Wetting Front Instability Research Articles

A two dimensional semi-continuum model to explain wetting front instability in porous media

Modelling fluid flow in an unsaturated porous medium is a complex problem with many practical applications. There is enough experimental and theoretical evidence that the standard continuum mechanics based modelling approach is unable to capture many important features of porous media flow. In this paper, a two-dimensional semi-continuum model is presented that combines ideas from continuum mechanics with invasion percolation models. The medium is divided into blocks of finite size that retain the nature of a porous medium. Each block is characterized by its porosity, permeability, and a retention curve. The saturation and pressure of the fluids are assumed to be uniform throughout each block. It is demonstrated that the resulting semi-continuum model is able to reproduce (1) gravity induced preferential flow with a spatially rich system of rivulets (fingers) characterized by saturation overshoot, (2) diffusion-like flow with a monotonic saturation profile, (3) the transition between the two. The model helps to explain the formation of the preferential pathways and their persistence and structure (the core and fringe of the fingers), the effect of the initial saturation of the matrix, and the saturation overshoot phenomenon.

Measurement of saturation overshoot under grass cover

The paper deals with non-destructive measurement of water infiltration into homogenous soil (Haplic Chernozem) covered by grass. The experimental site was located in Most pri Bratislave (Slovakia) in the Pannonian Basin at a height of 130 m above sea level. Radioactive tracer technique was used to determine the water content of the soil profile during water infiltration. A mixture of the radioactive iodine 131I (chemical form Na131I) and the NaI solution was used as a tracer. The tracer distribution in the soil was measured by the Geiger-Muller detector connected to the nuclear analyser. Gravity-driven fingers were detected in the soil under the grass cover as a consequence of the wetting front instability. The instability manifested itself as a non-monotonic moisture profile caused by saturation overshoot and a varying discharge from the soil profile in time.

Interplay between Fingering Instabilities and Initial Soil Moisture in Solute Transport through the Vadose Zone

Modeling water flow and solute transport in the vadose zone is essential to understanding the fate of soil pollutants and their travel times towards groundwater bodies. It also helps design better irrigation strategies to control solute concentrations and fluxes in semiarid and arid regions. Heterogeneity, soil texture and wetting front instabilities determine the flow patterns and solute transport mechanisms in dry soils. When water is already present in the soil, the flow of an infiltration pulse depends on the spatial distribution of soil water and on its mobility. We present numerical simulations of passive solute transport during unstable infiltration of water into sandy soils that are prone to wetting front instability. We study the impact of the initial soil state, in terms of spatial distribution of water content, on the infiltration of a solute-rich water pulse. We generate random fields of initial moisture content with spatial structure, through multigaussian fields with prescribed correlation lengths. We characterize the patterns of water flow and solute transport, as well as the mass fluxes through the soil column. Our results indicate a strong interplay between preferential flow and channeling due to fingering and the spatial distribution of soil water at the beginning of infiltration. Fingering and initial water saturation fields have a strong effect on solute diffusion and dilution into the ambient water during infiltration, suggesting an effective separation between mobile and inmobile transport domains that are controlled by the preferential flow paths due to fingering.

Quantitative analysis of wetting front instabilities in soil caused by treated waste water irrigation

Irrigation with treated waste water (TWW) is a common practice in agriculture, mainly in arid and semiarid areas as it provides a sustainable water resource available at all-season in general and at freshwater shortage in particular. However, TWW still contains abundant organic material which is known to decrease soil wettability, which in turn may promote flow instabilities that lead to the formation of preferential flow paths. We investigate the impact of long-term TWW irrigation on water wettability and infiltration into undisturbed soil cores from two commercially used orchards in Israel. Changes of water content during infiltration were quantitatively analysed by X-ray radiography. One orchard (sandy clay loam) had been irrigated with TWW for more than thirty years. In the other orchard (loamy sand) irrigation had been changed from freshwater to TWW in 2008 and switched back in some experimental plots to freshwater in 2012. Undisturbed soil cores were taken at the end of the dry and the rainy season to investigate the seasonal effect on water repellency and on infiltration dynamics in the laboratory. The irrigation experiments were done on field moist samples. A test series with different initial water contents was run to detect the influence on water movement at different wettabilities. In this study we show that the infiltration front stability is dependent on the history of waste water irrigation at the respective site and on the initial water content.

Effects of different management practices on vertical soil water flow patterns in the Loess Plateau

Different management practices are adopted to ensure sustainable development in agriculture and to maintain ecological environment security. However, the soil water infiltration types under different management practices were still unclear. This study was designed to assess the effect of different management practices on the water flow behavior of soil. Four management practices were carefully selected. Plot 1 was uncultivated field, Plot 2 contained alfalfa (Medicago sativa L.) and was untilled for two years (alfalfa field), Plot 3 contained maize (Zea mays L.) with conventional tillage from 2008 to 2015 (conventional tillage field), and Plot 4 contained maize with conservation tillage from 2008 to 2015 (conservation tillage field). Soil physical properties (e.g., gravimetric water content, soil bulk density, total porosity, and saturated water content) in the top 50cm layer were measured following conventional methods A dye tracer was introduced to these plots, and the different types of water flows were visualized using classified dye-stained patterns. In the uncultivated field, preferential flow was triggered by wetting front instabilities and generally confined to the upper 15cm of the soil profile. The presence of preferential paths (alfalfa taproot) in the alfalfa field resulted in high and continuous preferential flow. The macropore flow bypassed the compacted soil and was confined into two isolated patches, making it the dominant flow behavior in the conventional tillage field. Conservation tillage systems enhanced the continuity and connectivity of the macropore system and converted the shape of the preferential flow to an inverted triangular distribution. The order of continuity and connectivity degree for the macropore system from highest to lowest was alfalfa field, conservation tillage field, uncultivated field, and conventional tillage field. Above mentioned results that were newly achieved from this study highlighted a significant change in soil water storage and flow behaviors with different management practices compared with those of uncultivated land. The present study suggests that local governments and farmers would prefer alfalfa field and conservation tillage field to other management measures.

Hydropedology and Preferential Flow in the Tasmanian Texture‐Contrast Soils

The two‐way interaction between soil morphology and the processes governing soil water movement were investigated for a range of texture‐contrast soil profiles. The texture‐contrast soils consisted of a seasonally water‐repellent sandy loam A1 horizon over a bleached silica‐cemented A2e horizon and a mottled vertic clay subsoil. Differences in soil morphology and structure among sites had little influence on the proportion of soil that participated in infiltration or the maximum depth of infiltration; however, differences in subsoil structure influenced the processes by which water infiltrated and was stored within the B2 horizons. The occurrence of preferential flow was largely controlled by the effects of antecedent soil moisture content on water repellence in the A1 horizon, silica bridging in the A2e horizon, and clay shrinkage in the B2 horizons. Under dry soil conditions, infiltration resulted from up to five different forms of preferential flow. When soils were near field capacity, most forms of preferential flow ceased; however, wetting front instability and lateral flow developed in the A1 horizon. Preferential flows are not thought to have contributed to the pedogenesis of the texture‐contrast soils. Development of the contrasting soil texture horizons, sand infills, and bleached A2e horizons developed before and independently of the observed preferential flow processes in which reworked aeolian sands buried previously developed clay columns.

Development of Unstable Flow and Reduced Hydraulic Conductivity due to Water Repellence and Restricted Drainage

The effect of water repellence and antecedent soil moisture on wetting front stability and infiltration rate are reported for a seasonally water repellent topsoil. The effect of water repellence on infiltration was determined by comparing the in situ infiltration of water to that of a 7M ethanol solution. Wetting front stability was measured during infiltration of water into repacked, wettable and water repellent soils, within a Hele‐Shaw chamber. Water repellence restricted in situ movement of water through large macropores (>500 μm), which decreased intrinsic permeability by 1 to 2 orders of magnitude. In repacked soils, water repellence caused the development of unstable wetting fronts and reduced infiltration from 240 mm h−1 to 101.7 mm h−1. Infiltration into wettable soils at moisture contents near field capacity was expected to result in rapid infiltration and stable wetting fronts. However in repacked soils, wetting front instability developed, and infiltration rates were 190% lower when air and/or water movement through the base of the chamber was restricted. Infiltration into in situ soil was also slower at high antecedent soil moisture. The hydraulic conductivity of the 7M ethanol solution decreased significantly from 112.3 mm h−1 in dry water repellent conditions, to 35.6 mm h−1 in wettable soils at high antecedent moisture contents. Consequently the previously reported development of wetting front instability and reduced infiltration into in situ wettable soils at high moisture contents were confirmed and attributed to difficulty displacing existing soil water during infiltration of new water.

Reviewing classical studies in soil physics “Theoretical analysis of wetting front instability in soils” by J.-Y. Parlange and D.E. Hill Soil Science, Vol. 122, No. 4, 236–239 (1976)

Reviewing classical studies in soil physics “Theoretical analysis of wetting front instability in soils” by J.-Y. Parlange and D.E. Hill Soil Science, Vol. 122, No. 4, 236–239 (1976)

Stability analysis of a phase-field model of gravity-driven unsaturated flow through porous media

The formation of preferential flow paths during infiltration of water into homogeneous, dry soil is an important phenomenon whose explanation and prediction have remained elusive under the standard theories of multiphase flow in porous media. We have recently proposed a macroscopic phase-field model of unsaturated flow in porous media, which explains why such fingering occurs [L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 101, 244504 (2008)]. Here we present a linear stability analysis of the proposed model for constant-flux infiltration, which allows a quantitative description of the wetting front instability. The present analysis stresses the critical role of the initial water saturation and applied flux ratio in the asymptotic stability of the system, as well as in the transient growth of perturbations, which is consistent with the experimental evidence. The trends in the frequency and growth factor of the most unstable modes predicted by our analysis are also in quantitative agreement with experimental measurements.

Pressure Head Profile within Growing Fingers in Initially Dry Glass Beads

Wetting front instability is one of the mechanisms producing preferential flow in soils. In this study, we measured the pressure head within growing fingers in three-dimensional soil columns and examined the applicability of the prefingered flow theory and the similarity solution. The pressure head within a growing finger was measured during infiltration into a porous medium consisting of fine over coarse layered glass beads in a transparent, acrylic column. To ensure the measurement of pressure heads within growing fingers whose pathways cannot be known a priori, we made 10 insertion ports for every measurement position in the column. The fingertip velocity was essentially constant with time, while the infiltration rate increased. Fingers merged as they grew, which complicated the finger flow physics in three dimensions. The profiles of the pressure head were nearly linear during early finger growth. As the finger lengthened, the pressure head at all measured points decreased to an almost constant value. The prefingered flow model showed good applicability not only to induction zone formation, but also to the early finger growth when it remained saturated. Conversely, the similarity solution was not as applicable to growing fingers that were not in a steady state.

Wetting front instabilities: a three-dimensional experimental investigation

Wetting front instability or fingering experiments were conducted in three-dimensional infiltration columns, featuring stratified fine-over-coarse texture porous media, to investigate the influences of various soil and wetting phase properties on finger diameter and propagation velocity. The system parameter varied in this study included permeability, system flux rate, media size and gradation uniformity, initial moisture content, viscosity, density, and surface tension. The influence of each parameter is discussed and compared, where applicable, to the finding of previous studies. Finger diameter and velocity data were acquired using a neutron radioscopy based, real-time imaging system. Through the use of the imaging system, a very accurate and reliable experimental data set was produced for three-dimensional fingering events.

The Pressure Head Regime in the Induction Zone During Unstable Nonponding Infiltration: Theory and Experiments

Fingered flow rapidly moves water and pollutants from the root zone to the groundwater through a limited fraction of the unsaturated zone, limiting the possibilities for decay and adsorption. The onset of wetting front instability and the characteristics of the flow pattern under nonponding infiltration have received limited attention. We aim to theoretically and experimentally advance our understanding of pre‐fingered flow, and contrast fingered flow under ponding and nonponding conditions. We developed a Green‐Ampt based expression for the pressure head in a developing induction zone (from which fingers protrude) for the time before fingers developed. A uniform, nonponding water flux was applied to the surface of two‐dimensional glass bead porous media with a dry region above a capillary fringe. Microtensiometers recorded pressure heads in the induction zone. The pressure head data confirmed both the theoretical early‐time pre‐finger model, and a model developed earlier for late‐time lateral flow toward fully developed fingers. The physically more realistic constant flux boundary condition of our experiments gave larger finger spacings and travel times, compared to the frequently used set‐up with ponding infiltration into a fine‐over‐coarse porous medium.

Pressure head distribution during unstable flow in relation to the formation and dissipation of fingers

Abstract. Wetting front instability creates a shallow induction zone from which fingers emerge that rapidly transport water and solutes downwards. How the induction zone affects finger location and spacing is unknown. In the moist subsoil, fingers may well dissipate because the finger tips no longer have to overcome the water entry value. Both flow regions were investigated in a two-dimensional chamber with a fine-over-coarse glass bead porous medium. A capillary fringe was created by upward wetting through capillary rise. Upon ponding with dye-coloured water, fingers emerged, propagated downward and diverged when reaching the capillary fringe. Microtensiometers were installed in the induction zone, the fingers, and in the capillary fringe. In the induction zone, a lateral sinusoidal pressure head developed within minutes. Only in one of two experiments could the observed pressure head pattern be satisfactorily reproduced by a steady-state model assuming uniform induction zone properties and uniform infiltration. Later, fingers emerged below the pressure head minima. The induction zone did not affect finger properties. The pressure head in the induction zone was determined by the depth of the finger tips. The water requirement of the fingers dictated the lateral pressure head gradients. The pressure heads in the capillary fringe supported the hypothesis that the flow stabilised and dissipated there. Keywords: fingered flow, wetting front instability, unsaturated flow, microtensiometers, induction zone, capillary fringe

Stability analysis of the unsaturated water flow equation: 2. Experimental verification

In this study, we verify the stability analysis of the unsaturated flow equation presented in paper 1. We compare finger sizes measured in laboratory experiments with predictions by the stability model. Using measured unsaturated hydraulic properties which are fitted and extrapolated over the entire water content range, the model enables us to predict finger sizes over a wide range of nonponding infiltration rates. The model predicts an increase of finger diameter at high and low infiltration rates for all soils. Such increases were also observed in our experiments. The model yields reliable predictions of finger diameters at high and intermediate infiltration rates but does not perform as well at infiltration rates <1 cm/h. This is caused by experimental limitations in accurately measuring hydraulic conductivities at low infiltration rates. A sensitivity analysis for initial water content and the shape parameter of the hydraulic conductivity curve showed that a small change of the parameters resulted in a relatively small change of finger size at high and intermediate infiltration rates but at low infiltration rates the finger size change was large, i.e., several orders of magnitude. We conclude that the stability model presented in paper 1 can be used for the assessment of wetting front instabilities in homogeneous soils over a wide range of nonponding infiltration rates.

Modeling fingered flow of water in soils owing to wetting front instability: a review

Fingered flow in the unsaturated zone caused by wetting front instability enhances solute leaching to the groundwater. This paper reviews recent progress in fingered flow research, focusing on theoretical results and model development. A variety of stability criteria have been derived to predict wetting front instability, mainly through linear, and sometimes non-linear, stability analysis, but also by theoretically analyzing infiltration into dry soils, and by stochastic methods that take into account random variations of the soil properties, fluid pressure, and front location. These stability criteria are discussed and compared. Eight expressions for finger size are presented. They fall into three categories based on the dependence on the ratio of the infiltration rate to the soil hydraulic conductivity in the finger. Next, the modeling of finger growth is discussed. Because of its relevance to solute transport, recent advances in the measurement and modeling of finger behavior in moist soils are thoroughly reviewed. Various models (ranging from easily applied closed-form equations for risk assessment to sophisticated transient numerical codes) have been developed over the past 15 years. These are discussed and selected results are shown. Finally, some remaining gaps in our understanding are given. Among these are the role of the initial water content, the nature of the flow in the distribution zone above the fingers, the effect of soil heterogeneity on wetting front instability, and the combined effect of soil heterogeneity and wetting front instability on field-scale solute transport.

Effects of soil water repellency on infiltration rate and flow instability

Laboratory infiltration experiments were carried out to quantify the effects of soil water-repellency on infiltration rate and the wetting front instability. A two-dimensional transparent chamber (41.5cm wide, 50cm high and 2.8cm thick) was constructed for infiltration experiments using three water-repellent Ouddorp sands (The Netherlands) and a wettable silicon sand. The results showed that if the water-ponding depth (h0) at the soil surface was lower than the water-entry value (hwe) of repellent sands, infiltration would not start until the water drop penetration time (WDPT) is exceeded; and contrary to infiltration in wettable soils, the infiltration rate increased with time. However, infiltration could immediately start at any time when h0>hwe. The wetting front was unconditionally unstable for h0<hwe, resulting in fingered flow. However, the flow was conditionally stable for h0>hwe if the soil was not layered in a fine-over-coarse or wettable-over-repellent configuration, and if soil air was not compressed during infiltration. The occurrence of stable and unstable flow in repellent soils was consistent with the prediction based on a linear instability analysis. The findings can be used to improve irrigation efficiencies in water repellent soils, e.g. using high-ponding irrigation methods.

Soil water content dependent wetting front characteristics in sands

The initial soil water content affects wetting front instability. A series of experiments were conducted where water was infiltrated into a 20/30 sand with initial volumetric water contents of 0, 0.005, 0.01, 0.015, 0.02, 0.03, 0.04 and 0.047cm3/cm3. Both water content and matric potential were measured. Water content was measured with Synchrotron X-rays at the Cornell High Energy Synchrotron Source (CHESS) and matric potential with fast responding tensiometers. The flow field changed gradually from unstable fingered flow at 0% initial water content to a wetting pattern that can be described with Richards’ equation without hysteresis. For unstable flow, the matric potential and water content decreased a short distance behind the wetting front. Except in the initially dry soil, the finger pattern began to widen immediately after infiltration. The pressure and water content of the wetting front were hyperbolically related to the initial water content. In general, this research showed that in coarse soils when an unstable wetting front occurs both the matric potential and water content drop behind the wetting front while, when a stable Richards’ type wetting front forms, the matric potential and water content increase (slightly) behind the wetting front.

Modelling solute leaching during fingered flow by integrating and expanding various theoretical and empirical concepts

Wetting front instability (fingered flow) accelerates solute transport through the unsaturated zone to the groundwater table. Whether fingers widen or dissipate close to the groundwater is unclear. Water flow in a two-dimensional artificial capillary fringe below a dry layer exhibiting fingered flow was investigated. The flow diverged strongly in the wet soil, suggesting that fingers dissipate. Expressions for the finger radius in dry and wet soil were combined and adapted to a soil hydraulic property parameterization popular in numerical modelling. The modified equation provided finger radii for soils in humid and arid climates. The fingers in the arid soil were excessively wide. The finger radii were used to model solute transport, assuming fingers dissipated in the subsoil. Modelling was cumbersome for the arid climate. One shower may often be insufficient to trigger fingering in arid regions with short, heavy showers. In soils with shallow groundwater, the diverging subsoil flow determines solute leaching.

Prediction of fingering in porous media

Immiscible displacement, involving two fluids in a porous medium, can be unstable and fingered under certain conditions. In this paper, the original linear instability criterion of Chuoke et al. [1959] is generalized, considering wettability of two immiscible fluids to the porous medium. This is then used to predict 24 specific flow and porous medium conditions for the onset of wetting front instability in the subsurface. Wetting front instability is shown to be a function of the driving fluid wettability to the medium, differences in density and viscosity of the fluids, the magnitude of the interfacial tension, and the direction of flow with respect to gravity. Scenarios of water and nonaqueous‐phase liquid infiltration into the vadose zone are examined to predict preferential flow and contamination of groundwater. The mechanisms of finger formation, propagation, and persistence in the vadose zone are reviewed, and the existing equations for calculating the size, the number and velocity of fingers are simplified for field applications. The analyses indicate that fingers initiate and propagate according to spatial and temporal distribution of the dynamic breakthrough (water‐ or air‐entry) pressures in the porous medium. The predicted finger size and velocity are in close agreement with the experimental results.

SIMILITUDE REQUIREMENTS FOR MODELLING NAPL MOVEMENT WITH A GEOTECHNICAL CENTRIFUGE.

Keywords MASSACHUSETTS TECHNOLOGY INSTITUTE, MIT, EDINBURGH UNIVERSITY CENTRIFUGES, GEOTECHNICAL, MOVEMENT, MODELLING, NON AQUEOUS, PHASE, LIQUIDS, NAPL, TRANSPORT, SIMILITUDE, MODELS, GEOTECHNICS, MEDIA, POROUS, SCALING, STUDIES, SUBSURFACE, UNDERGROUND, WETTING, MIGRATION, INSTABILITY, BEHAVIOUR, GROUNDWATER, POLLUTION, REQUIREMENTS, RELATIONSHIPS... Show All