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

The equilibrium and stability of a liquid that partially fills a cylindrica l container with planar ends are examined. It is assumed that the free surf ace is axisymmetric and does not cross the symmetry axis of the container. Particular attention is given to the case where gravity is parallel to the cylinder's axis, and where the free surface has one contact line on the lat eral cylindrical wall and the other on one of the planar ends. The equilibr ium configuration of such a surface is determined by the wetting angle, alp ha, the Bond number, B, and the relative volume, V, of the annular region b ounded by the free surface and the solid container. Shapes of stable and cr itical surfaces have been analyzed, and the stability regions for arbitrary Bond numbers have been obtained in the alpha-V plane. The shape and stabil ity problems for a zero gravity configuration with both contact lines on th e lateral wall of the cylinder are 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. (C) 1999 American Institute of Physics. [S1070-6631(99)00812-0].