文档介绍：5. Axisymmetric Liquid Columns at Rest and
Under Rotation
An axisymmetric liquid surface has the advantage that the capillary equation
reduces to an ordinary differential equation of order two. In the absence of
gravity and rotation its solutions are unduloids or nodoids. The solutions in
the presence of gravity and rotation are easily obtained by a Runge–Kutta
integration. Liquid columns between coaxial circular disks have repeatedly
served as model systems for studying convection during crystal growth. Their
axial deformations can be classified by the number of nodes in the axial direc-
tion, and their lateral deformations by the number of nodes in the azimuthal
direction.
Rotating free liquid drops have repeatedly served as cosmological models,
for example for the formation of the s. Such drops may float freely or
may be positioned by acoustic or ic levitators. In theory, they
may also be supported by coaxial circular disks. By requiring a radial slope
at the disks and by increasing the aspect ratio of the disk separation to the
disk diameter towards infinity, a free drop can be simulated. The instabilities
of liquid columns and of free liquid drops are investigated in this chapter.
Introduction
Since the advent of research under microgravity conditions, there has been
strong interest in the stability of liquid bridges between coaxial circular disks.
This has been motivated by many fundamental problems in fluid physics, on
the one hand, and by numerous applications, on the other hand. Oscillations
of liquid columns may be excited accurately by vibration of the supporting
disks. Various sensors may be integrated into the disks thus allowing quantita-
tive measurements. During the D2 Spacelab mission the resonance frequencies
of liquid bridges were analyzed in situ by means of pressure sensors located
in the center of the supporting disks [Langbein 1991]. Liquid bridges also
are the primary subject of investigations of steady and oscilla