Abstract

The solution to the problem of the shape of the lateral surface of a vertical 3D catenoidal liquid bridge of small volume between two arbitrary convex solid surfaces in the axisymmetric case taking into account the gravity force is presented. A variational formulation of the initial problem is given. The solution is found by the iteration method under the assumption of a small Bond number. An algorithm of the iterative process is proposed. We have detected domains of variation of parameters in which the uniqueness of the solution is not observed. It is found that the maximal number of different lateral surface profiles of the liquid bridge, which correspond to a single chosen set of parameters, is four. By way of example, the problem of the liquid bridge shape between two spheres is solved.

中文翻译：

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考虑重力的凸面之间的垂直液桥形状问题

摘要

提出了一种在轴对称情况下考虑重力的解决方案，解决了在轴对称情况下两个任意凸形固体表面之间的小体积垂直3D链状液体桥的侧面形状问题。给出了初始问题的变体表述。该解决方案是在假定邦德数较小的情况下通过迭代方法找到的。提出了一种迭代过程的算法。我们已经检测到参数变化的域，其中未观察到解决方案的唯一性。已经发现，对应于单个选择的一组参数的液桥的不同侧面轮廓的最大数量为四个。举例来说，解决了两个球之间的液桥形状的问题。