Linear temporal and spatial stability formulations of two-dimensional surface waves on evaporating, isothermal, or condensing liquid films

Abstract

When a liquid film is under the evaporating or condensing condition, the flow stability is clearly different from that under an isothermal condition due to the thermal non-equilibrium effect at the interface, especially under a lower Reynolds number. Based on Prandtl's boundary layer theory and complete boundary conditions, the universal temporal and spatial stability formulations are established using the collocation method for two-dimensional surface waves of the evaporating or condensing and isothermal liquid films draining down an inclined wall. The evolution equations indicate that the flow stability is closely related to the Reynolds number, thermocapillarity, inclination angle, liquid property, and evaporation, isothermal, or condensation actions. The effects of the above factors are investigated with neutral stability curves at different Reynolds numbers, and stability characteristics are fully indicated in theory for evaporating or condensing films. Results show that the evaporation process destabilizes the film flow and condensation process stabilizes the film flow. Thermocapillarity has a stabilizing effect in an evaporation condition and an adverse effect in the condensation condition. For a lower Reynolds number, the vapor recoil and thermocapillary take dominant effects when compared to the inertia force in determining flow stability. At a higher Reynolds number, the flow stability is controlled by the inertia force. Present study indicates that the disturbance increases with an increase of the Reynolds number and inclination angle, and decreases with increase of Ka numbers. Furthermore, the effects of liquid properties and inclination angle are always significant. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 243–257, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20062