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Drainage dynamics controlled by corner flow: Application of the foam drainage equation

In fast drainage processes water is retained behind the front, defining the plant available water and hydraulic properties of the unsaturated region. In this study we show that the foam drainage equation (FDE) can be applied to predict macroscopic drainage dynamics behind the front because a network of liquid channels controls the liquid flow in both foams and crevices of the pore space. To predict drainage rates at the Darcy scale the FDE is solved numerically after adapting channel geometries and boundary conditions to experimental conditions. The FDE results were in good agreement with measured flow rates behind a drainage front in coarse and fine sand. A notable exception was rapid drainage from fine sand where saturated pore clusters persisted after front passage and drained faster compared to FDE predictions. The dominance of corner capillary flows implied by the good agreement with the FDE formulation could improve the scientific underpinning of the unsaturated hydraulic conductivity function and offers a more realistic view of the geometry of pathways for colloid and pathogen transport in unsaturated media.