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

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.