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Vladimir O.
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DOI: 10.17586/222614942018183529534
STABILITY OF VISCOUS FILM ON SURFACE OF SLIGHTLY INCLINED ROTATING VERTICAL CYLINDER
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Article in Russian
For citation: Melikhov I.F. Stability of viscous film on surface of slightly inclined rotating vertical cylinder. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 3, pp. 529–534 (in Russian). doi: 10.17586/222614942018183529534
Abstract
For citation: Melikhov I.F. Stability of viscous film on surface of slightly inclined rotating vertical cylinder. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 3, pp. 529–534 (in Russian). doi: 10.17586/222614942018183529534
Abstract
Subject of Research.The paper deals with the problem of viscous film evolution on a surface of rotating cylinder. The objective of the work is stability analysis of such system in the cases when the cylinder axis is nearly vertical.Stability of uniform film on a strictly vertical cylinder is analyzed, and the system dynamics under small timeperiodic deviations of cylinder axis is studied.Methods. Initial NavierStokes equations, which describe dynamics of viscous fluids, are considered with introduced small parameter – the ratio of fluid layer thickness to cylinder radius. This fact allows applying of asymptotic methods and helps to derive a simplified equation on the film thickness. The obtained equation is a nonlinear partialderivative equation and cannot be solved analytically in general form. Perturbation theory is applied for the subsequent analysis. Linear stability analysis for uniform film on the vertical cylinder surface is carried out. Response to timeperiodic perturbation of the cylinder tilt is studied. Main Results. In the case of strictly vertical cylinder, capillary forces imply instability of axisymmetric perturbations with a wavelength exceeding critical value. The obtained critical wavelength value is proportional to the cylinder radius. It is shown that when a cylinder axis oscillates around the vertical, nonuniform fluid layer appears with diametrically opposite thickening and thinning. In the case when the axis oscillation frequency is equal to the rotation frequency, a resonance appears.Practical Relevance. The obtained results might be used for better understanding and further improvement of existing manufacturing processes.
Keywords: viscous films, lubrication theory, fluid on cylinder surface, flow stability
Acknowledgements. The work is partially supported by the Government of the Russian Federation (grant 074U01).
References
Acknowledgements. The work is partially supported by the Government of the Russian Federation (grant 074U01).
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