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Bifurcation in a thin liquid film flowing over a locally heated surface

Published online by Cambridge University Press:  11 June 2013

Harshwardhan H. Katkar  and
Jeffrey M. Davis
Harshwardhan H. Katkar*
Affiliation:
Department of Chemical Engineering, University of Massachusetts, 686 North Pleasant Street, Amherst, MA 01003, USA
Jeffrey M. Davis
Affiliation:
Department of Chemical Engineering, University of Massachusetts, 686 North Pleasant Street, Amherst, MA 01003, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the nonlinear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of the Marangoni number using linear stability theory. Continuation along the Marangoni number using a nonlinear evolution equation is employed to trace the bifurcation diagram associated with the oscillatory instability. Hysteresis, a characteristic attribute of a subcritical Hopf bifurcation, is observed in a critical parametric region. The bifurcation is universally observed for both a non-volatile film and a volatile film.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 656 - 667
Copyright
©2013 Cambridge University Press 

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