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arXiv · 1403.5197

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

Harshwardhan H. Katkar·Jeffrey M. Davis
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Abstract

We investigate the non-linear 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 Marangoni number using linear stability theory. Continuation along the Marangoni number using non-linear evolution equation is used to trace bifurcation diagram associated with the oscillatory instability. Hysteresis, a characteristic attribute of a sub-critical Hopf bifurcation, is observed in a critical parametric region. The bifurcation is universally observed for both, a non-volatile film and a volatile film.

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Harshwardhan H. Katkar, Jeffrey M. Davis. 2014-03-20. Bifurcation in a thin liquid film flowing over a locally heated surface. https://doi.org/10.1017/jfm.2013.245

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