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Developed liquid film passing a trailing edge under the action of gravity and capillarity

Published online by Cambridge University Press:  10 July 2018

B. Scheichl Open the ORCID record for B. Scheichl [Opens in a new window] ,
R. I. Bowles  and
G. Pasias
B. Scheichl*
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Faculty of Mechanical Engineering, Technische Universität Wien, Tower BA/E322, Getreidemarkt 9, 1060 Vienna, Austria AC2T research GmbH (Austrian Excellence Center for Tribology), Viktor-Kaplan-Straße 2/C, 2700 Wiener Neustadt, Austria
R. I. Bowles
Affiliation:
Department of Mathematics, Faculty of Mathematical and Physical Sciences, University College London (UCL), Gower Street, London WC1E 6BT, UK
G. Pasias
Affiliation:
Department of Mathematics, Faculty of Mathematical and Physical Sciences, University College London (UCL), Gower Street, London WC1E 6BT, UK
*
†Email address for correspondence: bernhard.scheichl@tuwien.ac.at
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Abstract

We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.

JFM classification

Boundary Layers: Boundary Layers Interfacial Flows (free surface): Thin films Waves/Free-surface Flows: Waves/Free-surface Flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 924 - 953
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Copyright
© 2018 Cambridge University Press 

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