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Stability And Transient Dynamics Of Thin Liquid Films Flowing Over Locally Heated Surfaces, N Tiwari, Z Mester, Jm Davis

Jeffrey M. Davis

The dynamics and linear stability of a liquid film flowing over a locally heated surface are studied using a long-wave lubrication analysis. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that opposes the gravitationally driven flow and leads to the formation of a pronounced capillary ridge. The resulting free-surface shapes are computed, and their stability to spanwise perturbations is analyzed for a range of Marangoni numbers, substrate inclination angles, and temperature profiles. Instability is predicted above a critical Marangoni number for a finite band of wave numbers separated from zero, which is …