Shape and stability of doubly connected axisymmetric free surfaces in a cylindrical container

摘要

The equilibrium and stability of liquid that partially fills a cylindrical container with planar ends are examined. It is assumed that the free surface is axisymmetric and does not cross the symmetry axis of the container. Particular attention in given to the case where gravity is parallel to the cylinder's axis, and where the free surface has one contact line on the lateral cylindrical wall and the other on one of the planar ends. The equilibrium configuration of such a surface is determined by the wetting angle, #alpha#, the Bond number, B, and the relative volume, V, of the annular region bounded by the free surface and the solid container. Shapes of stable and critical surfaces have been analyzed, and the stability regions for arbitrary Bond numbers have been obtained in the #alpha#-V plane. The shape and stability problems for a zero gravity configuration with both contact lines on the lateral wall of the cylinder mare also studied. In addition, the stability of a free surface with at least one contact line coinciding with the edge formed by the lateral wall and a planar end is discussed.