On the Stability of Rotating Drops

作者：A. K. Nurse, Sam R. Coriell, Geoffrey B. McFadden · 发表于：Journal of Research of the National Institute of Standards and Technology · 年份：2015 · DOI：10.6028/jres.120.007 · 被引用次数：15 · 研究领域：Fluid Dynamics and Heat Transfer、Electrohydrodynamics and Fluid Dynamics、Surface Modification and Superhydrophobicity

We consider the equilibrium and stability of rotating axisymmetric fluid drops by appealing to a variational principle that characterizes the equilibria as stationary states of a functional containing surface energy and rotational energy contributions, augmented by a volume constraint. The linear stability of a drop is determined by solving the eigenvalue problem associated with the second variation of the energy functional. We compute equilibria corresponding to both oblate and prolate shapes, as well as toroidal shapes, and track their evolution with rotation rate. The stability results are obtained for two cases: (i) a prescribed rotational rate of the system ("driven drops"), or (ii) a prescribed angular momentum ("isolated drops"). For families of axisymmetric drops instabilities may occur for either axisymmetric or non-axisymmetric perturbations; the latter correspond to bifurcation points where non-axisymmetric shapes are possible. We employ an angle-arc length formulation of the problem which allows the computation of equilibrium shapes that are not single-valued in spherical coordinates. We are able to illustrate the transition from spheroidal drops with a strong indentation on the rotation axis to toroidal drops that do not extend to the rotation axis. Toroidal drops with a large aspect ratio (major radius to minor radius) are subject to azimuthal instabilities with higher mode numbers that are analogous to the Rayleigh instability of a cylindrical interface. Prolat...