Premium
Immiscible Displacement in Porous Media: Stability Analysis of Three‐Dimensional, Axisymmetric Disturbances With Application to Gravity‐Driven Wetting Front Instability
Author(s) -
Glass R. J.,
Parlange J.Y.,
Steenhuis T. S.
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr00836
Subject(s) - instability , porous medium , wetting , rotational symmetry , mechanics , displacement (psychology) , richards equation , vadose zone , stability (learning theory) , materials science , geotechnical engineering , porosity , geology , physics , computer science , composite material , water content , groundwater , psychology , machine learning , psychotherapist
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.