SALT-FINGER INSTABILITY IN AN ANISOTROPIC AND INHOMOGENEOUS POROUS SUBSTRATE UNDERLYING A FLUID LAYER

In the directional solidification of a binary liquid, salt-finger and plume convection are the two major types of fluid motion that occur when the lighter species is rejected from the solid. Fingering convection is usually observed prior to the initiation of plume formation. When the nominally planar liquid-solid interface is morphologically unstable, solidification is dendritic. Consequently, the melt is separated from the solid by a mushy zone consisting of solid dendrites and interdendritic liquid. This can be considered to be a porous layer with anisotropic and inhomogeneous permeability and, possibly, thermal and solutal diffusivities. A linear stability analysis is empoyed to study salt-finger instability in a fluid layer bounded above by a rigid wall and below by an anisotropic and inhomogeneous porous medium saturated by the same fluid. The effects of anisotropy and inhomogeneity on the stability characteristics are discussed for a variety of porous media. Results are also presented for a porous medium for which the anisotropy and inhomogeneity of the permeability and thermal and solutal diffusivities have been obtained experimentally during the directional solidification of aqueous ammonium chloride solutions. The nature of the instability modes relevant to the present problem are also discussed. Based on the present results, a relationship is proposed between salt-finger and plume convection during directional solidification. Methods for inhibiting salt-finger convection are also suggested, and the feasibility of their implementation is discussed.