Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

A long-wave lubrication analysis is used to study the influence of topographical features on the linear stability of noninertial coating flows over a locally heated surface. Thin liquid films flowing over surfaces with localized heating develop a pronounced ridge at the upstream edge of the heater. This ridge becomes unstable to transverse perturbations above a critical Marangoni number and evolves into an array of rivulets even in the limit of noninertial flow. Similar fluid ridges form near topographical variations on isothermal surfaces, but these ridges are stable to perturbations. The influence of basic topographical features on the stability of the locally heated film is analyzed. In contrast to its destabilizing influence on liquid films resting on heated, horizontal walls, even such nonoptimized topography is found to be effective at stabilizing the flowing film with respect to rivulet formation and subsequent rupture. Optimal topographical features that suppress variations in the free-surface sha...