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Research Papers: Fundamental Issues and Canonical Flows

Analytical Prediction of Flow Field in Magnetohydrodynamic-Based Microfluidic Devices

[+] Author and Article Information
Hussameddine S. Kabbani

Department of Mechanical Engineering, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4027

Martin J. Mack

Department of Civil and Environmental Engineering, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4027

Sang W. Joo

School of Mechanical Engineering, Yeungnam University, Gyongson 712-749, Republic of Korea

Shizhi Qian1

Department of Aerospace Engineering, Old Dominion University, Norfolk, VA 23529-0247sqian@odu.edu

www.mathworks.com

www.femlab.com

1

Corresponding author.

J. Fluids Eng 130(9), 091204 (Aug 13, 2008) (6 pages) doi:10.1115/1.2953302 History: Received January 03, 2008; Revised March 27, 2008; Published August 13, 2008

A new approximate solution for the velocity profile of steady incompressible magnetohydrodynamic (MHD) flows in a rectangular microchannel driven by the Lorentz force is proposed. Mean velocity and mass flow rate in a channel, subsequently derived, can be used efficiently for many MHD-based microfluidic applications, including the design of a MHD-based microfluidic network without resorting to costly full-scale computational fluid dynamics. The closed-form solutions, provided for both direct-current (dc) and alternating-current (ac) electric and magnetic fields, are in simple forms, without any series or functions to evaluate, and so can be readily used for inverse or control problems associated with MHD-based lab-on-a-chip (LOC) devices. Extensive comparisons with previous analytical, computational, and experimental results are performed, and summarized in the present study. The proposed solutions are shown to agree better with existing experimental and computational reports than previous approximations and are to be used in a broad range of MHD-based LOC applications with both dc and ac fields with required accuracy.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the MHD flow through a microchannel with height H, width W, and length L. An electric current (or a potential difference) is applied to two planar electrodes deposited along the opposing walls of the channel. The length and height of the planar electrodes are, respectively, LE and H. The electric current density J and magnetic field B are act, respectively, in the y- and z-directions.

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Figure 2

The volumetric flow rate versus the Lorentz force per unit length (F=IB) for aspect ratios (a) 0.475 and (b) 1.5. The solid line, triangles, dashed line, and dash-dotted line represent, respectively, the results from full numerical simulation, the present closed-form solution, the approximation by Lemoff and Lee (10), and the approximation by Kabbani (9).

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Figure 3

Comparisons with the experimental data obtained by Ho (5). (a) Flow rate versus channel width; (b) average velocity versus current applied. The solid line and the triangles represent, respectively, the results obtained from the present closed-form solution and the experimental data obtained from Ho (5).

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Figure 4

Schematic diagram of the MHD microfluidic network of Bau (4)

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Figure 5

(a) Schematic diagram of the closed microloop of Affanni and Chiorboli (1). (b) Pressure variations along the centerline of the loop. The solid line and triangles represent, respectively, the prediction from the present closed-form solution and numerical solution of full systems 1,2.

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Figure 6

The time-averaged velocity ⟨U¯⟩ as a function of the phase angle. The solid line and the triangles represent, respectively, the result obtained from the present closed-form solution and the experimental data obtained from Lemoff and Lee (10).

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