Equilibrium and Stability of Uncharged and Charged, Rotating Liquid Drops.
In view of their applications for nuclear physics, meteorology and space experiments, the equilibrium and the stability of rotating liquid drops are investigated. Successively, the cases of an uncharged drop, a homogeneously charged drop, an uncharged conducting drop in an external electric field and a charged conducting drop are considered. The equilibrium can be adequately approximated by a spheroid. The linearised equations of motion are solved by means of a normal mode analysis. A dispersion relation is derived by substituting this solutions in an energy integral, generalised for complex quantities. Criteria for the occurrence of instability and bifurcation are formulated in a general form. For the lowest order harmonics the results of previous investigations are recovered. The influence of higher order harmonics is discussed in detail. It also appears that a small viscosity changes the instability domain drastically. Some analogies with selfgravitating rotating masses are given. The instability of a rotating, uncharged drop with a toroidal shape is also studied. A dispersion relation is derived by means of a series expansion in the aspect ratio. Perturbations, symmetric around the rotation axis, are stable. Contrary, non-axial symmetric perturbations are unstable.
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- Physics: Fluid and Plasma