M. Gentile

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.

Hyperbolic diffusion with Christov-Morro theory

We employ recent ideas of C.I. Christov and of A. Morro to develop a theory for diffusion of a solute in a Darcy porous medium taking convection effects into account. The key point is that the solute evolution is not governed by a parabolic system of equations. Indeed, the theory developed is basically hyperbolic. This still leads to a model which allows for convective (gravitational) overturning in a porous layer, but in addition to the classical mode of stationary convection instability there is the possibility of oscillating convection being dominant for a lower salt Rayleigh number, if the relaxation time is sufficiently large.