文档介绍：9. Liquid Surfaces in Polyhedral Containers
Corners formed by three or more solid surfaces offer better wall contact to
liquids than do wedges (“wedge” is used here in the same sense as in Chap. 8,
. a wedge-shaped space between solid surfaces). Corners lower the free
energy of wetting liquids more than do wedges. Aliquid volume in a tripod
forms a spherical surface, . no liquid rates into the wedges, if for each
of the three wedges forming the tripod the sum of the dihedral angle and the
contact angles with the adjacent faces exceeds π. The volume and surface area
of such a drop may be calculated by subtracting the three segments outside
the faces from the spherical cap given by the intersection of the sphere with
the wedges.
If the sum of contact angles falls short of π, the liquid drop is sucked into
the wedges owing to the resulting capillary underpressure. Nevertheless, a
surplus volume is left in the corner. Far from the corner, the liquid surface
assumes a cylindrical shape. The corner volume extends into the wedges
exponentially. The surface of a liquid in a polyhedron may thus be pasted
together from cylindrical surfaces in the wedges and surplus volumes piled up
in the corners. The corresponding similarity relation is based on posing
the liquid volume into portions associated with the corners, the wedges and
their intersection at the corners. Although the specific corner volume requires
numerical simulation, this approach has the advantage that this volume has
to be determined only once for a given geometry.
Spherical Surfaces at Edges and Corners
Nonwetting Drops
Aliquid pletely wets a wedge if the sum of the dihedral angle
2α of the wedge and the contact angles γ1 and γ2 of the liquid with the
solid faces 1 and 2 is smaller than π, the sum of the angles in a triangle; see
Sect. and (). The concave shape gives rise to a capillary underpressure,
which sucks the liquid into the wedge. If several wedges are i