Abstract
The solution to the problem on the shape of the lateral surface of a vertical three-dimensional catenoidal liquid bridge of small volume between two arbitrary convex solid surfaces in the axisymmetric case, taking into account the action of gravity, is presented. A variational formulation of the original problem has given. The solution has found by the iteration method under the assumption that the Bond number has been small. The algorithm of iterative process has proposed. The parameters change areas for which there is no uniqueness of the solution to the problem have discovered. It has been established that the maximum number of different profiles of the liquid bridge lateral surface corresponding the single selected set of parameters has equal to four. As an example, the liquid bridge shape problem between two spheres was solved.
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