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Research Papers: Flows in Complex Systems

Unsteady Electrokinetic Flow in a Microcapillary: Effects of Periodic Excitation and Geometry

[+] Author and Article Information
Ali Jabari Moghadam

Faculty of Mechanical Engineering,
Shahrood University of Technology,
Shahrood 3619995161, 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 December 7, 2018; final manuscript received March 22, 2019; published online May 8, 2019. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 141(11), 111104 (May 08, 2019) (13 pages) Paper No: FE-18-1810; doi: 10.1115/1.4043337 History: Received December 07, 2018; Revised March 22, 2019

Oscillatory electrokinetic flow is numerically examined in a rectangular annulus microtube under the influence of various wave forms. When the inner and outer walls of the capillary are oppositely charged, an instantaneous two-direction flow field is produced and consequently the resultant flow rate is relatively reduced. A zero or negative flow rate may be achieved by appropriate design of the channel geometrical characteristics (e.g., hydraulic diameter) as well as the walls charges. In the case of sufficiently low kinematic viscosity and/or high excitation frequency, a relatively thin transient frictional layer is established close to the walls while the bulk fluid lags behind the liquid motion in the electric double layer by a phase shift. If different waveforms are combined together, fascinating outcomes can be obtained depending on the frequency of each individual wave. Applied electric fields with equal- and unequal-frequency combined waves may have the advantages of a double velocity field and a net mass flow rate, respectively. Interestingly, a direct flow pattern may be achieved by appropriately combining various waveforms with unequal frequencies. The mass flow rate decreases, with the constancy of the electrokinetic diameter, with approximately the square of hydraulic diameter. The Poiseuille number exhibits various characteristics depending on the excitation frequency as well as the type of wave especially in combination.

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Figures

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Fig. 1

Cross-sectional area of the microchannel

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Fig. 2

Various excitation waveforms over a period (0≤Ωθ≤2π): (a) square, (b) triangular, (c) combined (Ω1=Ω2), (d) combined (Ω1<Ω2), and (e) combined (Ω1>Ω2)

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Fig. 3

Velocity profiles over a period for (a) and (b) square, (c) and (d) triangular, and (e) and (f) combined waveforms

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Fig. 4

Velocity profiles over a period for various waveforms in combination

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Fig. 5

Variations of Q (for Dh=1) with time for (a) square, (b) triangular, (c) equal-frequency combined, and (d) unequal-frequency combined waves

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Fig. 6

(a), (b) Time variations of Q for Dh=0.9294 using square and triangular waveforms, respectively and (c), (d) time variations of Q for Dh=1 and various β values using unequal-frequency combined waves

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Fig. 7

Variations of Po with time for (a) square, (b) triangular, (c) equal-frequency combined, and (d) unequal-frequency combined waveforms

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Fig. 8

Poiseuille number over a steady period for (a) square, (b) triangular, (c) equal-frequency combined, and (d) unequal-frequency combined waveforms

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Fig. 9

Variations of velocity of representative points with time for (a) square, (b) triangular, and (c) equal-frequency combined waveforms

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Fig. 10

Effect of unequal-frequency combined waveform on transient velocities of representative points

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