Instability of a binary liquid film flowing down a slippery inclined heated plate

In this thesis we studied the stability of a binary liquid film flowing down a heated porous inclined plate. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier- tokes equations governing the flow with equations for the concentration and temperature. The effect of substrate permeability is incorporated by applying a specific slip condition at the bottom of the liquid layer. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We used a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld type equations. We also obtained an asymptotic solution which yielded an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. We present our findings by illustrating and interpreting our results for the critical Reynolds number for instability.