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Thermocapillary stabilization of the capillary breakup of an annular film of liquid

Published online by Cambridge University Press:  26 April 2006

Henk A. Dijkstra  and
Paul H. Steen
Henk A. Dijkstra
Affiliation:
Mathematical Sciences Institute and School of Chemical Engineering, Cornell University Ithaca, NY 14853, USA
Paul H. Steen
Affiliation:
Mathematical Sciences Institute and School of Chemical Engineering, Cornell University Ithaca, NY 14853, USA
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Abstract

It is known that the breakup by surface tension of a cylindrical interface containing a viscous liquid can be dampeu by axial motion of the underlying liquid and that for an annular film the capillary instability can be completely suppressed (disturbances of all wavelengths decay) by certain axial velocity profiles. Here, using a linear stability analysis, it is shown that complete stabilization can also occur for thermocapillary-driven axial motions. However, the influence of thermocapillary instabilities typically shrinks the window in parameter space where stabilization is found, relative to the isothermal case. The influence of Reynolds, surface tension, Prandtl, and Biot parameters on limits of stabilization is calculated using continuation techniques. It is observed that windows of stabilization first open with topological changes of the neutral curves in parameter space. A long-wave analysis unfolds the nature of the singularities responsible for several of these topological changes. The analysis also leads to the physical mechanism responsible for (longwave) stabilization and in certain cases to necessary conditions for (long-wave) stabilization.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 205 - 228
Copyright
© 1991 Cambridge University Press

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