified view of current lines at the channel outlet region

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Figure 15

Axial variation of midplane (y=H∕2) and wall electric potentials for Re=1, k=20, ζ*=−25, −50, −75mV, ΔP=80, and L=10

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Figure 16

Net charge density counters at the channel (a) inlet and (b) outlet for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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Figure 17

Axial variation of midplane (y=H∕2) net charge density for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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Figure 18

Axial variation of cross-section averaged electric current density components for Re=1, k=20, ζ*=−50mV, ΔP=80, and L=10

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