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Fingering instability on curved substrates: optimal initial film and substrate perturbations

Published online by Cambridge University Press:  17 April 2019

Gioele Balestra Open the ORCID record for Gioele Balestra [Opens in a new window] ,
Mohamed Badaoui ,
Yves-Marie Ducimetière  and
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]
Gioele Balestra*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, CH1015 Lausanne, Switzerland
Mohamed Badaoui
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, CH1015 Lausanne, Switzerland
Yves-Marie Ducimetière
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, CH1015 Lausanne, Switzerland
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, CH1015 Lausanne, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the stability of a thin Newtonian fluid spreading on a horizontal cylinder under the action of gravity. The capillary ridge forming at the advancing front is known to be unstable with respect to spanwise perturbations, resulting in the formation of fingers. In contrast to the classic case of a flow over an inclined plane, the gravity components along a cylindrical substrate vary in space and the draining flow is time-dependent, making a modal stability analysis inappropriate. A linear optimal transient growth analysis is instead performed to find the optimal spanwise wavenumber. We not only consider the optimal perturbations of the initial film thickness, as commonly done in the literature, but also the optimal topographical perturbations of the substrate, which are of significant practical relevance. We found that, in both cases, the optimal gains are obtained when the perturbation structures are the least affected by the time horizon. The optimal spanwise wavenumber is found to be dependent on the front location, due to the dependence of the characteristic length of the capillary ridge on its polar location.

JFM classification

Interfacial Flows (free surface): Fingering instability Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 726 - 761
Copyright
© 2019 Cambridge University Press 

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