Threedimensional coating and rimming flow : a ring of fluid on a rotating horizontal cylinder
Leslie, George Adam and Wilson, Stephen and Duffy, Brian (2013) Threedimensional coating and rimming flow : a ring of fluid on a rotating horizontal cylinder. Journal of Fluid Mechanics, 716. pp. 5182. ISSN 00221120 (https://doi.org/10.1017/jfm.2012.509)
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Abstract
The steady threedimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study “fullring” solutions, corresponding to a ring of continuous, finite and nonzero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no fullring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no fullring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semiwidth and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the noncritical fullring solution, and, in particular, show that the semiwidth and the ring profile are increasing functions of the load but, in general, nonmonotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting nonuniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upwardmoving side of the cylinder.


Item type: Article ID code: 42349 Dates: DateEventFebruary 2013PublishedNotes: now published  DOI not working Subjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 11 Dec 2012 16:46 Last modified: 27 Jun 2024 01:09 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/42349