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Mean curvature of liquid surfaces in cylindrical containers of arbitrary cross-section
Ist Teil von
Microgravity science and technology, 1996-01, Vol.9 (3), p.208-219
Erscheinungsjahr
1996
Link zum Volltext
Beschreibungen/Notizen
The curvature of capillary liquid menisci in cylindrical vessels of different cross-sections is obtained by an analytical approach avoiding the numerical simulation of the entire interface. By applying the 2D divergence theorem to the capillary equation, one obtains a relation between the area integral over the mean curvature or pressure drop, respectively, and the contact line integral over the direction of the normal of the boundary. This relation is not restricted to interfaces of constant mean curvature, but can account for any external potential as long as its gradient is orthogonal to the extension of the vessel. The analytical onset thereby is not merely applied for interfaces which project onto the entire cross section of the capillary, but for the first time is used also to obtain the curvature of interfaces extending vertically upwards over a significant subset of the base domain. In the latter case we require that the vertical interface assumes negligible curvature along the axis of the capillary. Examples are given for menisci in static and rotating capillaries of regular polygonal and rhombic cross section. The present approach is a powerful means of determining the properties of nonwedge-wetting interfaces, as well as wedge-wetting interfaces, in cylindrical vessels without requiring the numerical simulation of the entire meniscus. (Author)