Axisymmetric shapes and stability of charged drops in an external electric field

Journal Article · Mon May 01 04:00:00 EDT 1989 · Phys. Fluids A; (United States)

DOI:https://doi.org/10.1063/1.857377· OSTI ID:6273647

Basaran, O A; Scriven, L E

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), Journal Name: Phys. Fluids A; (United States) Vol. 1:5; ISSN PFADE
• Country of Publication: United States
• Language: English

Related Subjects

640440* -- Fluid Physics-- Electrohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CHARGE STATE
COMPUTERS
CONTAINERS
COULOMB FIELD
DIFFERENTIAL EQUATIONS
DROPLETS
ELECTRIC FIELDS
ELECTRICAL EQUIPMENT
ELECTRICAL INSULATORS
ELECTROHYDRODYNAMICS
EQUATIONS
EQUILIBRIUM
EQUIPMENT
FINITE ELEMENT METHOD
FLUID MECHANICS
GALERKIN-PETROV METHOD
HYDRODYNAMICS
ITERATIVE METHODS
LAPLACE EQUATION
LEVITATION
MECHANICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
SHAPE
STABILITY
SYMMETRY