Shapes, stability, and hysteresis of rotating and charged axisymmetric drops in a vacuum

J T Holgate,M Coppins

doi:10.1063/1.5023437

Abstract

The behavior of rotating and/or charged drops is a classic problem in fluid mechanics with a multitude of industrial applications. Theoretical studies of such liquid drops have also provided important insights into fundamental physical processes across nuclear and astrophysical lengthscales. However, the full nonlinear dynamics of these drops are only just beginning to be uncovered by experiments. These nonlinear effects are manifest in the high sensitivity of the breakup mechanisms to small perturbations of the initial drop shape and in observations of hysteresis in the transition between different drop shape families. This paper investigates the equilibrium shapes and stability of charged and rotating drops in a vacuum with an energy minimization method applied to spheroidal shapes and with numerical simulations using a finite-difference, level-set method. A good working formula for the stability limit of these drops is given by Lmax = 1.15 − 0.59x − 0.56x2, where L is the dimensionless angular momentum and x is the charge fissility parameter. These methods also provide a firm explanation for the hysteresis of rotating and charged drops.

Highlights

This paper investigates the equilibrium shapes and stability of charged and rotating drops in a vacuum with an energy minimization method applied to spheroidal shapes and with numerical simulations using a finite-difference, level-set method
A good working formula for the stability limit of these drops is given by Lmax = 1.15 − 0.59x − 0.56x2, where L is the dimensionless angular momentum and x is the charge fissility parameter
This paper has described the development of a spheroid energy minimization method and complementary simulations using the finite-difference, level-set (FDLS) method

Summary

Introduction

The first studies of the stability of liquid surfaces under electrostatic forces can be traced back to before 1600 when Gilbert described 89) “the case of a spherical drop of water standing on a dry surface; for a piece of amber applied to it at a suitable distance pulls the nearest parts out of their position and draws it up into a cone.”. Liquid drop models have subsequently been used to model phenomena across a vast range of lengthscales: from the fission of atomic nuclei to the shapes of astrophysical bodies.. An irresistible link between these lengthscales is made by noting the similarity of the electrostatic self-repulsion of a uniformly charged drop to the gravitational attraction of an astrophysical body; the equations describing these objects differ only by a scale factor and a single minus sign..

Methods

Results

Conclusion