Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A mechanism for linear instability in two-dimensional rimming flow

Author: S. B. G. O'Brien
Journal: Quart. Appl. Math. 60 (2002), 283-299
MSC: Primary 76D08; Secondary 76A20, 76D45, 76E17
DOI: https://doi.org/10.1090/qam/1900494
MathSciNet review: MR1900494
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Abstract: In rimming flow, a thin film of viscous liquid coats the inside of a cylinder whose axis is horizontal and which is rotating with constant angular velocity. It has been established experimentally that such flows are often unstable with a variety of secondary flow regimes having been observed experimentally [15]. We use a lubrication approximation extended to the first order in the dimensionless film thickness (including the small effects of the variation of the film pressure across its thickness and the surface tension) and study the stability of the steady solutions to two-dimensional disturbances. The modified evolution equation is found to have both asymptotically stable and unstable solutions arising from the pressure terms. Surface tension effects place a restriction on the critical wave number when instability occurs: in many cases, surface tension prevents instability.

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DOI: https://doi.org/10.1090/qam/1900494
Article copyright: © Copyright 2002 American Mathematical Society

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