Strathprints logo
Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow

Sullivan, J. M. and Paterson, C. and Wilson, S. K. and Duffy, B. R. (2012) A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow. Physics of Fluids, 24 (8). ISSN 1070-6631

[img] PDF (Sullivan-etal-PoF2012-ridge-subject-to-a-uniform-transverse-shear-stress)
Sullivan_etal_PoF2012_ridge_subject_to_a_uniform_transverse_shear_stress.pdf - Submitted Version

Download (211kB)

Abstract

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations.

Item type: Article
ID code: 41282
Notes: Date of Acceptance: 05/07/2012 (c) American Institute of Physics
Keywords: aerodynamics, computational fluid dynamics, contact angle, drops, external flows, perturbation theory, free surface, fluid drops, lubrication, shear flows, numerical solutions, Physics, Physics and Astronomy(all)
Subjects: Science > Physics
Department: Faculty of Science > Mathematics and Statistics > Mathematics
Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 28 Sep 2012 14:27
Last modified: 24 Jul 2015 10:02
Related URLs:
URI: http://strathprints.strath.ac.uk/id/eprint/41282

Actions (login required)

View Item View Item