Onset of Oscillatory Convection in Two Liquid Layers with Phase Change
Geoffrey B. McFadden, Sam R. Coriell
We perform linear stability calculations for horizontal fluid bilayers that can undergo a phase transformation in the presence of a vertical temperature gradient. We reconsider the oscillatory instability calculated by Huang and Joseph [J. Fluid Mech. 242 (1992) 235-247] for the water-steam system cooled from below when there is a large difference in the densities of the two fluids. We find that buoyancy and surface tension gradients are unimportant for this instability. Numerical solutions demonstrate that the properties of the vapor and liquid systems are sufficiently different at these temperatures that an approximate treatment is possible in which the equations for the vapor phase can be eliminated from the overall governing equations. Further analytical approximations suggested by the numerical solution are also presented, and the results are in good agreement with the numerical solution for the full set of governing equations. A simple model of the oscillatory instability is developed which gives insight into its origins.