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TECHNICAL PAPERS

# A Theoretical Discussion of a Menisci Micropump Driven by an Electric Field

[+] Author and Article Information
Alexandru Herescu

Michigan Technological University, Houghton, MI 49931

Jeffrey S. Allen1

Michigan Technological University, Houghton, MI 49931jstallen@mtu.edu

The Bond number, Bo, is the ratio of gravitational forces to capillary forces on a static gas–liquid interface. It is defined as $Bo≡ΔρgL2∕σ$, where $Δρ$ is the density difference across the interface, $g$ is the gravitational acceleration, $L$ is the characteristic length scale, and $σ$ is surface tension. If the Bond number is greater than one, then gravitational forces dominate the interface shape resulting in a flat interface which is perpendicular to the direction of the gravitational acceleration. If the Bond number is much less than one, the capillary forces dominate the static interface shape resulting in a meniscus.

1

Corresponding author.

J. Fluids Eng 129(4), 404-411 (Dec 08, 2006) (8 pages) doi:10.1115/1.2710241 History: Received July 31, 2006; Revised December 08, 2006

## Abstract

The potential for miniaturization of analytical devices made possible by advances in micro-fabrication technology is driving demand for reliable micropumps. A wide variety of micropumps exist with many types of actuating mechanisms. One such mechanism is electrohydrodynamic (EHD) forces which rely upon Coulomb forces on free charges and/or polarization forces on induced dipoles within the liquid to induce fluid motion. EHD has been used to pump liquid phases and to displace gas–liquid interfaces for enhanced boiling heat transfer as well as to displace gas/vapor bubbles. A novel concept for using EHD polarization forces to deflect a stationary meniscus in order to compress and pump a gaseous phase is described. The pumping mechanism consists in alternative compression of two gas volumes by continuous deflection of the two pinned menisci of an entrapped liquid slug in an electric field. Using the Maxwell stress relations, the electric field strength necessary to operate the pump is determined. The operational limits are determined by analyzing the stability limits of the two menisci from inertial and viscous standpoints, corroborated with the natural frequencies of the gas–liquid interfaces.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic of EHD Menisci micropump

Figure 2

Parameters and designations of the liquid plug used for the gas compression

Figure 3

Volume displaced by meniscus, ∀A=πa3f(θA)∕3, and static volume, ∀s, of Meniscus A side of the pump

Figure 4

Relation between θA and θB per Eq. 10

Figure 5

Dimensionless electric field stress, τE*, versus contact angle using water for the liquid plug with P0*=35.7 and CR=2 for various specific heat ratios, k

Figure 6

Electric field strength vs meniscus displacement for room temperature water and air as the working fluids. The uncompressed pressure is 100,000Pa, the pump radius is 50μm, and a specific heat ratio of 1.4. Table 1 lists additional parameters, dimensional, and nondimensional, associated with this pressure, radius, and fluid selection.

Figure 7

Relationship between dimensionless power, Γ, and the compression ratio, CR, for various specific heat ratios, k

Figure 8

Comparison of operational limits as a function of liquid column radius. The properties used are for water (ρ=1000kg∕m3, μ=0.001kg∕ms, σ=0.07N∕m) and for normal gravitational acceleration (g=9.81m∕s2). Stable menisci oscillation occurs at frequencies below the limits shown.

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