The Taylor Melcher Leaky Dielectric Model

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Annu. Rev. Fluid Mech. 1997. 29:27–64 Copyright c 1997 by Annual Reviews Inc. All rights reserved

ELECTROHYDRODYNAMICS: The Taylor-Melcher Leaky Dielectric Model Annu. Rev. Fluid Mech. 1997.29:27-64. Downloaded from www.annualreviews.org by Brown University on 08/07/11. For personal use only.

D. A. Saville
Department of Chemical Engineering, Princeton University Princeton, New Jersey 08544 KEY WORDS: electrified drops and jets, suspensions, interface charge, bulk charge

ABSTRACT
Electrohydrodynamics deals with fluid motion induced by electric fields. In the mid 1960s GI Taylor introduced the leaky dielectric model to explain the behavior of droplets deformed by a steady field, and JR Melcher used it extensively to develop electrohydrodynamics. This review deals with the foundations of the leaky dielectric model and experimental tests designed to probe its usefulness. Although the early experimental studies supported the qualitative features of the model, quantitative agreement was poor. Recent studies are in better agreement with the theory. Even though the model was originally intended to deal with sharp interfaces, contemporary studies with suspensions also agree with the theory. Clearly the leaky dielectric model is more general than originally envisioned.

INTRODUCTION
The earliest record of an electrohydrodynamic experiment is in William Gilbert’s seventeenth century treatise de Magnete, which describes the formation of a conical shape upon bringing a charged rod above a sessile drop (Taylor 1969). Nineteenth-century studies of drop dynamics revealed how radially directed forces stemming from interfacial charge offset surface tension (Rayleigh 1882), but until the 1960s most work focused on the behavior of perfect conductors, (mercury or water) or perfect dielectrics (apolar liquids such as benzene). This began to change following studies on poorly conducting liquids—leaky dielectrics—by Allan & Mason (1962). Another branch of electrohydrodynamics, electrokinetics, deals with the behavior of charged particles in aqueous electrolytes (Saville 1977, Russel et al 1989). However, there are significant differences between the behavior of electrolytes and leaky dielectrics. In electrolytes, electrokinetic phenomena are dominated by effects of interface 27 0066-4189/97/0115-0027$08.00

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charge derived from covalently bound ionizable groups or ion adsorption. Near a surface charged in this fashion, a diffuse charge cloud forms as electrolyte ions of opposite charge are attracted toward the interface. A concentration gradient forms so that diffusion balances electromigration. Then, when a field is imposed, processes in this diffuse layer govern the mechanics. In electrokinetics, applied field strengths are small, a few volts per centimeter, whereas in electrohydrodynamics the fields are usually much larger. With perfect conductors, perfect dielectrics, or leaky dielectrics, diffuse layers associated with equilibrium charge are usually absent. Accordingly, development of the two subjects proceeded more or less independently. Nevertheless, the underlying processes share many characteristics. Most obvious is that electric charge and current originate with ions; therefore, charge may be induced in poorly conducting liquids even though equilibrium charge is absent. The different treatments began to merge with the appearance of Taylor’s 1966 paper on drop deformation and Melcher & Taylor’s review of the topic (1969). Applications of electrohydrodynamics (EHD) abound: spraying, the dispersion of one liquid in another, coalescence, ink jet printing, boiling, augmentation of heat and mass transfer, fluidized bed stabilization, pumping, and polymer dispersion are but a few. Some applications of EHD are striking. For example, EHD forces have been used to simulate the earth’s gravitational field during convection experiments carried out during a space shuttle flight (Hart et al 1986). In this application, combining a...
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