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Flow of a thin liquid-metal film in a toroidal magnetic field

Published online by Cambridge University Press:  28 March 2019

D. Lunz Open the ORCID record for D. Lunz [Opens in a new window]  and
P. D. Howell Open the ORCID record for P. D. Howell [Opens in a new window]
D. Lunz*
Affiliation:
Mathematical Institute, Andrew Wiles Building, Oxford OX2 6GG, UK
P. D. Howell
Affiliation:
Mathematical Institute, Andrew Wiles Building, Oxford OX2 6GG, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the gravity-driven flow of a thin film of liquid metal on a conducting conical substrate in the presence of a strong toroidal magnetic field (transverse to the flow and parallel to the substrate). We solve the leading-order governing equations in a physically relevant asymptotic limit to find the free-surface profile. We find that the leading-order fluid flow rate is a non-monotonic bounded function of the film height, and this can lead to singularities in the free-surface profile. We perform a detailed stability analysis and identify values of the relevant geometric, hydrodynamic and magnetic parameters such that the flow is stable.

JFM classification

Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 835 - 876
Copyright
© 2019 Cambridge University Press 

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