文档介绍：10. Playing with Stability
A liquid drop on a horizontal plane is in a metastable state. Its energy is
independent of its position. In a microgravity environment, this is likewise
true for liquid drops in a spherical container. Apart from these trivial cases,
several container shapes with exotic properties are considered in this chapter.
It is possible to construct cylindrical container shapes (so-called proboscides)
in which liquid surfaces with equal curvatures but different energies and vol-
umes are possible, so that dp/dV = 0. The wedges in these containers are
wetted by a fluid only if the contact angle falls short of a critical contact
angle. However, at infinitesimal fill levels, the capillary underpressure which
causes the fluid to wet the wedges does not diverge towards infinity as for
planar wedges.
It is also possible to construct exotic axisymmetric containers in which
liquid surfaces with equal energies and volumes but different curvatures are
possible, so that dV/dp = 0. This may be achieved either by adjusting the
coating of a cylindrical tube to achieve a particular contact angle variation or
by adjusting the container shape to achieve a constant contact angle. From
the minimum-volume condition, it is clear that the resulting surfaces must
be unstable.
Proboscides
Finite Rhombic Prisms
Let us consider a long rhombic cylinder with acute dihedral angles 2α and
obtuse dihedral angles π− 2α. Let the container be initially filled with fluid
2, and then an immiscible fluid 1 is introduced, displacing fluid 2. Let the
contact angle of fluid 1 with the faces of the cylinder be γ and satisfy
1
α+ γ< π, γ<α. ()
2
In this case, the acute wedges are wetted by fluid 1, whereas the obtuse
wedges are not; see Fig. . Assume further that the contact angle of fluid
1 with the end caps of the vessel is approximately π/2. Fill ports for fluid 1
Dieter Langbein: Capillary Surfaces, STMP 178, 235–258 (2002)
c Springer-Verlag Be