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Dynamics of falling films on the outside of a vertical rotating cylinder: waves, rivulets and dripping transitions

Published online by Cambridge University Press:  26 October 2017

Manuel Rietz Open the ORCID record for Manuel Rietz [Opens in a new window] ,
Benoit Scheid ,
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window] ,
Nicolas Kofman ,
Reinhold Kneer  and
Wilko Rohlfs
Manuel Rietz*
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany
Benoit Scheid
Affiliation:
TIPs, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Bruxelles, Belgium
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, 1015 Lausanne, Switzerland
Nicolas Kofman
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, 1015 Lausanne, Switzerland
Reinhold Kneer
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany
Wilko Rohlfs
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Falling liquid films on the underside of a plate or on the outside of a rotating cylinder are subject to a destabilizing body force. The evolution of the film topology is determined by interactions between the Kapitza and the Rayleigh–Taylor instability, leading to complex patterning of the film surface and eventually fluid detachment from the substrate. This study experimentally investigates the evolution of the surface topology for a film on the outside of a vertical rotating cylinder of large radius. Shear at the liquid/air interface is suppressed through an outer, co-rotating cylinder. The film evolution is captured through high speed visualization in dependence of the control parameters, namely Reynolds number and rotation frequency. An increasing influence of the Rayleigh–Taylor instability for an increasing destabilizing body force (increasing rotational speed of the cylinder) is most notably observed in the form of a decreasing inception length of rivulet structures dominating the film topology. Wavelength as well as inception length of rivulets match the predictions from linear stability analysis of the classical Rayleigh–Taylor problem. In this context, experimental and supporting numerical results suggest that the emergence of rivulets occurs for any non-zero value of the destabilizing body force after a given evolution length that decreases with increasing body force. Fluid detachment from the substrate is found to be intimately related to the existence of rivulet structures. In dependence of the control parameters, detaching droplets are either observed as a result of interactions of solitary pulses of varying phase speed on rivulets, directly after destabilization of two-dimensional waves into rivulets or immediately at the fluid inlet. By comparison to the convective/absolute instability transition predicted by linear stability analysis of an integral boundary layer formulation of the problem in question, it is shown that the prediction of a predominant dripping mechanism lies beyond the scope of linear analysis.

JFM classification

Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 189 - 211
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Copyright
© 2017 Cambridge University Press 

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