Bidispersive vertical convection

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores. We consider a fluid-saturated bidispersive porous medium in the vertical layer x ∈(−1/2,1/2) with gravity in the − z (downward) direction. The walls of the layer are maintained at different constant temperatures. A suitable Rayleigh number is defined and we derive a global stability threshold below which no instability may arise. We additionally show that the porous layer is stable for all Rayleigh numbers provided the initial temperature gradient is bounded in a precise sense.