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Static rivulet instabilities: varicose and sinuous modes

Published online by Cambridge University Press:  05 January 2018

J. B. Bostwick Open the ORCID record for J. B. Bostwick [Opens in a new window]  and
P. H. Steen Open the ORCID record for P. H. Steen [Opens in a new window]
J. B. Bostwick*
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
P. H. Steen
Affiliation:
School of Chemical and Biomolecular Engineering and Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

A static rivulet is subject to disturbances in shape, velocity and pressure fields. Disturbances to interfacial shape accommodate a contact line that is either (i) fixed (pinned) or (ii) fully mobile (free) and preserves the static contact angle. The governing hydrodynamic equations for this inviscid, incompressible fluid are derived and then reduced to a functional eigenvalue problem on linear operators, which are parametrized by axial wavenumber and base-state volume. Solutions are decomposed according to their symmetry (varicose) or anti-symmetry (sinuous) about the vertical mid-plane. Dispersion relations are then computed. Static stability is obtained by setting growth rate to zero and recovers existing literature results. Critical growth rates and wavenumbers for the varicose and sinuous modes are reported. For the varicose mode, typical capillary break-up persists and the role of the liquid/solid interaction on the critical disturbance is illustrated. There exists a range of parameters for which the sinuous mode is the dominant instability mode. The sinuous instability mechanism is shown to correlate with horizontal centre-of-mass motion and illustrated using a toy model.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Liquid bridges
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 819 - 838
Copyright
© 2018 Cambridge University Press 

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