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

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.