Thu April 18th 2013
16:00
ZH286
Seminar Fluid rings and floating plates
Stephen Wilson

Details:

In this talk I shall describe two rather different, but not entirely unrelated, problems involving thin-film flow of a viscous fluid which I have found of interest and which may have some application to a number of practical situations, including condensation in heat exchangers and microfluidics.
The first problem, which is joint work with Adam Leslie and Brian Duffy at the University of Strathclyde, concerns the steady three-dimensional flow of a thin, slowly varying ring of fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder. Specifically, we study “full-ring” solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. These full-ring solutions may be thought of as a three-dimensional generalisation of the “full-film” solutions described by Moffatt (1977) for the corresponding two-dimensional problem. We describe the behaviour of both the critical and non-critical full-ring solutions. In particular, 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 upward-moving side of the cylinder.
The second problem, which is joint work with Phil Trinh and Howard Stone at Princeton University, concerns a rigid plate moving steadily on the free surface of a thin film of fluid. Specifically, we study two problems involving a rigid flat (but not, in general, horizontal) plate: the pinned problem, in which the upstream end of plate is pinned at a fixed position, the fluid pressure at the upstream end of the plate takes a prescribed value and there is a free surface downstream of the plate, and the free problem, in which the plate is freely floating and there are free surfaces both upstream and downstream of the plate. For
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