Axisymmetric shapes and stability of charged drops in an external electric field
A highly conducting charged drop that is surrounded by a fluid insulator of another density can be levitated by suitably applying a uniform electric field. Axisymmetric equilibrium shapes and stability of the levitated drop are found by solving simultaneously the augmented Young--Laplace equation for surface shape and the Laplace equation for the electric field, together with constraints of fixed drop volume, charge, and center of mass. The means are a method of subdomains, finite element basis functions, and Galerkin's method of weighted residuals, all facilitated by a large-scale computer. Shape families of fixed charge are treated systematically by first-order continuation. Previous analyses by Abbas et al. in 1967 and Abbas and Latham in 1969, in which the shapes of levitated drops are approximated as spheroids, are corrected. The new analysis shows that drops charged to less than the Rayleigh limit lose shape stability at turning points, with respect to external field strength, and that the instability seen in experiments of Doyle et al. in 1964 and others is not a bifurcation to a family of two-lobed shapes, but rather is a related imperfect bifurcation.
- Research Organization:
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
- OSTI ID:
- 6273647
- Journal Information:
- Phys. Fluids A; (United States), Vol. 1:5
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
DROPLETS
STABILITY
BOUNDARY CONDITIONS
CHARGE STATE
COMPUTERS
CONTAINERS
COULOMB FIELD
ELECTRIC FIELDS
ELECTRICAL INSULATORS
ELECTROHYDRODYNAMICS
EQUILIBRIUM
FINITE ELEMENT METHOD
GALERKIN-PETROV METHOD
LAPLACE EQUATION
LEVITATION
NONLINEAR PROBLEMS
SHAPE
SYMMETRY
DIFFERENTIAL EQUATIONS
ELECTRICAL EQUIPMENT
EQUATIONS
EQUIPMENT
FLUID MECHANICS
HYDRODYNAMICS
ITERATIVE METHODS
MECHANICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
640440* - Fluid Physics- Electrohydrodynamics