Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface

The stability of a thin, volatile liquid film falling under the influence of gravity over a locally heated, vertical plate is analyzed in the noninertial regime using a model based on long-wave theory. The model is formulated to account for evaporation that is either governed by thermodynamic considerations at the interface in the one-sided limit or limited by the rate of mass transfer of the vapor from the interface. The temperature gradient near the upstream edge of the heater induces a gradient in surface tension that opposes the gravity-driven flow, and a pronounced thermocapillary ridge develops in the streamwise direction. Recent theoretical analyses predict that the ridge becomes unstable above a critical value of the Marangoni parameter, leading to the experimentally observed rivulet structure that is periodic in the direction transverse to the bulk flow. An oscillatory, thermocapillary instability in the streamwise direction above the heater is also predicted for films with sufficiently large hea...