IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 35, NO. 1, JANUARY/FEBRUARY 1999 231 An Analytical Study of Electrohydrodynamic Induction Pumping of a Stratified Liquid/Vapor Medium Markus Wawzyniak and Jamal Seyed-Yagoobi, Member, IEEE Abstract—An analytical solution for the electrohydrodynamic induction pumping of a stratified liquid/vapor medium is pre- sented. A group of nondimensional parameters is being intro- duced. Four sets of boundary conditions representing four dif- ferent cases are considered. Results for the interfacial velocity as a function of all involved parameters are provided in nondi- mensional form. Nondimensional electric wave angular velocity, liquid height, and conductivity, as well as dielectric constant, are varied over a wide range, and the influences of the various parameters on the interfacial velocity are presented. The results are analyzed and explained from a fundamental point of view. Index Terms—Electrohydrodynamics, interface, pumping, two- phase flow. NOMENCLATURE Constant. Constant. Boundary condition. Electric field strength vector, V/m. Frequency, Hz. Height, m. Imaginary number . Current density, A/m . Wave number 1/m. Normal vector. Charge density, C/m . Surface charge density, C/m . Slip coefficient . Time, s. Velocity of interface in direction, m/s. Velocity vector, m/s. Electric permittivity, F/m. Dielectric constant . Wavelength, m. Kinematic viscosity, m /s. Electric field potential, V. Electric conductivity, S/m. Angular velocity , 1/s. Paper MSDAD 98–23, presented at the 1997 Industry Applications Society Annual Meeting, New Orleans, LA, October 5–9, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electrostatic Processes Committee of the IEEE Industry Applications Society. Manuscript released for publication August 15, 1998. The authors are with the Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123 USA (e-mail: release@tamu.edu; jyagoobi@mengr.tamu.edu). Publisher Item Identifier S 0093-9994(99)00458-2. Subscripts and Superscripts % Liquid height in percent of total height. % Liquid height in percent of total height. Characteristic. Liquid. Synchronous. Total. Vapor. In direction. In direction. Peak value. Time-averaged value. Conjugate complex value. Nondimensional value. I. INTRODUCTION T HE phenomenon of electrohydrodynamic (EHD) pump- ing of fluids has been investigated for some time. The earliest studies dealt with so-called “ion-drag” pumping. When charges are introduced to a liquid by means of local fluid ionization, the charges can be set in motion under the action of an electric field. The moving charges impart momentum to the fluid and set it in motion. This type of EHD pumping requires a net charge in the fluid, which, while having the potential to generate high velocities, may also lead to undesired changes in the fluid properties over time. A different type of EHD pumping which does not rely on a net charge was presented by Melcher in 1966 [1]. This method, called EHD induction pumping, takes advantage of free charges present in a medium as a result of an electric conductivity gradient. Such a gradient will always exist at the interface between two media. It may also be procured by exploiting the electric conductivity dependency on tempera- ture many fluids exhibit [2]–[4]. In any way, a conductivity gradient will lead to charge dissociation and generate an equal number of positive and negative charges, resulting in a net charge of zero. When applying an electric field, these charges will be attracted to locations exhibiting the opposite polarity, or they will be repelled from locations with the same polarity. To produce a net fluid motion, nevertheless, a dc electric field does not suffice. An electric traveling wave, generated at electrodes mounted along the flow passage, must be present. If the fluid is more conductive away from the electrodes, charges are attracted to an oppositely charged electrode. While the charges move toward the electrode, that electrode will 0093–9994/99$10.00  1999 IEEE