| Abstract: | A study is made of the problem of numerical determination of doubly connected axisymmetric equilibrium shapes of the interface of two immiscible liquids in an arbitrary axisymmetric vessel under conditions of reduced gravity. Problems of this kind are of practical interest in connection with the study of the behavior of fuel in the tanks of spacecraft 1]. It is assumed that the liquids are homogeneous and incompressible and have a temperature constant throughout the complete volume. In the investigation of the equilibrium of the interface of liquids under conditions of complete or partial weightlessness, it is necessary to take into account the forces of surface tension, which play a decisive part in such a situation. The equilibrium of liquids in a vessel with allowance for surface tension is described by a system of nonlinear equations 2]. In the present paper, the problem is solved by the Kantorovich— Newton iterative method 3], which makes it possible to reduce the nonlinear problem to a succession of linear problems solvable by the method of finite differences.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–137, September–October, 1981.I thank I. E. Tarapov and I. I. Ievlev for constant interest in the work and helpful comments. |
