Open Boundaries, Anomalous Diffusion and the Darcy-Bénard Instability

The classical problem of the Darcy-Bénard instability in a horizontal porous layer saturated by a binary fluid mixture and subject to a non-uniform solutal concentration field is revisited. In particular, a generalised anomalous diffusion model departing from the classical Fickian diffusion and accounting for subdiffusion or superdiffusion phenomena is employed. At the porous layer boundaries, a uniform vertical concentration gradient is imposed, so that an unstable density stratification arises. The boundaries are modelled as open, meaning that uniform pressure conditions are prescribed. A linear stability analysis of the basic rest state is carried out, showing how the departure from the classical Fickian diffusion affects dramatically the conditions for the onset of the instability.