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Bifurcation In A Thin Liquid Film Flowing Over A Locally Heated Surface

Harshwardhan H. Katkar, Jeffrey M. Davis

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AbstractWe 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.