Drainage characteristics of porous media are shaped by an interplay between gravitational, capillary and viscous forces that result in complex phase invasion patterns and dynamics. We propose a mechanistic model for viscous separation of temporary phase detention behind rapidly moving drainage fronts. The viscous-limited region forming behind the front tip (tip of furthest penetrated air finger) drains at a slower rate with a characteristic time scale s dictated by hydraulic decoupling expressed by the hydraulic properties of the medium. The region where saturation becomes viscously detained (temporarily entrapped) is determined by a critical water content u crit that defines a viscous length L V behind the front tip. Theory developed to predict the critical water content u crit and the characteristic secondary timescale s was in good agreement with measured drainage characteristics using neutron radiography and direct imaging. The observed critical water content u crit increased with higher drainage rates as predicted by theory with consideration of a percolation threshold. The observed slow drainage timescale s as a function of mean drainage rate depended on the critical water content u crit and the resulting counteracting effects of increased detained liquid volume and increased conductivity of the viscous limited region. The concept of drainage zonation illustrates how increasing flow rates enhances the extent of viscous limitations behind the main drainage front. The new insights could be useful for management of immiscible fluid displacement, quantification of averaging effects in experimental measurements (dynamic effects on p c -S relationship), and explain some of the underpinnings of the field capacity phenomenon.

Water drainage from porous media is a highly dynamic process often marked by rapid piston‐like air invasion events at the front and other rapid interfacial reconfigurations. Liquid phase entrapped behind the moving front drains at significantly slower rates often via gravity driven flow through corners and crevices. This distribution of slowly draining residual water phase determines the plant available water and biological functioning of soils. The study aims to determine the conditions for the flow regime transition from piston‐like invasion at a drainage front to slower corner dominated flow at the pore and sample scale. This transition was observed experimentally for sand and glass beads with fast X‐ray tomography, revealing water fragmentation into clusters of full pores interconnected by water corner films. The observed liquid morphology at the transition from piston to corner flow was reproduced by a quasi‐static pore network model and predicted by percolation theory. The amount of capillary‐retained water at flow transition controlling the subsequent drainage dynamics could be reproduced by an idealized star shaped pore whose geometry is deduced from macroscopic properties of the porous medium. Predictions of water content thresholds at flow transitions were in agreement with other critical saturation values associated with cessation of solute diffusion and of internal drainage (at field capacity) highlighting the criticality of water phase continuity disruption for formation of relatively stable unsaturated conditions controlled by slow corner flow that support life in soil.

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.

Similarity in liquid‐phase configuration and drainage dynamics of wet foam and gravity drainage from unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation—SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. The study provides new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions. Two novel analytical solutions for saturation profile evolution were derived and tested in good agreement with a numerical solution of the SFDE. The study and the proposed solutions rectify the original formulation of foam drainage dynamics of Or and Assouline (2013). The new framework broadens the scope of methods available for quantifying unsaturated flow in porous media, where the intrinsic conductivity and geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

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