Wetting front instability: 1. Theoretical discussion and dimensional analysis

Highly nonuniform moisture and solute transport in sandy soils has long been noted. A mechanism for nonuniform transport is an instability in the infiltration flow itself, or wetting front instability. When a wetting front becomes unstable, “fingers” form and move down through the vadose zone to the phreatic surface bypassing much of the unsaturated porous medium. In this paper a theoretical framework for wetting-front-instability experimentation is developed through classical dimensional analysis. Relationships between system parameters and initial/boundary conditions and unstable flow field behavior, as characterized by finger width and finger velocity, are derived. The scaling theory of E. E. Miller and R. D. Miller (1956) is used to generalize these relationships to similar porous media with different mean grain sizes and show the effects of coarseness and fluid properties. Other formulations for finger width, derived through linear stability analysis, are examined to arrive at possible functional forms not yielded by dimensional analysis.

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