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TECHNICAL PAPERS

# Electro-Osmotic Flow in Reservoir-Connected Flat Microchannels With Non-Uniform Zeta Potential

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

Mechanical Engineering Department, Ferdowsi University, Mashhad, Iran

H. Niazmand

Mechanical Engineering Department, Ferdowsi University, Mashhad, Iran and Mechanical Engineering Department, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

M. Renksizbulut

Mechanical Engineering Department, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1metin@uwaterloo.ca

J. Fluids Eng 128(6), 1133-1143 (Mar 24, 2006) (11 pages) doi:10.1115/1.2353261 History: Received February 09, 2006; Revised March 24, 2006

## Abstract

The effects of non-uniform zeta potentials on electro-osmotic flows in flat microchannels have been investigated with particular attention to reservoir effects. The governing equations, which consist of a Laplace equation for the distribution of external electric potential, a Poisson equation for the distribution of electric double layer potential, the Nernst-Planck equation for the distribution of charge density, and modified Navier-Stokes equations for the flow field are solved numerically for an incompressible steady flow of a Newtonian fluid using the finite-volume method. For the validation of the numerical scheme, the key features of an ideal electro-osmotic flow with uniform zeta potential have been compared with analytical solutions for the ionic concentration, electric potential, pressure, and velocity fields. When reservoirs are included in the analysis, an adverse pressure gradient is induced in the channel due to entrance and exit effects even when the reservoirs are at the same pressure. Non-uniform zeta potentials lead to complex flow fields, which are examined in detail.

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## Figures

Figure 4

(a) Velocity, and (b) pressure distributions in an ideal EOF with Re=0.02, ζ=−25mV, k=15, k=32, and k=100

Figure 1

Electro-osmotic flow between parallel plates with two identical reservoirs

Figure 2

A typical algebraically generated mesh

Figure 3

(a) EDL potential, and (b) the ionic concentrations n+ and n− distributions for an ideal EOF with Re=0.02, ζ=−25mV, k=15, k=32, and k=100

Figure 5

The effect of grid size on the velocity profile in an ideal EOF with Re=0.02, ζ=−25mV, k=32, L∕H=5 and Fy=1.02

Figure 6

EOF with constant zeta potential at micro-channel walls; ζ=−50mV, L∕H=10, Re=0.02, and k=32

Figure 7

EOF with constant zeta potential at micro-channel walls; ζ=−50mV, L∕H=10, Re=0.02, and k=32

Figure 8

Pressure distribution on the center plane of a microchannel between two identical reservoirs. EOF with ζ=−50mV, Re=0.02, k=32; (a)L∕H=10, (b)L∕H=30, (c)L∕H=60, (d)L∕H=100.

Figure 9

EOF with a linear change in zeta potential. L∕H=10, Re=0.02, k=32; (a) velocity vectors, (b) velocity and pressure distributions on center plane.

Figure 10

Comparison of terms in the momentum balance for the case described in Fig. 9

Figure 11

EOF with a linear change in zeta potential. L∕H=10, Re=0.02, k=32; (a) velocity vectors, (b) velocity and pressure distributions on center plane.

Figure 12

Comparison of terms in the momentum balance for the case described in Fig. 1

Figure 13

EOF with a parabolic change in zeta potential. L∕H=10, Re=0.02, k=32; (a) velocity vectors, (b) velocity and pressure distributions on center plane.

Figure 14

Comparison of terms in the momentum balance for the case described in Fig. 1

Figure 15

EOF with a patchy distribution of zeta potential such that ζ=−100mV in the patch zone and zero elsewhere. L∕H=10, Re=0.02, k=32; (a) velocity vectors, (b) streamlines, (c) pressure distribution on center plane.

Figure 16

EOF with a patchy distribution of zeta potential such that ζ=−100mV on patches and zero elsewhere. L∕H=10, Re=0.02, k=32; (a) velocity vectors, (b) streamlines, (c) pressure distribution on center plane.

Figure 17

EOF with a patchy distribution of zeta potential such that ζ=−100mV on patches and −25mV elsewhere. L∕H=10, Re=0.02, k=32; (a) velocity vectors, (b) streamlines, (c) pressure distribution on center plane.

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