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Microforces and the Theory of Solute Transport  [PDF]
Eliot Fried,Shaun Sellers
Physics , 1999,
Abstract: A generalized continuum framework for the theory of solute transport in fluids is proposed and systematically developed. This framework rests on the introduction of a generic force balance for the solute, a balance distinct from the macroscopic momentum balance associated with the mixture. Special forms of such a force balance have been proposed and used going back at least as far as Nernst's 1888 theory of diffusion. Under certain circumstances, this force balance yields a Fickian constitutive relation for the diffusive solute flux, and, in conjunction with the solute mass balance, provides a generalized Smoluchowski equation for the mass fraction. Our format furnishes a systematic procedure for generalizing convection-diffusion models of solute transport, allowing for constitutive nonlinearities, external forces acting on the diffusing constituents, and coupling between convection and diffusion.
Field scale variability of solute transport parameters and related soil properties
B. Lennartz,S. K. Kamra,S. Meyer-Windel
Hydrology and Earth System Sciences (HESS) & Discussions (HESSD) , 1997,
Abstract: The spatial variability of transport parameters has to be taken into account for a reliable assessment of solute behaviour in natural field soils. Two field sites were studied by collecting 24 and 36 small undisturbed soil columns at an uniform grid of 15 m spacing. Displacement experiments were conducted in these columns with bromide traced water under unsaturated steady state transport conditions. Measured breakthrough curves (BTCs) were evaluated with the simple convective-dispersive equation (CDE). The solute mobility index (MI) calculated as the ratio of measured to fitted pore water velocity and the dispersion coefficient (D) were used to classify bromide breakthrough behaviour. Experimental BTCs were classified into two groups: type I curves expressed classical solute behaviour while type II curves were characterised by the occurrence of a bromide concentration maximum before 0.35 pore volumes of effluent (MI<0.35) resulting from preferential flow conditions. Six columns from site A and 8 from site B were identified as preferential. Frequency distributions of the transport parameters (MI and D) of both sites were either extremely skewed or bimodal. Log-transformation did not lead to a normal distribution in any case. Contour maps of bromide mass flux at certain time steps indicated the clustering of preferential flow regions at both sites. Differences in the extent of preferential flow between sites seemed to be governed by soil structure. Linear cross correlations among transport parameters and independently measured soil properties revealed relations between solute mobility and volumetric soil water content at time of sampling, texture and organic carbon content. The volumetric field soil water content, a simple measure characterising the soil hydraulic behaviour at the sampling location, was found to be a highly sensitive parameter with respect to solute mobility and preferential flow situations. Almost no relation was found between solute transport parameters and independently determined soil properties when non-preferential and preferential samples were considered separately in regression analyses. Future work should concentrate to relate integrated parameters such as the infiltration rate or the soil hydraulic functions to solute mobility under different flow situations.
Comparison of three stream tube models predicting field-scale solute transport  [PDF]
D. Jacques,J. Vanderborght,D. Mallants,D.-J. Kim
Hydrology and Earth System Sciences (HESS) & Discussions (HESSD) , 1997,
Abstract: In this paper the relation between local- and field-scale solute transport parameters in an unsaturated soil profile is investigated. At two experimental sites, local-scale steady-state solute transport was measured in-situ using 120 horizontally installed TDR probes at 5 depths. Local-scale solute transport parameters determined from BTCs were used to predict field-scale solute transport using stochastic stream tube models (STM). Local-scale solute transport was described by two transport models: (1) the convection-dispersion transport model (CDE), and (2) the stochastic convective lognormat transfer model (CLT). The parameters of the CDE-model were found to be lognormally distributed, whereas the parameters of the CLT model were normally distributed. Local-scale solute transport heterogeneity within the measurement volume of a TDR-probe was an important factor causing field-scale solute dispersion. The study of the horizontal scale-dependency revealed that the variability in the solute transport parameters contributes more to the field-scale dispersion at deeper depths than at depths near the surface. Three STMs were used to upscale the local transport parameters: (i) the stochastic piston flow STM-I assuming local piston flow transport, (ii) the convective-dispersive STM-II assuming local CDE transport, and (iii) the stochastic convective lognormal STM-III assuming local CLT. The STM-I considerably underpredicted the field-scale solute dispersion indicating that local-scale dispersion processes, which are captured within the measurement volume of the TDR-probe, are important to predict field-scale solute transport. STM-II and STM-III both described the field-scale breakthrough curves (BTC) accurately if depth dependent parameters were used. In addition, a reasonable description of the horizontal variance of the local BTCs was found. STM-III was (more) superior to STM-II if only one set of parameters from one depth is used to predict the field-scale solute BTCs at several depths. This indicates that the local-scale solute transport process, as measured with TDR in this study, is in agreement with the CLT-hypothesis.
Meta-analysis of the effects of soil properties, site factors and experimental conditions on solute transport
J. K. Koestel, J. Moeys,N. J. Jarvis
Hydrology and Earth System Sciences (HESS) & Discussions (HESSD) , 2012,
Abstract: Preferential flow is a widespread phenomenon that is known to strongly affect solute transport in soil, but our understanding and knowledge is still poor of the site factors and soil properties that promote it. To investigate these relationships, we assembled a database from the peer-reviewed literature containing information on 733 breakthrough curve experiments under steady-state flow conditions. Most of the collected experiments (585 of the 733 datasets) had been conducted on undisturbed soil columns, although some experiments on repacked soil, clean sands, and glass beads were also included. In addition to the apparent dispersivity, we focused our attention on three indicators of preferential solute transport: namely the 5%-arrival time, the holdback factor, and the ratio of piston-flow and average transport velocities. Our results suggest that, in contrast to the 5%-arrival time and the holdback factor, the piston-flow to transport velocity ratio is not related to preferential macropore transport but rather to the exclusion or retardation of the applied tracer. Confirming that the apparent longitudinal dispersivity is positively correlated with the travel distance of the tracer, our results also illustrate that this relationship is refined if the normalized 5%-tracer arrival time is also taken into account. In particular, we found that the degree of preferential solute transport increases with apparent dispersivity and decreases with travel distance. A similar but weaker relationship was observed between apparent dispersivity, 5%-tracer arrival time, and lateral observation scale, such that the degree of preferential transport increases with lateral observation scale. However, we also found that the travel distance and the lateral observation scale in the investigated dataset are correlated, which makes it difficult to distinguish their influence on these transport characteristics. We also found that the strength of preferential transport increased at larger flow rates and water saturations, which suggests that macropore flow was a more important flow mechanism than heterogeneous flow in the soil matrix. Nevertheless, our data show that heterogeneous flow in the soil matrix also occasionally leads to strong preferential transport. Furthermore, we show that preferential solute transport under steady-state flow depends on soil texture in a threshold-like manner: moderate to strong preferential transport was found to occur only for undisturbed soils that contain more than 8% clay. Preferential flow characteristics were also absent for columns filled with glass beads, clean sands, or sieved soil. No clear effect of land use on the pattern of solute transport could be discerned, probably because the available dataset was too small and too strongly affected by cross-correlations with experimental conditions. Our results suggest that, in developing pedotransfer functions for solute transport properties of soils, it is critically important to accoun
A Nonlinear Solute Transport Model and Data Reconstruction with Parameter Determination in an Undisturbed Soil-Column Experiment  [PDF]
Gongsheng Li,De Yao,Yongzai Wang,Xianzheng Jia
Mathematical Problems in Engineering , 2011, DOI: 10.1155/2011/679531
Abstract: A real undisturbed soil-column infiltrating experiment in Zibo, Shandong, China, is investigated, and a nonlinear transport model for a solute ion penetrating through the column is put forward by using nonlinear Freundlich's adsorption isotherm. Since Freundlich's exponent and adsorption coefficient and source/sink terms in the model cannot be measured directly, an inverse problem of determining these parameters is encountered based on additional breakthrough data. Furthermore, an optimal perturbation regularization algorithm is introduced to determine the unknown parameters simultaneously. Numerical simulations are carried out and then the inversion algorithm is applied to solve the real inverse problem and reconstruct the measured data successfully. The computational results show that the nonlinear advection-dispersion equation discussed in this paper can be utilized by hydrogeologists to research solute transport behaviors with nonlinear adsorption in porous medium. 1. Introduction Soil and groundwater pollution has become a serious threat to sustainable development throughout the world. It is important to characterize physical/chemical reactions quantitatively in the solute transport processes in the soil and groundwater. To understand the behaviors of the soil in the presence of infiltrating contaminants, soil-column experiments are often performed in laboratory or in field. There are disturbed and undisturbed soil-column experiments. For an undisturbed soil-column experiment, the structure of the soil layers and any contaminants within the column is preserved when the soil is transferred to the experimental apparatus. Generally speaking, for an undisturbed soil-column experiment, some complicated physical/chemical reactions could happen in the liquid phase and the solid phase when solute ions are being transported through the column with the inflow. As we know, there are a lot of researches on solute transport behaviors in soil-column infiltrating experiments since the 1980s. Typical work could belong to the researching group of Nielsen and Van Genuchten. Nielsen et al. [1] put forward general equations of advection-dispersion type to describe solute transport behaviors, and Van Genuchten and Wagenet [2] constructed solute transport models of two sites/two regions in the soils. With development of computational tool and technique, numerical methods and software packages based on convection-dispersion equations are widely utilized on researches of soil-column infiltrating experiments (see, e.g., [3,4,5,6,7,8,9,10). Recently, the authors have even
Investigation of Interactive Effects on Water Flow and Solute Transport in Sandy Loam Soil Using Time Domain Reflectometry  [PDF]
Hasan Merdun
Sensors , 2012, DOI: 10.3390/s120709749
Abstract: Surface-applied chemicals move through the unsaturated zone with complex flow and transport processes due to soil heterogeneity and reach the saturated zone, resulting in groundwater contamination. Such complex processes need to be studied by advanced measurement and modeling techniques to protect soil and water resources from contamination. In this study, the interactive effects of factors like soil structure, initial soil water content (SWC), and application rate on preferential flow and transport were studied in a sandy loam field soil using measurement (by time domain reflectometry (TDR)) and modeling (by MACRO and VS2DTI) techniques. In addition, statistical analyses were performed to compare the means of the measured and modeled SWC and EC, and solute transport parameters (pore water velocity and dispersion coefficient) in 12 treatments. Research results showed that even though the effects of soil structural conditions on water and solute transport were not so clear, the applied solution moved lower depths in the profiles of wet versus dry initial SWC and high application rate versus low application rates. The effects of soil structure and initial SWC on water and solute movement could be differentiated under the interactive conditions, but the effects of the application rates were difficult to differentiate under different soil structural and initial SWC conditions. Modeling results showed that MACRO had somewhat better performance than VS2DTI in the estimation of SWC and EC with space and time, but overall both models had relatively low performances. The means of SWC, EC, and solute transport parameters of the 12 treatments were divided into some groups based on the statistical analyses, indicating different flow and transport characteristics or a certain degree nonuniform or preferential flow and transport in the soil. Conducting field experiments with more interactive factors and applying the models with different approaches may allow better understanding of flow and transport processes in addition to the simulations of them in the unsaturated zone.
Comparison between field measurements and numerical simulation of steady-state solute transport in a heterogeneous soil profile
J. Vanderborght,D. Jacques,D. Mallants,P.-H. Tseng
Hydrology and Earth System Sciences (HESS) & Discussions (HESSD) , 1997,
Abstract: : Field-scale solute dispersion is determined by water flow heterogeneity which results from spatial variability of soil hydraulic properties and soil moisture state. Measured variabilities of soil hydraulic properties are highly sensitive to the experimental method. Field-scale dispersion derived from leaching experiments in a macroporous loam soil was compared with field-scale dispersion obtained with numerical simulations in heterogeneous random fields. Four types of random fields of hydraulic properties having statistical properties derived from four different types of laboratory measurements were considered. Based on this comparison, the measurement method depicting heterogeneities of hydraulic properties most relevant to field-scale solute transport was identified. For unsaturated flow, the variability of the hydraulic conductivity characteristic measured on a small soil volume was the most relevant parameter. For saturated flow, simulated dispersion underestimated the measured dispersion and it was concluded that heterogeneity of macroscopic hydraulic properties could not represent solute flow heterogeneity under these flow conditions. Field-scale averaged solute concentrations depend both on the detection method and the averaging procedure. Flux-averaged concentrations (relevant to practical applications) differ from volume-averaged or resident concentrations (easy to measure), especially when water flow is more heterogeneous. Simulated flux and resident concentrations were subsequently used to test two simple one-dimensional transport models in predicting flux concentrations when they are calibrated on resident concentrations. In the first procedure, solute transport in a heterogeneous soil is represented by a 1-D convection dispersion process. The second procedure was based on the relation between flux and resident concentrations for a stochastic convective process. Better predictions of flux concentrations were obtained using the second procedure, especially when water flow and solute transport are very heterogeneous.

Xu Xiuyuan,Chen Tongbin,

地理研究 , 1998,
Abstract: The transport and distribution of dissolved chemicals are influenced by water movement in the soil system. In order to understand the advances in underground water pollution, salt transport in salt affected soils and salt accumulation in coast soils affected by seawaters, the studies of the past 2 decades on the theoretical development and practical applications of solute transport simulation in soil water systems are reviewed. The theories and numerical simulations on dispersions, adsorption, uptake and transport of solutes in unsaturated and saturated soils are discussed in the presented paper.
Physiological Interpretation of Solute Transport Parameters for Peritoneal Dialysis  [PDF]
Jacek Waniewski
Computational and Mathematical Methods in Medicine , 2001, DOI: 10.1080/10273660108833073
Abstract: A mathematical model for solute distribution within the tissue due to combined processes of diffusion and convective transport through the tissue, through the capillary wall, and by lymphatic absorption, during the exchange of the solute between an organ and external medium is applied for the description of the transport of small, middle and macro — molecules. The analytical solutions of the transport equations for the steady state are described. A parameter that characterizes the concentration profiles, the penetration depth, for combined diffusive and convective transport through the tissue is described as a function of the penetration depths for pure diffusive and pure convective transport components. The equation for the solute transport across the tissue surface is similar to a phenomenological formula widely used for the description of clinical and experimental peritoneal dwell studies. The phenomenological transport parameters may therefore be interpreted using the local transport coefficients for the tissue, the capillary wall, and lymphatic absorption. Theoretical estimations of those parameters are in good agreement with clinical data about solute transport in patients on continuous ambulatory peritoneal dialysis.
Estimation of Soil Hydraulic and Solute Transport Parameters from Transient Field Experiments using Inverse Modeling  [cached]
F. Abbasi,F. Tajik
Journal of Science and Technology of Agriculture and Natural Resources , 2007,
Abstract: Estimation of unsaturated soil hydraulic and solute transport properties by Inverse modeling has thus far been limited mostly to analyses of one-dimensional experiments in the laboratory, often assuming steady-state conditions. This is partly because of the high cost and difficulties in accurately measuring and collecting adequate field-scale data sets, and partly because of difficulties in describing spatial and temporal variability in the soil hydraulic properties. In this study we estimated soil hydraulic and solute transport parameters from several two-dimensional furrow irrigation experiments under transient conditions. Three blocked-end furrow irrigation experiments were carried out, each of the same duration but with different amounts of infiltrating water and solutes resulting from water depths of 6, 10, and 14 cm in the furrows. Two more experiments were carried out with the same amounts of applied water and solute, and hence for different durations, on furrows with water depths of 6 and 10 cm. The saturated hydraulic conductivity (Ks) and solute transport parameters in the physical equilibrium convection-dispersion (CDE) and physical nonequilibrium mobile/ immobile (MIM) transport models were inversely estimated using the Levenberg-Marquardt optimization algorithm in combination with the HYDRUS-2D numerical code. Estimated Ks-values ranged from 0.0389 to 0.0996 cm min-1, with a coefficient of variation of 48%. Estimated immobile water contents (θim) were more or less constant at a relatively low average value of 0.025 cm3 cm-3, whereas the first-order exchange coefficient (ω) varied between 0.10 and 19.52 min-1. The longitudinal dispersivity (DL) ranged from 2.6 to 32.8 cm, and the transverse dispersivity (DT) from 0.03 to 2.20 cm. DL showed some dependency on water level and irrigation/solute application time in the furrows, but no obvious effect was found on Ks and other transport parameters. Agreement between measured and predicted infiltration rates was satisfactory, whereas soil water contents were somewhat overestimated and solute concentrations underestimated. Differences between predicted solute distributions obtained with the CDE and MIM transport models were relatively small. This finding and the value of optimized parameters indicate that observed data were sufficiently well described using the simpler CDE model, and that immobile water did not play a major role in the transport process.
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