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Mechanics
On the solid cylinder rotating about the axis with a constant angular speed, disposes a thin film of viscous incompressible liquids. The axis of the cylinder is directed perpendicularly to a gravity. Stationary flows is considered, on a free boundary the surface tension is taken into account. The thin layer equations are solved. Such equations for the first time have been received by V.V.Pukhnachov. They depend on two control parameters: Galileo number $ eta $ and capillary number $ delta $. If the first parameter is equal to zero then the gravity is equal to zero. If the second parameter zero then the surface tension is equal to zero.
At what values of these parameters the solutions are exist and how many theirs? This question has been investigated numerically by a method of collocations. On the plane $ (eta, delta) $ the domain is found, for each point of it at least two solutions exists. For second regime of the flow, unknown before, the form of a free surface has a dropping form. Change of flow characteristics for both solutions is investigated with varying the Galileo number and capillary number. It is numerically investigated the branching of solutions and with small $ delta $ the points of secondary bifurcation are found.
The work is supported by the Russian Foundation for Basic Research (Project No. 04-01-00355).
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)