(116a) Stabilizing Influence of Topography On Thin Liquid Films Flowing Over Locally Heated Surfaces
Thin liquid films flowing over surfaces with localized heating develop a pronounced ridge at the upstream edge of the heater due to the gradient in surface tension that opposes the flow. This ridge becomes unstable to transverse perturbations above a critical Marangoni number and evolves into an array of rivulets, which corresponds to the rivulet instability observed in experiments that can lead to film rupture. Similar fluid ridges form near topographical variations on isothermal surfaces at small capillary numbers, but these ridges are strongly stable to perturbations because the topography induces a net capillary pressure gradient that causes rearrangement of fluid in the flow direction. In this work, a long-wave, lubrication analysis is used to study the influence of topographical features on the linear stability of thin liquid films that flow over a locally-heated surface. The effects of basic step-down and mound features in the flow direction are analyzed. In contrast to liquid films on heated, horizontal surfaces, for which topography is destabilizing, even such non-optimized topography is found to be effective at stabilizing the flowing film with respect to rivulet formation and subsequent rupture. The critical Marangoni number at the instability threshold increases substantially (by over a factor of four) with appropriate topography, even for non-zero Biot numbers.
An energy analysis is used to provide insight into the mechanism by which the topography stabilizes the flow. While the streamwise gradient in the capillary pressure induced by the topographical feature is the expected stabilization mechanism because it is strongly stabilizing for isothermal flow over topography, this term is destabilizing for topographical features on the locally-heated surface. Upon the addition of topography, stabilization is primarily due to the streamwise capillary flow induced by the variation in the curvature of the perturbation in the flow direction. This term provides additional energy damping primarily because of the effect of the topography on the steady base state, through which the various physical effects isolated in the energy analysis are nonlinearly coupled. Because the stabilizing effect of the topographical features is only weakly sensitive to the governing parameters and particular temperature profile, the use of such features could be a simple but effective method of stabilization for sufficiently thin films.