The Mathematical Institute, University of Oxford, Eprints Archive

Rivulet flow round a horizontal cylinder subject to a
uniform surface shear stress

Paterson, C. and Wilson, S.K. and Duffy, B.R. (2013) Rivulet flow round a horizontal cylinder subject to a
uniform surface shear stress.
Quarterly Journal of Mechanics and Applied Mathematics . (Submitted)

[img]
Preview
PDF
2MB

Abstract

The steady flow of a slowly varying rivulet with prescribed flux in the azimuthal direction round a large stationary horizontal cylinder subject to a prescribed uniform azimuthal surface shear stress is investigated. In particular, we focus on the case where the volume flux is downwards but the shear stress is upwards, for which there is always a solution corresponding to a rivulet flowing down at least part of one side of the cylinder. We consider both a rivulet with constant non-zero contact angle but slowly varying width (i.e. de-pinned contact lines) and a rivulet with constant width but slowly varying contact angle (i.e. pinned contact lines), and show that they have qualitatively different behaviour. When shear is present, a rivulet with constant non-zero contact angle can never run all the way from the top to the bottom of the cylinder, and so we consider the scenario in which an infinitely wide two-dimensional film of uniform thickness covers part of the upper half of the cylinder and “breaks” into a single rivulet with constant non-zero contact angle. In contrast, a sufficiently narrow rivulet with constant width can run all the way from the top to the bottom of the cylinder, whereas a wide rivulet can do so only if its contact lines de-pin, and so we consider the scenario in which the contact lines of a wide rivulet de-pin on the lower half of the cylinder.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1732
Deposited By: Peter Hudston
Deposited On:30 Jul 2013 13:08
Last Modified:29 May 2015 19:25

Repository Staff Only: item control page