English

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

Fluid Dynamics 2014-03-21 v1

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.

Keywords

Cite

@article{arxiv.1403.5197,
  title  = {Bifurcation in a thin liquid film flowing over a locally heated surface},
  author = {Harshwardhan H. Katkar and Jeffrey M. Davis},
  journal= {arXiv preprint arXiv:1403.5197},
  year   = {2014}
}

Comments

Revised manuscript published at http://dx.doi.org/10.1017/jfm.2013.245