Immiscible Displacement in Porous Media: Stability Analysis of Three‐Dimensional, Axisymmetric Disturbances With Application to Gravity‐Driven Wetting Front Instability

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Abstract
As water infiltrates downward into an air‐filled, water wettable porous medium, the wetting front which forms may become unstable and allow the formation of downward moving fingers within the vadose zone. In this paper we first review stability criteria and estimated finger widths determined from linear stability theory in two‐dimensional systems. Two approaches reported in the literature which employ different formulations for the interfacial boundary conditions, yield different estimates of the finger width. We extend the analyses to investigate finger diameter in three‐dimensional systems by considering axisymmetric disturbances. Results of the three‐dimensional analyses are illustrated through comparison to previously reported experimental results in three‐dimensional systems. Because either approach gives similar results for low system fluxes, in practice, it probably will not matter which formulation is used. However, one approach represents the data better and contains only traditionally measured porous media properties.