The Effect of Boundary Conditions on the Onset of Buoyancy-Driven Convection in a Brine-Saturated Porous Medium

The effect of a boundary condition on the onset of buoyancy-driven convection in a fluid-saturated porous medium was analyzed theoretically. Taking into account of the partially permeable zone, new linear stability equations and boundary conditions are derived in the semi-infinite domain. For the linear stability analysis, we express disturbance fields employing the spectral theory and obtain the stability conditions using eigenanalysis and initial value problem approaches. The present linear stability limits were consistently determined regardless of the solution methods. The present analyses suggest that the capillary transition zone makes the system more unstable.