Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Linear stability of rimming flow


Author: S. B. G. O'Brien
Journal: Quart. Appl. Math. 60 (2002), 201-211
MSC: Primary 76D08; Secondary 76A20, 76E17
DOI: https://doi.org/10.1090/qam/1900490
MathSciNet review: MR1900490
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Abstract: We consider the case of rimming flow where a thin film of viscous liquid coats the walls of a cylinder whose axis is horizontal and which is rotating with constant angular velocity. It has been experimentally established that such flows are often unstable and that the liquid often segregates into ``rings'' along the length of the tube. Using a leading-order lubrication theory, we utilise recently established steady solutions [10], which in some instances contain shocks, to examine the linear stability of the flow when subjected to two-dimensional disturbances. All solutions are shown to be at least neutrally stable. We suggest that further investigations should include higher-order (small) effects and that the origin of the observed instabilities lies in these terms.


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Additional Information

DOI: https://doi.org/10.1090/qam/1900490
Article copyright: © Copyright 2002 American Mathematical Society


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