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Thermocapillary control of rupture in thin viscous fluid sheets

Published online by Cambridge University Press:  11 October 2005

B. S. TILLEY
Affiliation:
Franklin W. Olin College of Engineering, Olin way, Needham, MA 02492, USA
M. BOWEN
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK Present Address: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan.

Abstract

We consider the evolution of a thin viscous fluid sheet subject to thermocapillary effects. Using a lubrication approximation we find, for symmetric interfacial deflections, coupled evolution equations for the interfacial profile, the streamwise component of the fluid velocity and the temperature variation along the surface. Initial temperature profiles change the initial flow field through Marangoni-induced shear stresses. These changes then lead to preferred conditions for rupture prescribed by the initial temperature distribution. We show that the time to rupture may be minimized by varying the phase difference between the initial velocity profile and the initial temperature profile. For sufficiently large temperature differences, the phase difference between the initial velocity and temperature profiles determines the rupture location.

Type
Papers
Copyright
© 2005 Cambridge University Press

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