Coupled effect of viscosity and density gradients on fingering instabilities of a miscible slice in porous media

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Miscible displacements in porous media exhibit interesting spatio-temporal patterns. A deeper understanding of the physical mechanisms of these emergent patterns is relevant in a number of physicochemical processes. Here, we have numerically investigated the instabilities in a miscible slice in vertical porous media. Depending on the viscosity and density gradients at the two interfaces, four distinct flow configurations are obtained, which are partitioned into two different groups, each containing a pair of equivalent flows until the interaction between the two interfaces. An analysis of the pressure drop around the respective unstable interface(s) supports numerical results. We classify the stabilizing and destabilizing scenarios in a parameter space spanned by the log-mobility ratio (R) and the displacement velocity (U). When the viscosity and density gradients are unstably stratified at the opposite interfaces, the stability characteristics are very complex. The most notable findings of this paper are the existence of a stable region between two unstable regions in the R–U plane and occurrence of secondary instabilities. We further show that the stability regions in the R–U plane depend strongly on the slice width, and beyond a threshold value of it the stable zone remains almost unaltered. For thin sample, the stable region expands and the secondary instabilities disappear.