Liquid surface in regular N-pods

The shape of liquid surfaces in regular N-pods in the absence of gravity is considered. A liquid volume in the vertex of a regular N-pod wets the adjacent faces if the sum of the liquid's contact angle gamma with the faces and half the dihedral angle alpha between adjacent faces is smaller than pi/2. A suggestion for why the surface shape in the wedge approaches its cylindrical shape at infinity exponentially:ii is given. The range of this exponential decrease is related to the curvature of the meniscus and the angles alpha and gamma: The decrement of the decrease generally shows a weak dependence on alpha + gamma, predominantly depending on the liquid volume. Extremely close to the wetting limit, when alpha + gamma approaches pi/2, the decrement vanishes. The exponential meniscus shape leads to a similarity relation and allows small relative liquid volumes in polyhedrons to be split up into partial volumes ascribed to the corners and others ascribed to the wedges. The respective relations among volume, curvature, contact angle and corner geometry are obtained by numerical simulation and the limits of applicability are discussed. This greatly simplifies the calculation of liquid surfaces in the limit of small liquid volumes. The results obtained apply to liquid surfaces in a Space environment, e.g. to metallic melts in crucibles and to propellants and other technical fluids in tanks and reservoirs, as well as to liquid surfaces on Earth, e.g., to liquids trapped in polyhedral pores and to liquid foams, provided their characteristic length is sufficiently small compared to the capillary length.