Instabilities in a fluid layer with phase changes

The onset of convection in a bottom heated horizontal fluid layer containing two different phases is investigated with emphasis on the effect of the location of the phase change interface. A general analysis, applicable when the phase boundary is at any location in the layer, is used to determine how both exothermic and endothermic phase changes influence layer instability. A perturbation analysis is presented for phase change boundaries close to the bottom of the fluid layer. Stability of the layer depends on three dimensionless parameters: RαRα, a latent heat parameter; S  , a phase boundary distortion parameter; and ξξ, a phase boundary location parameter. Both exothermic and endothermic phase changes can be either stabilizing or destabilizing depending on S   and RαRα. Application is made to the exothermic olivine–spinel (in Earth and Mars) and perovskite–post-perovskite (in Earth) phase transitions and the endothermic spinel–perovskite phase change (in Earth). The perturbation analysis provides a quantitative analytic criterion to predict whether a phase change near the lower boundary is stabilizing or destabilizing. When the exothermic phase change is stabilizing (destabilizing), the layer is most stable (unstable) when the phase change is in the middle.