A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Wave-induced seepage flux into anisotropic seabeds

Considerable effort has been devoted to quantifying the wave-induced soil response in a porous seabed in the last few decades. Most previous investigations have focused on the analysis of pore pressure and effective stresses within isotropic sediments, despite strong evidence of anisotropic soil behaviour reported in the literature. Furthermore, the seepage flux, which is important in the context of contaminant transport, has not been examined. In this paper, we focus on water wave-driven seepage in anisotropic marine sediments of finite thickness. The numerical results predict that the effects of hydraulic anisotropy and anisotropic soil behaviour on the wave-driven seepage in marine sediment are significant. Copyright (C) 2001 John Wiley & Sons, Ltd.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Dormancy release in Australian fire ephemeral seeds during burial increases germination response to smoke water or heat

Fire ephemerals are short-lived plants that primarily germinate after fire. Fresh and laboratory-stored seeds are difficult to germinate ex situ, even in response to fire-related cues such as heat and smoke. Seeds of eight Australian fire ephemeral species were buried in unburnt and recently burnt sites of natural bushland during autumn. Seeds were exhumed after 6 and 12 months and incubated in water and smoke water, either with or without a heat treatment at 70 degrees C for 1 h. Generally, germination did not increase after 6 months of burial, but after 12 months of burial germination was enhanced in seven of the eight species. Actinotus leucocephalus produced higher germination following 12 months of burial without any further treatment, and smoke water and heat further improved germination. The four Gyrostemonaceae species, Codonocarpus cotinifolius, Gyrostemon racemiger, Gyrostemon ramulosus and Tersonia cyathiflora, only germinated in the presence of smoke water, and their germination was enhanced by burial. Burial improved germination in response to a heat treatment in Grevillea scapigera and Alyogyne huegelii seeds, but did not enhance Alyogyne hakeifolia germination. During concurrent dry laboratory storage of seeds at 15 degrees C, only Actinotus leucocephalus produced increased germination in response to smoke water and heat over time. In summary, soil burial can alter the dormancy status of a number of Australian fire ephemeral seeds, rendering them more responsive to germination cues such as smoke water and heat. The requirement for a period of burial before seeds become responsive to smoke and/or heat would ensure that seeds persist in the soil until a subsequent fire, when there is an increase in nutrients available for growth and reduced competition from other plants.

Effect of vehicle pretreatment on the flux, retention, and diffusion of topically applied penetrants in vitro

Purpose. The flux of a topically applied drug depends on the activity in the skin and the interaction between the vehicle and skin. Permeation of vehicle into the skin can alter the activity of drug and the properties of the skin barrier. The aim of this in vitro study was to separate and quantify these effects. Methods. The flux of four radiolabeled permeants (water, phenol, diflunisal, and diazepam) with log K-oct/water values from 1.4 to 4.3 was measured over 4 h through heat-separated human epidermis pretreated for 30 min with vehicles having Hildebrand solubility parameters from 7.9 to 23.4 (cal/cm(3))(1/2). Results. Enhancement was greatest after pretreatment with the more lipophilic vehicles. A synergistic enhancement was observed using binary mixtures. The flux of diazepam was not enhanced to the same extent as the other permeants, possibly because its partitioning into the epidermis is close to optimal (log K-oct 2.96). Conclusion. An analysis of the permeant remaining in the epidermis revealed that the enhancement can be the result of either increased partitioning of permeant into the epidermis or an increasing diffusivity of permeants through the epidermis.

Quantifying effects of soil heterogeneity on groundwater pollution in four sites in the USA

Four sites located in the north-eastern region of the United States of America have been chosen to investigate the impacts of soil heterogeneity in the transport of solutes (bromide and chloride) through the vadose zone (the zone in the soil that lies below the root zone and above the permanent saturated groundwater). A recently proposed mathematical model based on the cumulative beta distribution has been deployed to compare and contrast the regions' heterogeneity from multiple sample percolation experiments. Significant differences in patterns of solute leaching were observed even over a small spatial scale, indicating that traditional sampling methods for solute transport, for example the gravity pan or suction lysimeters, or more recent inventions such as the multiple sample percolation systems may not be effective in estimating solute fluxes in soils when a significant degree of soil heterogeneity is present. Consequently, ignoring soil heterogeneity in solute transport studies will likely result in under- or overprediction of leached fluxes and potentially lead to serious pollution of soils and/or groundwater. The cumulative beta distribution technique is found to be a versatile and simple technique of gaining valuable information regarding soil heterogeneity effects on solute transport. It is also an excellent tool for guiding future decisions of experimental designs particularly in regard to the number of samples within one site and the number of sampling locations between sites required to obtain a representative estimate of field solute or drainage flux.

Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Prediction of steady-state flux through variably saturated zones within a septic absorption trench

This paper describes effluent flow dynamics within a septic absorption system and the prediction of flow through the biomat and sub-biomat zone. Using soil hydraulic properties in a one dimensional model we demonstrate how soil hydraulic properties interact with biomat resistances to determine long-term acceptance rate (LTAR). The LTAR is a key parameter used in the Australian and New Zealand Standard AS1547:2000 to calculate the area of trench required to ensure trenches are not overloaded. Results show that several orders of magnitude variation in saturated hydraulic conductivity (Ks) collapse to a one order of magnitude variation in LTAR. These results are calculated from a model using basic flow theory, allowing LTAR to be estimated for any combination of biomat resistance and soil hydraulic properties. To increase the reliability of prediction of septic trench hydrology, HYDRUS 2D was used to model two dimensional flow. For more permeable soils, the exfiltration zone above sidewall biomat growth is shown to be a key pathway for excess effluent flow.

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψa is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of Ψa. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψa, fsingle and fcovered are related. The Monte-Carlo data was an excellent match with analytical solutions of fcovered and fsingle as a function of Ψa. At low Ψa, the proportion of the surface covered by drops (fcovered) was equal to Ψa. As Ψa increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops (fsingle) falls exponentially with increasing Ψa. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for fsingle by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.

Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation. (c) 2006 Elsevier Ltd. All rights reserved.

Experimental Analysis of Froude Number Effect on Air Entrainment in the Hydraulic Jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in rectangular horizontal flume with partially-developed inflow conditions. The vertical distributions of void fraction and air bubbles count rate were recorded for inflow Froude number Fr1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction Cmax increases with the increasing Fr1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was provided.

High-Frequency Suspended Sediment Flux Measurements in a Small Estuary

In small estuaries, the predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure. Herein detailed turbulence measurements and suspended sediment concentrations were conducted simultaneously and continuously at high-frequency for 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. The data analyses provided an unique characterisation of the turbulent mixing processes and suspended sediment fluxes. The turbulence was neither homogeneous nor isotropic, and it was not a Gaussian process. The integral time scales for turbulence and suspended sediment concentration were about equal during flood tides, but differed significantly during ebb tides. The field experiences showed that the turbulence measurements must be conducted at high-frequency to characterise the small eddies and the viscous dissipation process, while a continuous sampling was necessary to characterise the time-variations of the instantaneous velocity field, Reynolds stress tensor and suspended sediment flux during the tidal cycles.

A review of the use of the basic cation saturation ratio and the "ideal" soil

The use of 'balanced' Ca, Mg, and K ratios, as prescribed by the basic cation saturation ratio (BCSR) concept, is still used by some private soil-testing laboratories for the interpretation of soil analytical data. This review aims to examine the suitability of the BCSR concept as a method for the interpretation of soil analytical data. According to the BCSR concept, maximum plant growth will be achieved only when the soil’s exchangeable Ca, Mg, and K concentrations are approximately 65 % Ca, 10 % Mg, and 5 % K (termed the ‘ideal soil’). This ‘ideal soil’ was originally proposed by Firman Bear and co-workers in New Jersey (USA) during the 1940s as a method of reducing luxury K uptake by alfalfa (Medicago sativa L.). At about the same time, William Albrecht, working in Missouri (USA), concluded through his own investigations that plants require a soil with a high Ca saturation for optimal growth. Whilst it now appears that several of Albrecht’s experiments were fundamentally flawed, the BCSR (‘balanced soil’) concept has been widely promoted, suggesting that the prescribed cationic ratios provide optimum chemical, physical, and biological soil properties. Our examination of data from numerous studies (particularly those of Albrecht and Bear, themselves) would suggest that, within the ranges commonly found in soils, the chemical, physical, and biological fertility of a soil is generally not influenced by the ratios of Ca, Mg, and K. The data do not support the claims of the BCSR, and continued promotion of the BCSR will result in the inefficient use of resources in agriculture and horticulture.