Mobile-immobile Transport Model Research Articles

Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching.

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.

Numerical approach for modeling fractal mobile/immobile transport model in porous and fractured media

The fractal mobile/immobile model of the solute transport is based on the assumption that the waiting times in the immobile region follow a power-law, and this leads to the application of fractional time derivatives. The model covers a wide family of systems that include heat diffusion and ocean acoustic propagation. This paper develops an efficient computational technique, stemming from the radial basis function-generated finite difference (RBF-FD), to solve the fractal mobile-immobile transport model (FMTM). The time fractional derivative of the FMTM is discretized via the shifted Grünwald-Letnikov formula with second-order accuracy. On the other hand, the spatial derivative is approximated using the local RBF-FD method. The main benefit of the local collocation technique is that we only need to consider discretization points present in each of the sub-domains around the collocation point. The stability and convergence analysis of the proposed method are proven via the energy method in the L2 space. The numerical results for the FMTM on regular and irregular domains confirm the theoretical formulation and efficiency of the proposed scheme.

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations.

A local weak form meshless method to simulate a variable order time-fractional mobile–immobile transport model

In this study, a simulation of an anomalous mobile–immobile transport process in complex systems is produced numerically. The process is mathematically described as a two-dimensional time-fractional mobile–immobile advection–diffusion equation in Coimbra variable order derivative sense. A local weak form meshless method combined with a time stepping approach is discussed and implemented to simulate the model. For this purpose, firstly, an implicit difference stepping method is used to semi-discretize the model in time direction. For full discretization, a set of regularly distributed nodes is created in the primary spatial domain and the local radial point interpolation method is used to construct the spatial shape functions on the distributed data-sites. Then an efficient meshless procedure based on combination of local Petrov–Galerkin method and collocation technique is formulated to treat in the interior and on the boundary of the primal spatial domain, respectively. Finally, some benchmark problems are presented on regular and irregular domains to verify the validity, efficiency and accuracy of the method.

Tracer, Dissolved Organic Carbon, and Colloid Leaching from Erosion‐Affected Arable Hillslope Soils

Core Ideas Pedogenetic processes are spatially related to the slope positions in arable soil landscapes. The Regosol is affected by erosion‐induced CaCO3 and reduced organic C contents. The leaching potential for colloids and DOC was reduced in the truncated Regosol soil. Soil erosion modifies transport properties in the form of the effective dispersivity. In a morainic arable soil landscape, tillage and water erosion created truncated soil profiles at exposed steep slope positions and colluvial soils in depressions. This study examined the effects of erosion‐induced pedogenetic dynamics on flow and transport properties, colloid mobilization, and dissolved organic C (DOC) leaching for an uneroded Luvisol (LV) at the plateau and a strongly eroded Regosol (RG) at the slope position. Unsaturated steady‐flow experiments were performed on intact soil columns (20‐cm diameter, 16–18 cm high) extracted from the Luvisol (Ap, E, and Bt horizons; three depths) and the Regosol (Ap and CBkl horizons; two depths) in three replicates. Together with a 3H2O tracer, the leaching of colloids and DOC and the electrical conductivity were determined in the percolate. Colloid concentration was obtained from turbidity data. Effective dispersion coefficients, Deff, were determined by fitting the convection–dispersion equation and the mobile–immobile transport model (program CXTFIT) to 3H2O breakthrough curves (BTCs). Values of Deff were lower for Luvisol (20.1 ± 0.3 cm2 d−1; mean ± standard deviation) than for Regosol columns (30.2 ± 12.6 cm2 d−1). The pore structure of the Regosol topsoil was influenced by incorporation of CaCO3 from glacial till. The plow pan in the Luvisol caused an increased heterogeneity in the BTCs. Differences in transport properties and leaching potentials for colloids (LV: 98 ± 9 mg L−1; RG: 15 ± 4 mg L−1) and DOC (LV: 13.7 ± 3.7 mg L−1; RG: 6.9 ± 1.1 mg L−1) suggested a gradual change in the solid‐phase composition and structure of these contrasting soils.

Changes in water table level influence solute transport in uniform porous media

AbstractChanges in the water table level result in variable water saturation and variable hydrological fluxes at the interface between the unsaturated and saturated zone. This may influence the transport and fate of contaminants in the subsurface. The objective of this study was to examine the impact of a decreasing and an increasing water table on solute transport. We conducted tracer experiments at downward flow conditions in laboratory columns filled with two different uniform porous media under static and transient flow conditions either increasing or decreasing the water table. Tracer breakthrough curves were simulated using a mobile–immobile transport model. The resulting transport parameters were compared to identify dominant transport processes. Changes in the water table level affected dispersivities and mobile water fractions depending on the direction of water table movement and the grain size of the porous media. In fine glass beads, the water flow velocity was similar to the decline rate of the water table, and the mobile water fraction was decreased compared with steady‐state saturated conditions. However, immobile water was negligible. In coarse glass beads, water flow was faster because of fingered flow in the unsaturated part, and the mobile water fraction was smaller than in the fine material. Here, a rising water table led to an even smaller mobile water fraction and increased solute spreading because of diffusive interaction with immobile water. We conclude that changes of the water table need to be considered to correctly simulate transport in the subsurface at the transition of the unsaturated–saturated zone. Copyright © 2014 John Wiley & Sons, Ltd.

Modeling water flow and bacterial transport in undisturbed lysimeters under irrigations of dairy shed effluent and water using HYDRUS-1D

HYDRUS-1D was used to simulate water flow and leaching of fecal coliforms and bromide (Br) through six undisturbed soil lysimeters (70 cm depth by 50 cm diameter) under field conditions. Dairy shed effluent (DSE) spiked with Br was applied to the lysimeters, which contained fine sandy loam layers. This application was followed by fortnightly spray or flood water irrigation. Soil water contents were measured at four soil depths over 171 days, and leachate was collected from the bottom. The post-DSE period simulations yielded a generally decreased saturated water content compared to the pre-DSE period, and an increased saturated hydraulic conductivity and air-entry index, suggesting that changes in soil hydraulic properties (e.g. via changes in structure) can be induced by irrigation and seasonal effects. The single-porosity flow model was successful in simulating water flow under natural climatic conditions and spray irrigation. However, for lysimeters under flood irrigation, when the effect of preferential flow paths becomes more significant, the good agreement between predicted and observed water contents could only be achieved by using a dual-porosity flow model. Results derived from a mobile-immobile transport model suggest that compared to Br, bacteria were transported through a narrower pore-network with less mass exchange between mobile and immobile water zones. Our study suggests that soils with higher topsoil clay content and soils under flood irrigation are at a high risk of bacteria leaching through preferential flow paths. Irrigation management strategies must minimize the effect of preferential flow to reduce bacterial leaching from land applications of effluent.

Experimental and Modeling Investigation of Unsaturated Solute Transport with Water‐Table Fluctuation

We studied the transport of a nonreactive tracer in an unconsolidated weathered granite column under steady‐state flow and transient flow induced by water‐table fluctuation in the bottom half of the column. Experiments reproducing one‐dimensional vertical flow and tracer transport were performed at two infiltration rates, 12 and 22 mm h−1. Breakthrough data were used (i) to compare tracer dispersion under steady‐state and transient flow, (ii) to analyze the mechanisms responsible for tracer transport under both flow conditions, and (iii) to test the ability of existing transport models to reproduce observed breakthrough curves (BTCs). The BTCs under steady‐state flow are typical of physical nonequilibrium transport in a dual‐porosity medium. The shapes of BTCs under transient flow are less common, showing multiple peaks. The spreading of the tracer was one order of magnitude greater under transient flow than under steady‐state flow. We attribute the multiple‐peak shape of BTCs and the greater spreading under transient flow to rapid convection in a rapid mobile domain. Diffusion and advection could account for tracer exchanges between the slow mobile domain, which is active during unsaturated water flow, and the rapid mobile domain, which becomes active as soon as the pore space is fully saturated. Water flow was simulated with the Richards equation using HYDRUS‐1D. A mobile–immobile transport model coupled to the Richards equation reproduced the BTCs satisfactorily under steady‐state flow at both infiltration rates; however, it was unable to reproduce the multiple peaks of tracer concentrationse under a fluctuating water‐table regime.

TRANSPORT AND FATE OF ATRAZINE IN MIDWESTERN RIPARIAN BUFFER STRIPS1

ABSTRACT: The fate of pesticides entering the Riparian Buffer Strips (RBS) has not been well documented. This study compared the transport and fate of atrazine in soil of three‐, five‐, and nine‐year‐old switchgrass (Panicum virgatum L.) RBS to that in adjacent soils cropped to a corn‐soybean rotation or a grass‐alfalfa pasture. Undisturbed soil columns were collected from the RBS and cropped areas within the Bear Creek watershed, near Roland, Iowa. Atrazine and bromide breakthrough curves obtained using intact soil columns under saturated conditions were described by a two‐region, mobile‐immobile transport model. Preferential flow of bromide and atrazine was evident in five‐and nine‐year‐old RBS soil, but there was little difference in transport characteristics between these two RBS soils and the adjacent cropped soils. There was a trend towards an increase in dispersion coefficients between the five‐and nine‐year‐old RBS sites, which suggests an increased degree of preferential flow with increasing RBS age. Despite similar texture and organic C contents, atrazine sorption was significantly greater in RBS soil than the adjacent cropped soil. Cropped soil degraded atrazine faster than the RBS soil. The rapid degradation of atrazine in the corn‐soybean soil adjacent to the five‐year‐old RBS (atrazine half‐life of 19 days) appeared to be due to a larger population of atrazine‐degrading microorganisms. Atrazine‐degrading microorganisms in the corn‐soybean soil were 50,940 cells g‐1 soil compared with 2,970 cells g‐4 soil in 5‐year‐old RBS soil which resulted in 60 percent mineralization of [14C‐UL‐atrazine] in the corn‐soybean soil.

Aging effects on cadmium transport in undisturbed contaminated sandy soil columns.

Limited information is available on the effects of contaminant aging (i.e., the contact time of Cd with the soil) on Cd transport in soils. We conducted displacement experiments in which indigenous Cd and freshly applied Cd were leached simultaneously from undisturbed samples of three Spodosol horizons. Sorption of Cd was described using Freundlich isotherms, whereas transport was described as a convection-dispersion process. Parameter optimization analysis using a mobile-immobile transport model applied to nonsorbing tracer displacement data showed that 16 to 22% of the water in the columns was immobile. The low dimensionless mass transfer coefficients in the mobile-immobile model were indicative of diffusion-limited transfer between mobile and immobile water, and hence physical nonequilibrium. A two-site kinetic sorption model could be fitted closely to breakthrough curves of the non-aged Cd for three soil horizons. No conclusive evidence was found that contaminant aging in soil affects cadmium transport. On the one hand, predictions of aged Cd leaching, using parameters estimated from displacement experiments with nonaged Cd, differed from those for the aged Cd in the E horizon. On the other hand, no meaningful differences in transport behavior between aged and non-aged Cd were found for the humus Bh and Bh/C horizons. The two-site kinetic rate coefficient alphac was found to depend on water flux, further indicating that mass transfer between sorption sites and the liquid is limited by diffusion rather than by kinetic sorption.

Transect study on solute transport in a macroporous soil

Solute transport experiments using a non-reactive tracer were conducted on short, undisturbed, saturated columns of a sandy loam soil. All columns, 20 cm in diameter and 20 cm long, were collected along a transect of 35 m. Most of the soil columns had pre-existing macropores. The columns were leached at a steady flow-rate under ponding conditions. The resulting breakthrough curves (BTCs) showed a large heterogeneity. Several of the BTCs displayed early breakthrough and long tailing. All the data were interpreted in terms of dimensional time moments, the classical convection-dispersion equation (CDE) and the mobile-immobile transport model (MIM). Experimental time moments were found to vary significantly among the different BTCs. Analysis of the time moments also revealed that the variance of the field-scale BTC was several times larger than the average of the local-scale variance. The pore water velocity v and dispersion coefficient D were obtained by fitting the CDE to the local-scale BTCs, resulting in an average dispersivity of 7.4 cm. Frequency distributions for the CDE parameters v and D were equally well described by a normal or log-normal probability density function (pdf). When a log-normal pdf for D is considered, the variance of the loge transformed D values (σ 1nD 2 ) was found to be 2.1. For the MIM model, two additional parameters were fitted : the fraction of mobile water, θ m /θ, and the first-order mass transfer coefficient, a. The MIM was more successful in describing the data than the CDE transport model. For the MIM model, the average dispersivity was about 2 cm. The MIM parameters v, D and θ m /θ were best described by a log-normal pdf rather than a normal pdf. Only the parameter α was better described by a normal pdf. Mobile water fractions, θ m /θ ranged from 0.01 to 0.98, with a mean of 0.43 (based on a log-normal pdf). When the CDE and MIM were applied to the data, the fitted pore water velocities, v, compared favourably with the effective pore water velocities, v eff , obtained from moment analysis.

Estimating solute transport in undisturbed soil columns using time-domain reflectometry

Time-domain reflectometry (TDR) was used to monitor solute breakthrough curves (BTC's) in 30 saturated undisturbed soil columns collected along a 35-m-long transect in the field. The BTC's were obtained by relating the bulk soil electrical conductivity, EC a, to the relative concentration of a KCl solute pulse applied to the soil surface. Values of EC a were estimated by measuring the soil's impedance to an electromagnetic wave generated by a cable tester. Parallel two-rod TDR probes inserted horizontally at a depth of 10 cm were used to monitor the soil's impedance during transport of the KCl solute pulse. Calculated experimental time moments indicated that the BTC data were very variable in time and space. This variability was attributed in part to the relatively small volume of soil sampled with the TDR probes, and in part to the natural heterogeneity of the sandy loam soil. The observed BTC's were classified into three groups. One group showed bell-shaped curves consistent with the classical convection-dispersion equation (CDE). A second group was characterized by early breakthrough and long tailing. The BTC's in this group could be described by a mobile-immobile transport model (MIM). A third group of BTC's showed irregular shapes with several peaks. Time moments were used to compare the estimated (from the moments), fitted (CDE and MIM) and independently measured pore-water velocities. The disparities between the observed and fitted velocities suggest that for structured soil several TDR probes may be necessary in order to obtain reasonable estimates of column-scale solute transport behaviour.