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Research Papers: Fundamental Issues and Canonical Flows

Exact Solution of AC Electro-Osmotic Flow in a Microannulus

[+] Author and Article Information
Ali Jabari Moghadam

Assistant Professor of Mechanical Engineering
Department of Mechanical Engineering,
Shahrood University of Technology,
Shahrood, Iran
e-mail: jm.ali.project@gmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received January 24, 2013; final manuscript received April 4, 2013; published online June 6, 2013. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 135(9), 091201 (Jun 06, 2013) (10 pages) Paper No: FE-13-1049; doi: 10.1115/1.4024205 History: Received January 24, 2013; Revised April 04, 2013

The time-periodic electro-osmotic flow in a microannulus is investigated based on the linearized Poisson–Boltzmann equation. An exact solution of the velocity distribution is obtained by using the Green's function approach. The influences of the geometric radius ratio, the wall ζ potential ratio, the electrokinetic radius, and the dimensionless frequency on velocity profiles are presented. Variations of the geometric radius ratio (between zero and one) can lead to quite different flow behaviors. The wall ζ potential ratio affects the magnitude and direction of the velocity profiles within the electric double layer near the two walls of a microannulus. Depending on the frequency and the geometric radius ratio, the walls identically and/or oppositely charged, both may result in the two-opposite-direction flow in the annulus. For high frequency, the electro-osmotic velocity variations are restricted mainly within a thin layer near the two cylindrical walls. Increasing the electrokinetic radius leads to decrease the electric double layer thickness as well as the maximum velocity near the walls.

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Figures

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Fig. 1

The annulus geometry

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Fig. 3

Steady-state time-periodic nondimensional velocity profiles with α = 0.5, χ = 500, and Ω = 30 for one period (0 < Ωθ ≤ 2π) of the sinusoidal waveform at (a) β = 1, (b) β = 0.5, (c) β = 0, and (d) β = −1

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Fig. 4

Steady-state time-periodic nondimensional velocity profiles with α = 0.5, χ = 500, and Ω = 300 for one period (0 < Ωθ ≤ 2π) of the sinusoidal waveform at (a) β = 1, (b) β = 0.5, (c) β = 0, and (d) β = −1

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Fig. 5

Steady-state time-periodic nondimensional velocity profiles with α = 0.5, χ = 500, and Ω = 3000 for one period (0 < Ωθ ≤ 2π) of the sinusoidal waveform at (a) β = 1, (b) β = 0.5, (c) β = 0, and (d) β = −1

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Fig. 6

Steady-state time-periodic nondimensional velocity profiles with α = 0.5, χ = 1000, and Ω = 3000 for one period (0 < Ωθ ≤ 2π) of the sinusoidal waveform at (a) β = 1, (b) β = 0.5, (c) β = 0, and (d) β = −1

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Fig. 7

Steady-state time-periodic nondimensional velocity profiles with χ = 1000 and Ω = 300 for one period (0 < Ωθ ≤ 2π) of the sinusoidal waveform at (a) α = 0.5, β = 1, (b) α = 0.5, β = −1, (c) α = 0.8, β = 1, and (d) α = 0.8, β = −1

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Fig. 8

Transient stage nondimensional velocity of the annulus midpoint with χ = 500 and three various values of β for impulsively started flows of the sinusoidal waveform at (a) α = 0.5, Ω = 30, (b) α = 0.5, Ω = 300, (c) α = 0.8, Ω = 30, and (d) α = 0.8, Ω = 300

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Fig. 9

Near-wall nondimensional velocity profiles for α = 0.5, χ = 500, Ω = 3000, and β = 1 adjacent to (a) the inner cylinder and (b) the outer cylinder

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Fig. 2

Dimensionless potential distributions at two different values of χ for Z0 = 0.5, α = 0.5, and (a) β = 1 and (b) β = −1

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