A stability investigation of two-dimensional surface waves on evaporating, isothermal or condensing liquid films - Part III, Temporal stability of traveling waves

The temporal stability equation of the two-dimensional traveling waves of evaporating or condensing liquid films falling down on an inclined wall is established based on the Prandtl boundary layer theory and complete boundary conditions. By investigating the flow temporal characteristics curves, including the stability curves and stability curves of the fastest wave, the effects on flow stability of evaporating, isothermal and condensing states, thermo-capillarity, Reynolds number, fluid property and inclined angle are discussed, and are compared in different Reynolds numbers. The theoretical study indicated that evaporation process destabilizes the film flow and condensation process stabilizes the film flow, the thermo-capillarity take a destabilizing effect in evaporation condition and an adverse effect in condensation condition. Present study indicates that the temporal growth rate increases with increase of the Reynolds number and inclination angle, and decreases with increase of Kapitza numbers. And the effects on flow stability of liquid properties and inclination angle are always significant. (authors)