Falling films over phase-changing planes

We study the interplay between shear, buoyancy, and phase change on the stability of a flow of a liquid over an inclined, phase-changing plane under the influence of gravity. In the absence of buoyancy and phase change, this flow is known to exhibit a long-wavelength instability – which was first identified by Yih (Phys. Fluids. 6(3), pp. 321-334, 1963) – and a short-wavelength shear-mode instability – identified by Kelly (Phys. Fluids. A: Fluid Dynamics 1(5), pp. 819-828, 1989). We use a combination of linear stability and asymptotic analyses to study the effects of stratification and phase boundary on these instabilities, and find that they significantly affect the flow dynamics