Axisymmetric shapes and stability of isolated charged drops
Axisymmetric equilibrium shapes and stability of isolated charged drops are found by solving simultaneously the Young--Laplace equation for surface shape and the Laplace equation for the electric field. Families of two-, three-, and four-lobed shapes that branch from the trunk family of spheres are treated systematically by means of the Galerkin/finite element method and a tessellation that deforms with the free surface. The results show that at the limit found by Rayleigh in 1882 the spherical family exchanges stability with a family of two-lobed shapes, a transcritically bifurcating family, one arm of which proves to consist of stable shapes. The results are reinforced by those of approximating the stable drop shapes as oblate spheroids. Thus oblate drops carrying charge in excess of the Rayleigh limit ought to be seen in experiments, though none have yet been reported.
- Research Organization:
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
- OSTI ID:
- 6143880
- Journal Information:
- Phys. Fluids A; (United States), Vol. 1:5
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DROPLETS
STABILITY
BOUNDARY CONDITIONS
CHARGE STATE
COORDINATES
DISTURBANCES
ELECTRIC FIELDS
EQUILIBRIUM
FINITE ELEMENT METHOD
GALERKIN-PETROV METHOD
LAPLACE EQUATION
LEGENDRE POLYNOMIALS
SHAPE
SURFACES
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
POLYNOMIALS
640440* - Fluid Physics- Electrohydrodynamics