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On a nonlinear thermocapillary effect in thin liquid layers

Published online by Cambridge University Press:  26 April 2006

Alexander Oron  and
Philip Rosenau
Alexander Oron
Affiliation:
Faculty of Mechanical Engineering and Center for Research in Nonlinear Phenomena, Technion–Israel Institute of Technology, Haifa 32000, Israel
Philip Rosenau
Affiliation:
Faculty of Mechanical Engineering and Center for Research in Nonlinear Phenomena, Technion–Israel Institute of Technology, Haifa 32000, Israel Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Abstract

Dilute aqueous solutions of long alcohol chains were recently found to cause a quadratic dependence of surface tension on the temperature without affecting other bulk properties of the liquid: σ = σ0 + αQ(T − T0)2, αQ > 0. The impact of such Marangoni instability on the behaviour of a thin liquid layer is studied in this work. We derive an equation describing a nonlinear spatiotemporal evolution of a thin film. The behaviour of the perturbed film in the absence of gravity, critically depends on whether the temperature T0, yielding a minimal surface tension, is attained on the surface of the film. When this is the case, a qualitatively new behaviour is observed: perturbations of the film interface may evolve into continuous steady patterns that do not rupture. Otherwise, the observed patterns due to the linear and quadratic Marangoni effects are qualitatively similar and result in the rupture of the film into separate drops.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 273 , 25 August 1994 , pp. 361 - 374
Copyright
© 1994 Cambridge University Press

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