A new type of instability: explosive disturbances in a liquid film inside a rotating horizontal cylinder

We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating around this axis. An asymptotic equation is derived, which takes into account two orders of the so-called lubrication approximation. The equation admits a solution describing a...

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Bibliographic Details
Published in:Journal of fluid mechanics 2003-12, Vol.497, p.201-224, Article S0022112003006633
Main Authors: BENILOV, E. S., O'BRIEN, S. B. G., SAZONOV, I. A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Physics
Thin films
Viscous instability
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Summary:We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating around this axis. An asymptotic equation is derived, which takes into account two orders of the so-called lubrication approximation. The equation admits a solution describing a steady-state distribution of film around the cylinder, and we examine the stability of this solution. It is demonstrated that the linearized problem admits infinitely many harmonic solutions, all of which have real frequencies (are neutrally stable). On the other hand, there are non-harmonic solutions that ‘explode’ (develop singularities) in a finite time. Systems having solutions of both types simultaneously have never been described in the literature. An example of this phenomenon is the main result of this paper.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112003006633