Electrohydrodynamics of Thin Flowing Films

[+] Author and Article Information
Evan M. Griffing

Department of Chemical and Biomolecular Engineering, North Carolina State University, 911 Partners Way, Raleigh, NC 27695

S. George Bankoff

Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208

Michael J. Miksis

Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208miksis@northwestern.edu

Robert A. Schluter

Department of Physics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208

According to the source Newark Electronics, their “Static-Free” aerosol produces a surface resistance 106108ohms. Using a conservative estimate of the relevant capacitance, 10pF, the relaxation time constant is less than 103s.

J. Fluids Eng 128(2), 276-283 (Sep 03, 2005) (8 pages) doi:10.1115/1.2169811 History: Received May 05, 2004; Revised September 03, 2005

Thin films of oil flowing down a nearly-vertical plate were subjected to a strong normal electrostatic field. Steady-state height profiles were measured by fluorescence imaging. For electrode potentials less than that required to produce an instability, the two-dimensional response of the interface was <1%. Calculations of the fluid height coupled with the electric field solution were identical to uncoupled calculations for electric fields below the stability threshold. Pressure profiles under the film and three-dimensional effects are also discussed.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Gravity-driven flow on a plate with an inclination of β is subjected to an electric field. The field produces an electrostatic tension at the interface, producing a spatially-varying steady state height profile.

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Figure 2

The experimental apparatus used to measure fluid height and pressure profiles, instability potentials, and leak rates

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Figure 3

At the inlet, capillarity produces a meniscus, which causes a greater flow at the edges. This leads to a thicker film and a hump that persists far downstream. A Teflon boundary increased the contact angle, which was shown to decrease the hump size.

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Figure 4

Cross-sectional view of the fluid manometer, which was connected to the back of the inclined plate. A traveling microscope (not shown) was used to measure the meniscus height. In order to obtain consistent results, a receding contact angle and a new manometer was required for each set of measurements.

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Figure 5

An image of the oil film flowing down a vertical plate in front of a glass electrode. The image contrast and brightness have been increased to highlight the features. The contact line is outlined with a white line, and the continuation of the electrode past the image edge is drawn in to indicate size. The parameters were ϕH=25kV, Ĥ=0.0237m, l=0.05m, and K¯=0.0169.

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Figure 6

The experimental pressure profile under a Convoil 20 film for Re=0.25, ϕH=25kV, Ĥ=0.0237m, and l=0.05m is compared to the pressure exerted by the electric field on the fluid surface. Both dimensional and dimensionless pressures are shown. The x axis is dimensionless, to show the position of the electrode which spans the region −0.5<x<0.5. The experimental pressure is very close to that which would be exerted on the surface of a conducting film, probably owing to deformation of field lines within the cavity.

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Figure 7

The experimental height profiles as a function of Reynolds number for K¯=1.69×10−2. Both h and x are dimensionless. The electrode extends from −0.5<x<0.5. There is a small decrease in amplitude under the full electrode length as the Reynolds number is increased. This would be expected to be negligible for Re>100, as in ELFR design calculations based on liquid metals, provided that Re<ReC. C¯ is specified by Re and the physical properties of oil, and is C¯=[2.99×104, 2.47×104, 2.25×104, 2.917×104].

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Figure 8

Contact line at the edge of the oil flow: The electric field causes a contraction in the flow width, which is asymmetric about x=0. The flow contraction increases with K¯ for the small Reynolds number, Re=0.07 and large capillary number C¯=2.99×104. The parameters x and z are both scaled by 0.05m. Additional experimental parameters are: Ĥ=0.0237m, l=0.05m, and ϕH=[5,10,15,20,25,30]kV.

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Figure 9

Contact line at the edge of the oil flow: Increasing the Reynolds number decreases the magnitude of the film contraction for the given electric field F=1055kV∕m, which corresponds to K¯=1.69×10−2. The parameters x and z are both scaled by 0.05m. Additional experimental parameters are: Ĥ=0.0237m, l=0.05m, ϕH=25kV, and C¯=[2.99×104, 2.47×104, 2.25×104, 2.917×104]. If Re is increased by a factor of 1000, as in the proposed ELFR, this effect should be negligible.

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Figure 10

A dielectric oil flows under a charged electrode, which spans −0.5<x<0.5. The parameters x and z are both scaled by 0.05m. For high values of the field, a peak forms under the trailing edge of the electrode, and a transverse instability develops. The change in h between each contour line is 0.017. (a) For low values of the electric field, the fluid passes through undisturbed. (b)–(d) For larger field strength, the hump at the fluid edge increases in height.

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Figure 11

The experimental height profile at Reynolds number 0.16 is compared to the steady-state solution of the lubrication equation. The x axis is dimensionless, so that the electrode spans from −0.5<x<0.5. There is a decrease in amplitude of the experimentally-measured standing wave as the Reynolds number is increased. The electric field number is K¯=1.69×10−2.

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Figure 12

The maximum height in the peak under the trailing edge of the electrode for coupled and uncoupled solutions. Parameters of the Convoil 20 film were used. The electrode parameters were l=0.08m, Ĥ=0.00326, 0.00576, 0.01076m. The fluid parameters were Re=0.07, C¯=3.0×104.

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Figure 13

An uncoupled calculation of the steady-state profile under an electrode of l=0.08m, Ĥ=0.00326m, and ϕH=5kV. The physical properties of Convoil 20 are used, except for the dielectric constant; we assume that the fluid is an electrical conductor (ϵf=∞). The flow is specified by Re=0.16, and the electric field number is K¯=0.038.

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Figure 14

Coupled and uncoupled calculations of the steady-state profile under an electrode of l=0.08m, Ĥ=0.00326m, and ϕH=3.5kV. Physical properties of Convoil 20 are used, except for the surface tension and conductivity; surface tension values of 0.032N∕m(a) and 0.32N∕m(b) were used, and the fluid was assumed to be a conductor (ϵf=∞). The dimensionless parameters were Re=0.16, K¯=0.0186, and C¯=1.23×105(a) and C¯=1.23×104(b).



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