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Thermal rupture of a free liquid sheet

Published online by Cambridge University Press:  14 February 2018

G. Kitavtsev Open the ORCID record for G. Kitavtsev [Opens in a new window] ,
M. A. Fontelos  and
J. Eggers
G. Kitavtsev*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
M. A. Fontelos
Affiliation:
Instituto de Ciencias Matemáticas, (ICMAT, CSIC-UAM-UCM-UC3M), C/ Serrano 123, 28006 Madrid, Spain
J. Eggers
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Email address for correspondence: [email protected]
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Abstract

We consider a free liquid sheet, taking into account the dependence of surface tension on the temperature or concentration of some pollutant. The sheet dynamics are described within a long-wavelength description. In the presence of viscosity, local thinning of the sheet is driven by a strong temperature gradient across the pinch region, resembling a shock. As a result, for long times the sheet thins exponentially, leading to breakup. We describe the quasi-one-dimensional thickness, velocity and temperature profiles in the pinch region in terms of similarity solutions, which possess a universal structure. Our analytical description agrees quantitatively with numerical simulations.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Micro-/Nano-fluid dynamics: Microfluidics Low-Reynolds-number flows: Slender-body theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 555 - 578
Copyright
© 2018 Cambridge University Press 

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