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Research Papers: Fundamental Issues and Canonical Flows

Dispersion in Electro-Osmotic Flow Through a Slit Channel With Axial Step Changes of Zeta Potential

[+] Author and Article Information
Chiu-On Ng

e-mail: cong@hku.hk

Bo Chen

Department of Mechanical Engineering,
The University of Hong Kong,
Pokfulam Road, Hong Kong

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received November 14, 2012; final manuscript received July 6, 2013; published online August 6, 2013. Assoc. Editor: Prof. Ali Beskok.

J. Fluids Eng 135(10), 101203 (Aug 06, 2013) (8 pages) Paper No: FE-12-1575; doi: 10.1115/1.4024958 History: Received November 14, 2012; Revised July 06, 2013

An analytical study is presented in this paper on hydrodynamic dispersion due to steady electro-osmotic flow (EOF) in a slit microchannel with longitudinal step changes of ζ potential. The channel wall is periodically patterned with alternating stripes of distinct ζ potentials. Existing studies in the literature have considered dispersion in EOF with axial nonuniformity of ζ potential only in the limiting case where the length scale for longitudinal variation is much longer than the cross-sectional dimension of the channel. Hence, the existing theories on EOF dispersion subject to nonuniform charge distributions are all based on the lubrication approximation, by which cross-sectional mixing is ignored. In the present study, the general case where the length of one periodic unit of wall pattern (which involves a step change of ζ potential) is comparable with the channel height, as well as the long-wave limiting case, are investigated. The problem for the hydrodynamic dispersion coefficient is solved numerically in the general case, and analytically in the long-wave lubrication limit. The dispersion coefficient and the plate height are found to have strong, or even nonmonotonic, dependence on the controlling parameters, including the period length of the wall pattern, the area fraction of the EOF-suppressing region, the Debye parameter, the Péclet number, and the ratio of the two ζ potentials.

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Figures

Grahic Jump Location
Fig. 1

Electro-osmotic flow through a slit channel, of which the walls are periodically patterned with alternating stripes of higher ζ potential ζ0 (EOF-supporting region) and lower ζ potential ζs (EOF-suppressing region). The stripes are perpendicular to the principal direction of the flow. The channel height is 2h, and the length of one unit of wall pattern is 2l, where the ratio l/h≥O(1). The EOF-suppressing stripe is of width 2al, where 0≤a≤1 is the area fraction of the suppression region.

Grahic Jump Location
Fig. 2

Dispersion coefficient for uniformly charged walls Xe = D∧T(a = 0), given in Eq. (37), as a function of κ∧

Grahic Jump Location
Fig. 3

Dispersion coefficient D∧T as a function of the period length l∧, for κ∧ = 10, a = 0,0.1,0.3,0.5,0.7,0.9, and (a) ζ∧s = 0, (b) ζ∧s = 0.5. The solid lines are for Pe = 10, while the dashed lines are for Pe = 20. The dotted lines represent the long-wave limits l∧>>1 for the corresponding values of a. The long-wave limits are calculated using the analytical formula given in Eq. (34).

Grahic Jump Location
Fig. 4

Dispersion coefficient D∧T as a function of the area fraction of the EOF-suppressing region 0≤a≤1, for κ∧ = 10,100,1000, Pe = 10, ζ∧s = 0, and (a) l∧ = 1, (c) l∧ = 5, (e) l∧ = ∞. Corresponding plots for the normalized plate height H∧ = 2D∧T/u¯∧ are shown in (b), (d), and (f).

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