Abstract
We consider the plane problem of the equilibrium of a capillary surface. We study the stability of a two-dimensional surface with respect to plane and spatial disturbances. We give data which can be used for deciding the question of the stability of any symmetric equilibrium surface in a field of gravitational forces and in conditions of weightlessness. We solve the problems of the stability of a liquid in a rectangular and a sectorial channel and also the problem of the separation of a plane drop from a horizontal wall.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
M. A. Belyaeva, A. D. Myshkis, and A. D. Tyuptsov, “Hydrostatics in weak gravitational fields. Equilibrium forms of a liquid surface,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr. No. 5 (1964).
M. A. Belyaeva, L. A. Slobozhanin, and A. D. Tyuptsov, “Hydrostatics in weak force fields,” in: Introduction to the Dynamics of a Body with a Liquid in Conditions of Weightlessness [in Russian], Vychisl. Tsentr Akad. Nauk SSSR, Moscow (1968).
L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1953).
F. L. Chernous'ko, “The problem of the equilibrium of a liquid subjected to the action of gravitational forces and surface tension,” in: Introduction to the Dynamics of a Body with a Liquid in Conditions of Weightlessness [in Russian], Vychisl. Tsentr Akad. Nauk SSSR, Moscow (1968).
Ya. I. Frenkel', “Behavior of liquid drops on the surface of a solid,” Zh. Éksp. Teor. Fiz.,18, No. 7 (1948).
K. D. Vachagin and V. S. Nikolaev, “Behavior of drops of liquid on a solid surface, Tr. Kazansk. Khim.-Tekhnol. Inst., No. 27 (1961).
A. D. Myshkis, L. A. Slobozhanin, and A. D. Tyuptsov, “Small disturbances of an equilibrium surface of a capillary liquid,” Prikl. Mat. Mekh.,39, No. 4 (1975).
L. A. Slobozhanin and A. D. Tyuptsov, “Determination of the equilibrium state of a capillary liquid in a vessel,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4 (1973).
L. A. Temkin, V. S. Temkina, and G. V. Shcherbina, “Calculation of the free surface of a capillary liquid in a vessel,” in: Computational Mathematics and Computer Technology [in Russian], No. 5, Khar'kov (1974).
P. Konkus, “Capillary stability of a free surface of a liquid in an inverted rectangular channel with a curvature which changes sign,” Raketn. Tekh. Kosmonavt.,2, No. 12 (1964).
N. D. Kopachevskii, “Hydrodynamics in weak gravitational fields. Plane problems on the oscillations of an ideal liquid in a vessel,” Zh. Vychisl. Mat. Mat. Fiz.,13, No. 4 (1973).
E. Pitts, “The stability of pendent liquid drops, Part 1. Drops formed in a narrow gap,” J. Fluid Mech.,59, Pt. 4 (1973).
L. A. Slobozhanin and A. D. Tyuptsov, “Characteristic parameter of stability of an axially symmetric equilibrium surface of a capillary liquid,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4 (1974).
L. A. Slobozhanin and A. D. Tyuptsov, “Evolution and separation of drops and bubbles which grow slowly,” Zh. Prikl. Mekh. Tekh. Fiz., No. 1 (1975).
L. A. Slobozhanin and A. D. Tyuptsov, “Stable equilibrium of the surface of a capillary liquid when it is in contact with the edge of a solid,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1 (1974).
Yu. A. Buevich and V. V. Butkov, “Some rules governing the dispersion of liquids flowing slowly out of a plane slit,” Teor. Osn. Khim. Tekhnol.,3, No. 4 (1969).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 57–68, January–February, 1976.
The authors are grateful to A. D. Myshkis and A. D. Tyuptsov for their evaluation and their useful comments.
Rights and permissions
About this article
Cite this article
Slobozhanin, L.A., Shcherbakova, N.S. Cylindrical equilibrium surfaces of a capillary liquid and their stability. Fluid Dyn 11, 49–59 (1976). https://doi.org/10.1007/BF01023394
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01023394