Axisymmetric steady flows driven by an electric field about a deformable fluid drop suspended in an immiscible fluid are studied within the framework of the leaky dielectric model. Deformations of the drop and the flow fields are determined by solving the nonlinear free-boundary problem composed of the Navier-Stokes system governing the flow field and Laplace's system governing the electric field. The solutions are obtained by using the Galerkin finite-element method with an elliptic mesh generation scheme. Under conditions of creeping flow and vanishingly small drop deformations, the results of finite-element computations recover the asymptotic results. When drop deformations become noticeable, the asymptotic results are often found to underestimate both the flow intensity and drop deformation. By tracking solution branches in parameter space with an arc-length continuation method, curves in parameter space of the drop deformation parameter D versus the square of the dimensionless field strength E usually exhibit a turning point when E reaches a critical value Ec. Along such a family of drop shapes, steady solutions do not exist for E > Ec. The nonlinear relationship revealed computationally between D and E2 appears to be capable of providing insight into discrepancies reported in the literature between experiments and predictions based on the asymptotic theory. In some special cases with fluid conductivities closely matched, however, drop deformations are found to grow with E2 indefinitely and no critical value Ec is encountered by the corresponding solution branches. For most cases with realistic values of physical properties, the overall electrohydrodynamic behaviour is relatively insensitive to effects of finite-Reynolds-number flow. However, under extreme conditions when fluids of very low viscosities are involved, computational results illustrate a remarkable shape turnaround phenomenon: a drop with oblate deformation at low field strength can evolve into a prolate-like drop shape as the field strength is increased.

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When the ratio of the drop radius to the distance separating any two drops and the relative importance of gravitational to surface forces are both small, the small amplitude oscillations of a drop of one viscous fluid immersed in another fluid are governed by the nonlinear dispersion relation derived by Miller and Scriven (1968). The dispersion relation has been solved numerically to determine the character of oscillations for arbitrary values of drop size, physical properties of the two fluids, and interfacial tension. The new theoretical results determine the range of validity of the low-viscosity approximation of Miller and Scriven, and are also shown to be essential for proper interpretation of many previously reported experimental results. New experimental measurements of natural frequencies of oscillation of water drops falling in 2-ethyl-1 -hexanol, a system having properties characteristic of many others in solvent extraction, agree well with the theoretical predictions when drop radius is smaller than a critical size. The frequencies of oscillations of larger drops are better described by the dispersion relation due to Subramanyam (1969), which accounts for the relative motion of the two phases.

Electrostatic spraying is important in many applications where very fine droplets are desirable. Most electrostatic spraying systems developed to date, however, require that the electrical conductivity of the dispersed fluid is higher than that of the surrounding fluid. This work reports on an experimental investigation of the mechanism for successful electrostatic spraying of a nonconductive fluid into a conductive one. The key role played by the electric stress on the interface between the nonconductive and conductive fluids is evidenced by examining the variations of the emitted drop size, electrical current, and pressure inside the nozzle as functions of the applied voltage, nozzle geometry and distance between the high-voltage nozzle-electrode and the grounded electrode immersed in the surrounding fluid. A comparison of nonconductive-in-conductive and conductive-in-nonconductive spraying systems reveals a difference in behavior that is consistent with the theory of electrohydrodynamics.The use of electrostatic fields to produce fine sprays of liquid droplets from nozzles dates back to as early as 1750 when Abbe Nollet, a professor of physics at Turin and Paris, conducted experiments with an electrified nozzle that was attached to the outlet of a water vessel (Felici, 1959). With the continuation of scientific studies over the years, electrostatic spraying has found many important applications, such as the production of ultrafine powders, electrostatic printing, paint spraying, and crop spraying (Bailey, 1984). Recently developed applications of electrostatic spraying in chemical processing have included the emulsion-phase contactor, which is an electrically-driven solvent extraction device (Scott and Wham, 1989), and the electric dispersion reactor, which is a multiphase reactor capable of efficient production of microreactor droplets . Based on the experience gained from numerous studies, most investigators to date have concluded that electrostatic spraying can be successfully applied only for dispersing relatively high-conductivity fluids into low-conductivity fluids (Bailey, 1986). Electrostatic spraying of nonconductive fluids into conductive fluids has been considered virtually impossible until recent experiments by Sato and coworkers (1979, 1980a,b, 1993). Despite its scientific interest and technological

A hysteresis phenomenon has been revealed through experiments conducted with large-amplitude forced oscillations of pendant drops in air. Under strong excitation, the frequency response of a drop forced at constant amplitude exhibits jump behavior; a larger peak response amplitude ε↓ appears at a lower frequency ω↓ during a downward (↓) variation of forcing frequency than during an upward (↑) variation, viz. ε↓≳ε↑ and ω↓<ω↑. Similar results are obtained when forcing amplitude is varied at constant frequency. This behavior is characteristic of a system with a soft nonlinearity. These findings indicate that oscillating pendant drops constitute a convenient system for studying nonlinear dynamics.