文档介绍：4. Stability Criteria
The capillary equation is the Euler–Lagrange equation resulting from min-
imizing the energy of the liquid under the constraints of constant liquid
volume, constant angular momentum, constant frequency of rotation, etc.
A solution of the capillary equation, however, is not automatically stable.
One may have reached a saddle point or even a maximum of the energy in-
stead. Around an extremum, the energy of the liquid can be represented by
a quadratic form in the coordinates, which may be transformed to its princi-
pal axes. If all eigenvalues of this transformation are positive, the surface is
stable.
A simpler, sufficient but not necessary, stability criterion is the minimum-
volume condition. If, within a family of solutions of the capillary equation, the
liquid volume exhibits an extremum as a function of the capillary pressure,
an instability has been reached. If the volume is plotted versus the pressure
or another independent parameter, the stability limits are easily shown up.
A further effective method of studying stability limits relies on intuition to-
gether with experimental evidence. One may simply guess the most critical
deformation and check its relevance by linear stability analysis.
Stability of Capillary Surfaces
Capillary instability of liquid surfaces is an everyday experience. The best-
known example is the free liquid jet. Water flowing from a garden hose or from
a tap in the kitchen breaks after a while into droplets, see Fig.
other hand, honey running down from a spoon does not seem to break. This
obviously is a matter of viscosity and time. The surface tension attempts to
reduce the total surface area of the liquid but has to work against the inertia
and viscosity of the liquid. Any gain in energy due to a surface deformation
is used up primarily by acceleration of the liquid, . it turns into ic
energy. The characteristic time of acceleration is given by the ratio of the
mass of t