Steady rimming flows with surface tension

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, th...

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Bibliographic Details
Published in:Journal of fluid mechanics 2008-02, Vol.597, p.91-118
Main Authors: BENILOV, E. S., BENILOV, M. S., KOPTEVA, N.
Format: Article
Language:English
Subjects:
Applied fluid mechanics
Exact sciences and technology
Fluid dynamics
Fluid mechanics
Fluids
Fundamental areas of phenomenology (including applications)
Hydrodynamics, hydraulics, hydrostatics
Physics
Steady flow
Surface tension
Thin films
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Summary:We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder's bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112007009585