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Flow on the surface of sloped rotating cylinder

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Abstract

Viscous flow of fluid film on outer surface of a sloped rotating cylinder in gravitational field is studied. Thickness of the fluid layer is assumed to be small compared to the cylinder radius, which allows asymptotic analysis. Governing equation for the thickness dynamics is derived. The equation accounts for viscous effects, gravity, centrifugal and capillary forces. A criterion for existence of steady flow on the sloped cylinder is obtained. Linear stability of stationary solution for the vertical cylinder is given. Film thickness response to oscillations of the cylinder axis around vertical line is studied. Numerical model is implemented for the case of arbitrary slope angle.

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Acknowledgements

This work was partially financially supported by the Government of the Russian Federation (Grant 08-08), by Grant 16-11-10330 of Russian Science Foundation.

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Authors and Affiliations

  1. ITMO University, Kronverkskiy, 49, P.O. Box 197101, St. Petersburg, Russia

    Ivan F. Melikhov, Sergey A. Chivilikhin & Igor Y. Popov

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  1. Ivan F. Melikhov
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  2. Sergey A. Chivilikhin
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  3. Igor Y. Popov
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Correspondence to Igor Y. Popov.

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Melikhov, I.F., Chivilikhin, S.A. & Popov, I.Y. Flow on the surface of sloped rotating cylinder. Z. Angew. Math. Phys. 71, 101 (2020). https://doi.org/10.1007/s00033-020-01323-7

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