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On the Hamiltonian structure and three-dimensional instabilities of rotating liquid bridges

Kruse, Hans Peter and Mahalov, Alex and Marsden, Jerrold E. (1999) On the Hamiltonian structure and three-dimensional instabilities of rotating liquid bridges. Fluid Dynamics Research, 24 (1). pp. 37-59. ISSN 0169-5983 . http://resolver.caltech.edu/CaltechAUTHORS:20100820-140308840

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Abstract

We consider a rotating inviscid liquid drop trapped between two parallel plates. The liquid–air interface is a free surface and the boundaries of the wetted regions in the plates are also free. We assume that the two contact angles at the plates are equal. We present drop shapes that generalize the catenoids, nodoids and unduloids in the presence of rotation. We describe profile curves of these drops and investigate their stability to three-dimensional perturbations. The instabilities are associated with degeneracies of eigenvalues of the corresponding Hamiltonian linear stability problem. We observe that these instabilities are present even in the case when the analogue of the Rayleigh criterion for two-dimensional stability is satisfied


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0169-5983(98)00005-7DOIUNSPECIFIED
http://iopscience.iop.org/1873-7005/24/1/A04/PublisherUNSPECIFIED
Additional Information:© IOP Publishing. Received 2 February 1998 , accepted for publication 9 February 1998. This version: January 27, 1998. We are grateful to Edgar Knobloch and Jürgen Scheurle for helpful comments and their interest. The research of HPK was partially supported by the DFG under the contract Sch 233/3-2 as well as a former Feodor Lynen- Fellowship of the Alexander von Humboldt-Foundation during a stay at the Fields Institute and the Department of Mathematics, University of California, Berkeley. That of AM was partially supported by AFOSR grant F49620-93-1-0172 and the ASU Center for Environmental Fluid Dynamics and that of JEM was partially supported by the Department of Energy and the California Institute of Technology.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (German Research Council) (DFG)Sch 233/3-2
Air Force Office of Scientific Research (AFOSR)F49620-93-1-0172
Department of EnergyUNSPECIFIED
California Institute of TechnologyUNSPECIFIED
Subject Keywords:Soft matter, liquids and polymers. Fluid dynamics.Surfaces, interfaces and thin films
Classification Code:PACS: 68.03.Cd; 47.55.D-; 47.32.Ef
Record Number:CaltechAUTHORS:20100820-140308840
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100820-140308840
Official Citation:Hans Peter Kruse et al 1999 Fluid Dyn. Res. 24 37 doi: 10.1016/S0169-5983(98)00005-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19564
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 Sep 2010 21:04
Last Modified:26 Dec 2012 12:20

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