Abstract
We derive equations describing the motion of a viscous incompressible capillary film on the surface of a rotating cylinder in the transverse gravity field. As a result, we obtain an equation for the film thickness that has fourth order in two space variables and first order in time. We study both space-periodic solutions in the axial coordinate and localized solutions of this equation in the stationary case. We also discuss the stability of stationary solutions. Analysis of the one-dimensional problem shows that its solution strongly depends on the Galileo number and that such a solution does not exist if this number is large. Bibliography: 15 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 165–185.
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Pukhnachov, V.V. Capillary/Gravity Film Flows on the Surface of a Rotating Cylinder. J Math Sci 130, 4871–4883 (2005). https://doi.org/10.1007/s10958-005-0382-x
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DOI: https://doi.org/10.1007/s10958-005-0382-x