A study of free surface electrohydrodynamics
Abstract
Free-surface electrohydrodynamics (EHD) is a complex phenomena that is difficult to describe, explain, and predict. An analytical and numerical study is performed to assist in the understanding of free-surface EHD (background material is included). Rayleigh-type critical charge relationships are derived for spherical droplets of perfect and imperfect insulative liquids. Also, mathematical models and a simulator are developed to analyze free-surface EHD in two dimensions. Several configurations are investigated with the simulator. Analytical results indicate that if charge is uniformly dispersed throughout a spherical droplet of perfectly insulating fluid, breakup is possible. If the dielectric constant of the liquid is approximately equal to that of the surrounding air, the charge limit is approximately 10% less than that of a conducting fluid. If ionizable impurities are in the fluid but no transfer of charge occurs between the electrode and the fluid, breakup can still occur. If the liquid's dielectric constant is large, the total charge on the electrode is not much different from the Rayleigh number. A unique donor-cell method was developed to approximate the charge flow equation, properly conserving charge in each cell. A pseudo-surface charge method was also developed. The results were shown to be good for low curvature, simple geometries. Simulation results indicate that the effects of inertia can be substantial in the rise of dielectrophoretic fluid between two electrified plates. The initial stages of the radial breakup of a charged conducting fluid cylinder consisted of wave-like oscillations along the surface. The shape of an insulating jet from a nozzle was seen to be highly dependent on the electric field configuration. In the initial formation of a conducting jet, a 10% increase in applied voltage resulted in about a 10% increase in fluid velocity. The "width" of the jet increased with increasing viscosity. Variation in the applied voltage did not influence the shape of the jet at a fixed reference location. A set of time sequential graphs illustrated the fascinating formation and breakup of an electrified jet.
Degree
Ph.D.
Advisors
Weeks, Purdue University.
Subject Area
Electrical engineering|Mechanical engineering|Fluid dynamics|Gases
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