J. W. Biggar

Water movement in glass bead porous media: 2. Experiments of infiltration and finger flow

This paper presents experimental observations of infiltration and finger flow in glass beads. In paper 1 (Lu et al., this issue), we showed that the total surface tensile force is much greater in initially wet profiles than in initially dry profiles. During capillary rise in glass beads, the “jump” process takes place for an initially dry condition, whereas in an initially wet profile not only a jump process but a film thickening associated with film flow characterizes capillary rise. In this paper, infiltration experiments into initially dry glass beads show that the wetting front is relatively saturated and flat compared with the unsaturated and irregular wetting front into an initially wet profile. In the experiments of finger flow, photographs show that the tip of the finger is completely water saturated and that no partially saturated zones exist around the saturated tip. The fingers initiated in a dry zone disappear when they reach an initially wet lower zone even when the packing conditions of the glass beads are identical. Hence the criterion for instability when water is applied at a rate less than the value of the saturated hydraulic conductivity does not apply to an initially wet condition. When a fine layer of glass beads lies on a coarse layer that is initially dry, fingering will take place during infiltration and flow is unstable. If the coarse lower layer is initially wet, finger flow does not develop, and the flow remains stable. More investigations are required to ascertain threshold values of the initial water content causing instability of water movement in porous media.

Water movement in glass bead porous media: 1. Experiments of capillary rise and hysteresis

Experimental observations of capillary rise and hysteresis of water or ethanol in glass beads are presented to improve our understanding of those physical processes in porous media. The results provide evidence that capillary rise into porous media cannot be fully explained by a model of cylinders. They further demonstrate that the “Ink bottle” model does not provide an adequate explanation of hysteresis. Glass beads serving as a model for ideal soil are enclosed in a rectangular glass chamber model. A TV camera associated with a microscope was used to record the processes of capillary rise and drainage. It is clearly shown during capillary rise that the fluid exhibits a “jump” behavior at the neck of the pores in an initially dry profile or at the bottom of the water film in an initially wet profile. Under an initially dry condition, the jump initiates at the particle with smallest diameter. The jump process continues to higher elevations until at equilibrium the surface tensile force is balanced by the hydrostatic force. The wetting front at that time is readily observed as flat and saturated. Under an initially wet condition, capillary rise occurs as a water film thickening process associated with the jump process. Trapped air behind the wetting front renders the wetting front irregular and unsaturated. The capillary rise into an initially wet porous medium can be higher than that into an initially dry profile. During the drying process, large surface areas associated with the gas-liquid interface develop, allowing the porous medium to retain more water than during the wetting process at the same pressure. That mechanism explains better the hysteresis phenomenon in porous media in contrast to other mechanisms that now prevail.

Evaluation of methods for determining soil-water retentivity and unsaturated hydraulic conductivity

The transport of dissolved contaminants through the vadose zone is a major source of soil and groundwater contamination. Soil hydraulic properties must be determined to accurately describe water and contaminant transport and potential environmental impacts. Comparisons were made of three field and three laboratory methods for estimating soil-water retention, &thetas;(Ψ), and unsaturated hydraulic conductivity functions, K(&thetas;). Instrumentation was installed in 36 field plots, and two redistribution cycles were conducted. Field data obtained from each cycle were utilized in three outflow-based field methods; (i) instantaneous profile method, (ii) Libardis method, and (iii) a nonlinear least squares approach. Undisturbed soil cores were extracted from 24 field plots at six depths and used in laboratory tests. Techniques consisted of (i) a multi-step outflow approach coupled with (a) “inverse methodology” for transient conditions and (b) a least-squares approach for equilibrium conditions and (ii) a particle size distribution model. Parametric models were coupled with the modeling efforts. The results obtained by the in situ instantaneous profile method for both soil hydraulic functions were considered to hold the greatest validity. However, the multi-step outflow methods produced feasible &thetas;(Ψ) curves, and the inverse methodology was time efficient. Libardis method for determining K(&thetas;) relationships was accurate at deep profile depths but failed at shallow ones.

Fractal description of wetting front instability in layered soils.

Fractal theory was applied to describe fingering structure and to estimate the effective surface tension at the wetting front during infiltration. A scale length of mean pore size was used to estimate the microscopic system length of fingering. After bulk surface tension was replaced by effective surface tension in a linear stability theory, theoretical maximum wavelengths agreed with those of experimental results when fingering developed in quartz sand beneath Oakley sand, but not beneath Yolo clay.

Probability Distribution of Solute Travel Time for Convective Transport in Field‐Scale Soils Under Unsteady and Nonuniform Flows

This study addresses the development of probability distributions of travel times for one-dimensional (vertical) solute transport in soils. The field-scale soils are considered heterogeneous, with stationary fluctuations of soil hydraulic properties in the horizontal direction but nonstationary fluctuations of these properties in the vertical direction due to layering of the soil, which induces nonstationary heterogeneity. Approximate ensemble probability distribution functions of conservative solute travel time for vertical convective solute transport were derived directly from the convective transport stochastic partial differential equation, under both deterministic and stochastic soil surface water flux (infiltration rate) and under unsteady and nonuniform soil water flows. General depth-varying initial and time-varying boundary conditions were used in these derivations. The magnitude of the approximation in the theoretical probability distribution functions of travel time is quantified mathematically. Utilizing the soil water content data from a University of California, Davis, field site, it is shown that the mathematical condition for this approximation is satisfied for this field. The spatial heterogeneity is represented through a nonstationary soil water content random field which covaries both in time and in space. Dispersion emerges naturally in the derived ensemble probability distribution functions of solute travel time, owing to the stochasticity of soil water content at field scale. Then the theoretical expression for mean solute concentration over a field is derived, by means of the theoretical solute travel time distribution, as a function of time and soil depth, under vertical transport with rectangular pulse solute loading for the upper boundary condition. Comparisons of theoretical probability density functions of solute travel time against their empirical counterparts, obtained from field experimental observations under steady but nonuniform soil water flow, show good agreement. Comparisons of theoretical mean solute concentrations, as they evolve with time and soil depth, against field experimental observations also show good agreement. However, further field experiments under unsteady flow conditions are required for the comprehensive validation of the developed theory.