Nonideal Transport Research Articles

A Non-Ideal Transport Model of Bipolar Membranes to Understand and Manage Multi-Ion Interactions in Water Electrolysis

Water electrolysis provides a means of producing H2 gas without carbon emissions. However, H2 production through water electrolysis is more costly compared to methods using fossil fuels. A key element to the cost of water electrolysis is the need to purify the water fed to the electrolyzer. Impure feeds can lead to corroding electrodes (e.g. chloride oxidation) and fouling of commonly-used monopolar membranes (i.e., cation and anion exchange membranes). Bipolar Membranes (BPMs), consisting of a cation and anion exchange membranes with a water dissociation catalyst at the interface, pose unique advantages. Because each layer can be tuned independently, BPMs enable higher control of co-ion transport and impurities, unlike monopolar membranes. However, challenges arise in rationally-designing BPMs for impure water electrolysis due to a lack of fundamental understanding of the coupled interactions between water, mobile ions, and fixed charge groups.In this study, we develop a continuum model to systematically investigate the use of BPMs for water electrolysis with impure feedstocks (e.g. seawater). The model defines the flux of each species using a modified Nernst-Planck-Poisson framework while explicitly considering non-ideal contributions to chemical potential from ion-ion, ion-membrane, swelling, electrostatic, steric, and solvation interactions to the electrochemical potential. The simulations quantify the effect of these interactions and membrane properties on ion transport, and how they could be modulated to mitigate the deleterious effects of impurities and co-ions. Our analysis shows that simple dilute-solution theory is not capable of predicting the effect of impurities on BPM water electrolysis and identifies the dominant interactions that dictate transport in BPMs. This study provides guidelines for modelling water electrolysis and materials design strategies for water electrolysis in non-ideal conditions.

Achieving Ideal and Environmentally Stable n-Type Charge Transport in Polymer Field-Effect Transistors.

Realizing ideal charge transport in field-effect transistors (FETs) of conjugated polymers is crucial for evaluating device performance, such as carrier mobility and practical applications of conjugated polymers. However, the current FETs using conjugated polymers as the active layers generally show certain non-ideal transport characteristics and poor stability. Here, ideal charge transport of n-type polymer FETs is achieved on flexible polyimide substrates by using an organic-inorganic hybrid double-layer dielectric. Deposited conjugated polymer films show highly ordered structures and low disorder, which are supported by grazing-incidence wide-angle X-ray scattering, near-edge X-ray absorption fine structure, and molecular dynamics simulations. Furthermore, the organic-inorganic hybrid double-layer dielectric provides low interfacial defects, leading to excellent charge transport in FETs with high electron mobility (1.49 ± 0.46 cm2V-1s-1) and ideal reliability factors (102 ± 7%). Fabricated polymer FETs show a self-encapsulation effect, resulting in high stability of the FET charge transport. The polymer FETs still work with high mobility above 1 cm2V-1s-1 after storage in air for more than 300 days. Compared with state-of-the-art conjugated polymer FETs, this work simultaneously achieves ideal charge transport and environmental stability in n-type polymer FETs, facilitating rapid device optimization of high-performance polymer electronics.

Three-segmented counterflow pilot-scale electrodialysis for ammonia and potassium treatment in liquid anaerobic digestate: A trade-off among advanced ion removal, nutrients concentration limitation, and energy consumption

In this paper, a three-segmented counterflow (COUN) electrodialysis (ED) for ammonia (NH4+-N) and potassium (K+) treatment in liquid anaerobic digestate (LAD) was proposed to break the high-concentration limit of nutrient recovery without sacrificing the ion removal performance and energy efficiency. The effects of the COUN operation mode on ED performance were studied based on pilot-scale experiments. The results indicate that the COUN mode improves the distribution of concentration difference (Δc). Hence, the ion fluxes of NH4+-N and K+ have increased by 51.0% and 25.3%, respectively. A highly concentrated product (NH4+-N at 10428 ± 225 mg/L and K+ at 7500 ± 156 mg/L) can be obtained, and the concentration multiples of NH4+-N and K+ have increased by 14.1% and 9.8%, respectively, with slight effects on their removal rates. The current efficiency for NH4+-N and K+ was increased by 38.1% and 14.5%, reaching 54.7 ± 3.5% and 12.4 ± 0.5%, respectively, and the final energy consumption of 3.8 ± 0.2 kWh/kg-N) has reduced by 31.8%. The non-ideal transport mechanisms associated with the Δc (back-diffusion and water osmosis) have been taken into consideration. The COUN mode is a new exploration of the ED operating patterns to alleviate the detrimental effect of high Δc. It will provide a reference for designing and operating large-scale engineering projects for nutrient recovery by ED process and a trade-off among advanced ion removal, high-concentration limitation, and energy consumption.

Groovy Electrodes Enable Facile O2 and H+ Transport in PEMFCs

Polymer electrolyte membrane fuel cells (PEMFCs) are promising alternative to internal combustion engines, owing to their capability to produce on-demand power with zero local carbon emissions. However, PEMFCs suffer from limitations related to performance, particularly for heavy-duty vehicle applications [1]. A major contributor to the performance loss is the cathode electrode; uncontrolled conventional electrode structures lead to non-ideal transport pathways of O2 and H+ [2], subsequently leading to performance loss. Here, we report an alternative electrode structure termed groovy electrodes, fabricated via patterned Si templates. Si templates with desired patterns are fabricated through photolithography and deep-reactive ion etching techniques (Fig. 1a), and an electrode layer is coated onto the template and subsequently transferred to the membrane or the gas diffusion layer. The resulting electrode features ordered grooves with consistent depth and width (Fig. 1b-c). We will present how this alternative structure enables improved H+ transport (enabled by higher ionomer content) with grooves facilitating effective O2 transport to reaction sites. We will also demonstrate the benefits of a groovy electrode for the durability of PEMFCs. Reference Cullen et al., Nat. Energy, 6, 462 (2021).Ramaswamy et al., J. Electrochem. Soc., 167, 064515 (2020). Figure 1

Investigation of Base Transport Mechanism in Silicon-Germanium Heterojunction Bipolar Transistor Operating over Wide Temperature Range

A high breakdown voltage silicon-germanium heterojunction bipolar transistor operated over a wide temperature range from 300 K to 10 K has been investigated. The measured Gummel characteristics illustrate that the collector current and base current both shift to the higher voltage as the temperature decreases. The fT/fmax are extracted to be 23/40 GHz at 300K, 28/40 GHz at 90 K, and 25/37GHz at 10K, respectively. The effective amplification range becomes narrow as the temperature decreases. And the ideality factor of base current in the low current region is shown to be temperature-dependent and its value is much larger than 2 at cryogenic temperatures. This phenomenon indicates that the base current is not only contributed by drift, diffusion, and Shockley-Read-Hall recombination, but also by trap-assisted tunneling. The Hurkx local trap-assisted tunneling has been used to analyze the non-ideal base transport mechanism. And a calibrated TCAD device model is developed to further verify this non-ideal transport mechanism.

Release of Per- and Polyfluoroalkyl Substances from Aqueous Film-Forming Foam Impacted Soils.

Per- and polyfluoroalkyl substances (PFASs) are highly mobile in the saturated subsurface, yet aqueous film-forming foam (AFFF)-impacted source zones appear to be long lasting PFAS reservoirs. This study examined the release of over one hundred anionic and zwitterionic PFASs from two AFFF-impacted surface soils under saturated conditions with packed soil columns. Perfluoroalkyl acids (PFAAs) were released more rapidly than their polyfluorinated precursors, while anionic PFASs that were present in partially uncharged states were released more slowly than PFASs that were present entirely as anions, as were zwitterionic PFASs with terminal cationic functional groups when compared with analogous zwitterions with only anionic terminal groups. Nonideal transport was observed in both per- and polyfluorinated classes, as soil column effluent concentrations of slowly released PFASs increased by up to 107-fold with sustained artificial groundwater flow. A flow-interruption experiment suggested the influence of rate-limited desorption on diverse PFAS classes, including PFAAs with as few as four perfluorinated carbons. These results suggest that during infiltration the slow, rate-limited desorption of anionic and zwitterionic PFAA precursors may result in these compounds comprising an increasingly large fraction of the remaining PFASs in AFFF-impacted surface soils.

Electrochemical Modeling of GITT Measurements for Improved Solid-State Diffusion Coefficient Evaluation

Galvanostatic Intermittent Titration Technique (GITT) is widely used to evaluate solid-state diffusion coefficients in electrochemical systems. However, the existing analysis methods for GITT data require numerous assumptions, and the derived diffusion coefficients typically are not independently validated. To investigate the validity of the assumptions and derived diffusion coefficients, we employ a direct pulse fitting method for interpreting GITT data that involves numerically fitting an electrochemical pulse and subsequent relaxation to a one-dimensional, single-particle, electrochemical model coupled with non-ideal transport to directly evaluate diffusion coefficients that are independently verified through cycling predictions. Extracted from GITT measurements of the intercalation regime of FeS2 and used to predict the discharge behavior, our non-ideal diffusion coefficients prove to be two orders of magnitude more accurate than ideal diffusion coefficients extracted using conventional methods. We further extend our model to a polydisperse set of particles to show the validity of a single-particle approach when the modeled radius is proportional to the total volume-to-surface-area ratio of the system.

Ideal versus Nonideal Transport of PFAS in Unsaturated Porous Media

Per- and poly-fluoroalkyl substances (PFAS) adsorb at air-water interfaces during transport in unsaturated porous media. This can cause surfactant-induced flow and enhanced retention that is a function of concentration, which complicates characterization and modeling of PFAS transport under unsaturated conditions. The influence of surfactant-induced flow and nonlinear air-water interfacial adsorption (AWIA) on PFAS transport was investigated with a series of miscible-displacement transport experiments conducted with a several-log range in input concentrations. Perfluorooctane sulfonic acid (PFOS), perfluorooctanoic acid (PFOA), and ammonium perfluoro 2-methyl-3-oxahexanoate (GenX) were used as model PFAS. The results were interpreted in terms of critical reference concentrations associated with PFAS surface activities and their relationship to the relevancy of transport processes such as surfactant-induced flow and nonlinear AWIA for concentration ranges of interest. Analysis of the measured transport behavior of PFAS under unsaturated-flow conditions demonstrated that AWIA was linear when the input concentration was sufficiently below the critical reference concentration. This includes the absence of significant arrival-front self-sharpening and extended elution tailing of the breakthrough curves, as well as the similarity of retardation factors measured for a wide range of input concentrations. Independently-predicted simulations produced with a comprehensive flow and transport model that accounts for transient variably-saturated flow, surfactant-induced flow, nonlinear rate-limited solid-phase sorption, and nonlinear rate-limited AWIA provided excellent predictions of the measured transport. A series of simulations was conducted with the model to test the specific impact of various processes potentially influencing PFOS transport. The simulation results showed that surfactant-induced flow was negligible and that AWIA was effectively linear when the input concentration was sufficiently below the critical reference concentration. PFAS retention associated with AWIA can be considered to be ideal in such cases, thereby supporting the use of simplified mathematical models. Conversely, apparent nonideal transport behavior was observed for experiments conducted with input concentrations similar to or greater than the critical reference concentration.

Thermodynamic limits of using fertilizer osmosis to produce mechanical work via pressure retarded osmosis

The potential for concentrated fertilizer to drive water treatment, nutrient recovery, and/or power generation has received increased attention. Recently the concept of fertilizer-driven pressure retarded osmosis (or “Green PRO”) was introduced to the literature and experimentally validated. The limits of power from fertilizer osmosis however have not yet been established, and therefore the potential for this energy source to supply meaningful farm loads is uncertain. In this paper, a combination of analytical, numerical, and experimental methods are used to establish the thermodynamic and process limits of fertilizer energy conversion via PRO. The results indicate that up to 125 Wh/kg of energy is released from fertilizer when it is diluted in water. PRO process dynamics including operation at constant applied pressure, and the need to maintain high power levels throughout the batch process, limit conversion to work to up to 14.9 Wh/kg. Further, experimentally-calibrated simulation results suggest that only up to 6.8 Wh/kg can be expected when considering non-ideal transport dynamics such as reverse solute flux and concentration polarization. The effect of feed source concentration and recovery ratio on batch process dynamics are investigated, and it is found that using wastewater as feed may be comparable to scenarios where clean irrigation feed with high recovery is used. The potential of common hydroponic plant crops is evaluated, and results indicate that advances in membrane technology may allow energy recovery to approach 5% of typical greenhouse electricity consumption.

Simulating PFAS adsorption kinetics, adsorption isotherms, and nonideal transport in saturated soil with tempered one-sided stable density (TOSD) based models

Reliable quantification of per- and polyfluoroalkyl substances (PFAS) adsorption and mobility in geomedia provides critical information (i.e., evaluation and prediction) for risk characterization and mitigation strategy development. Given the limited PFAS data available and various competing theories for modeling pollutant kinetics, it is indispensable to better understand and quantify the adsorption and transport of PFAS in geomedia using generalized models built upon a consistent physical theory. This study proposed a universal physical law (called the tempered stable law) in PFAS adsorption/transport by interpreting PFAS adsorption kinetics and nonideal transport as a nonequilibrium process dominated by adsorption/desorption with multiple rates following the tempered one-sided stable density (TOSD) distribution. This universal TOSD function led to novel TOSD-based models which were then tested by successfully simulating PFAS adsorption kinetics, adsorption isotherms, and nonideal transport data reported in the literature. Model comparisons and extensions were also discussed to further check the feasibility of the TOSD models and their adaptability to capture PFAS transport in more complex geomedia at all scales.

Simulating PFAS transport influenced by rate-limited multi-process retention

The transport of per- and poly-fluoroalkyl substances (PFAS) in the vadose zone is complicated by the fact that multiple mass-transfer processes can contribute to their retention and retardation. In addition, PFAS transport at some sites can be further complicated by the presence of organic immiscible liquids (OIL). Mass-transfer processes are inherently rate limited and, therefore, have the potential to cause nonideal transport of PFAS. The objectives of this research were to: (1) develop a solute-transport model that explicitly accounts for multiple retention processes, including adsorption at air-water and OIL-water interfaces, adsorption by the solid phase, and diffusive mass-transfer between advective and nonadvective domains, and (2) apply the model to measured transport data to delineate which processes are rate limited and contribute to observed nonideal transport. Breakthrough curves for transport of two PFAS and one hydrocarbon surfactant in sand obtained from prior miscible-displacement experiments exhibited nonideal transport. The multiprocess model effectively simulated the measured transport data. The results of the analyses indicate that adsorption at the air-water and OIL-water interface can generally be treated as effectively instantaneous for transport in porous media. The rate limitations associated with solid-phase adsorption and diffusive mass transfer between advective and nonadvective domains were of greater significance.

Nonideal Transport and Extended Elution Tailing of PFOS in Soil

The objective of this research was to examine the influence of nonideal sorption/desorption on the transport of polyfluorinated alkyl substances (PFASs) in soil, with a specific focus on characterizing and quantifying potential extended, mass-transfer-limited elution behavior. Perfluorooctane sulfonic acid (PFOS) was used as a representative PFAS, and miscible-displacement experiments were conducted with two soils comprising contrasting geochemical properties. The influence of nonlinear, rate-limited, hysteretic, and irreversible sorption/desorption on transport was investigated through experiments and model simulations. The breakthrough curves measured for PFOS transport in the two soils were asymmetrical and exhibited extensive elution tailing, indicating that sorption/desorption was significantly nonideal. The widely used two-domain sorption kinetics model could not fully simulate the observed transport behavior, whereas a multirate model employing a continuous distribution of sorption domains was successful. The overall results indicated that sorption/desorption was significantly rate-limited and that nonlinear, hysteretic, and irreversible sorption/desorption had minimal impact on PFOS transport. Comparison of PFOS transport data to data reported for two hydrophobic organic contaminants (HOCs) showed that the HOCs exhibited much more extensive elution tailing, likely reflecting differences in sorption/desorption mechanisms. The projected influence of rate-limited sorption/desorption on PFOS transport at the field scale was investigated through simulation. The results of the study suggest that rate-limited sorption/desorption may affect the field-scale transport of PFOS and other PFAS for systems influenced by transient or short-residence-time conditions and in some cases could possibly increase the amount of flushing required to reduce PFOS concentrations to levels below those associated with human-health concerns.

Permeation, sorption, and diffusion of CO2-CH4 mixtures in polymers of intrinsic microporosity: The effect of intrachain rigidity on plasticization resistance

CO2-CH4 mixed-gas sorption and permeation properties of a ladder polymer (PIM-Trip-TB) were measured experimentally at 35 °C to interpret nonideal transport behavior of polymers of intrinsic microporosity (PIMs). Both CH4 and CO2 mixed-gas solubilities were lower than those in the pure-gas environment mainly due to competitive sorption. In the range of pressures tested, the CO2/CH4 mixed-gas solubility selectivity of PIM-Trip-TB coincided on average with the value at infinite dilution, and at all pressures, it was higher than the pure-gas solubility selectivity. Because CO2 diffusion coefficient was found insensitive to mixture effects, we inferred that the increased diffusion coefficient of CH4 and the consequent loss of CO2/CH4 permselectivity in mixture environment were correlated to CO2-induced alteration of the selective diffusion domains of PIM-Trip-TB. Similar effects were also found for PIM-1 by an analysis of pure- and mixed-gas experimental permeation and sorption data. The increase of CH4 mixed-gas diffusion coefficients from the pure-gas values was more pronounced for both PIMs (PIM-Trip-TB and PIM-1) than for a conventional low-free volume polymer 6FDA-mPDA polyimide reported previously; this indicates that the high intrachain rigidity in PIMs cannot restrain unfavorable mixture effects on CO2/CH4 diffusion and permeability selectivity.

Quantification of non-ideal effects on diagenetic processes along extreme salinity gradients at the Mercator mud volcano in the Gulf of Cadiz

We present a transport-reaction model (TRACTION) specifically designed to account for non-ideal transport effects in the presence of thermodynamic (e.g. salinity or temperature) gradients. The model relies on the most fundamental concept of solute diffusion, which states that the chemical potential gradient (Maxwell’s model) rather than the concentration gradient (Fick’s law) is the driving force for diffusion. In turn, this requires accounting for species interactions by applying Pitzer’s method to derive species chemical potentials and Onsager coefficients instead of using the classical diffusion coefficients. Electrical imbalances arising from varying diffusive fluxes in multicomponent systems, like seawater, are avoided by applying an electrostatic gradient as an additional transport contribution.We apply the model to pore water data derived from the seawater mixing zone at the submarine Mercator mud volcano (MMV) in the Gulf of Cadiz. Two features are particularly striking at this site: (i) Ascending halite-saturated fluids create strong salinity (NaCl) gradients in the seawater mixing zone that result in marked chemical activity, and thus chemical potential gradients. The model predicts strong transport-driven deviations from the mixing profile derived from the commonly used Fick’s diffusion model, and is capable of matching well with the profile shapes observed in the pore water concentration data. Even better agreement to the observed data is achieved when ion pairs are transported separately. (ii) The formation of authigenic gypsum (several wt%) occurs in the surface sediments, which is typically restricted to evaporitic surface processes. Very little is known about the gypsum paragenesis in the subseafloor and we first present possible controls on gypsum solubility, such as pressure, temperature, and salinity (pTS), as well as the common ion and ion pairing effects. Due to leaching of deep diapiric salt, rising fluids of the MMV are saturated with respect to gypsum (as well as celestite and barite). Several processes that could drive these fluids towards gypsum supersaturation and hence precipitation were postulated and numerically quantified. In line with the varied morphology of the observed gypsum crystals, gypsum paragenesis at the MMV is likely a combination of two temperature-related processes. Gypsum solubility increases with increasing temperature, especially in strong electrolyte solutions and the first mechanism involves the cooling of saturated fluids along the geothermal gradient during their ascent. Secondly, local temperature changes, i.e. cooling during the transition from MMV activity towards dormancy results in the cyclic build-up of gypsum.The model showed that the interpretation of field data can be majorly misguided when ignoring non-ideal effects in extreme diagenetic settings. While at first glance the pore water profiles at the Mercator mud volcano would indicate strong reactive influences in the seawater mixing zone, our model shows that the observed species distributions are in fact primarily transport-controlled. The model results for SO4 are particularly intriguing, as SO4 is shown to diffuse into the sediment along its increasing (!) concentration gradient. Also, a pronounced gypsum saturation peak can be observed in the seawater mixing zone. This peak is not related to the dissolution of gypsum but is simply a result of the non-ideal transport forces acting on the activity profile of SO4 and Ca profiles.

Impact of non-ideal transport modeling on supercritical flow simulation

The simulation of a supercritical fluid flow requires sophisticated models for real gas thermodynamic and non-ideal phenomena. They both are presently addressed through the simulation of a non-reacting and reacting high pressure H2/O2 splitter-plate configuration. In particular, the diffusion velocity of species is evaluated through the gradient of chemical potential (dlNI=Xl(∇μl)T) expressed with the Peng–Robinson equation of state, or with the classical low-pressure approach dlI=∇Xl, which only uses the gradient of the lth species molar fraction, Xl. In addition, the high pressure binary diffusion coefficients are estimated by the correction of Kurochkin et al. or with the Takahashi approach. The results for the non-reaction case are consistent with the literature for mean and rms values using dlI. The use of dlNI has a limited impact but the temperature profiles become steeper. In the reactive case, the two approaches lead to a difference of 50 K on the average temperature just downstream of the injector and about 100 K further downstream. A non-ideal transport is then required for the modeling of supercritical flow simulation.

Charge-Trapping-Induced Non-Ideal Behaviors in Organic Field-Effect Transistors.

Organic field-effect transistors (OFETs) with impressively high hole mobilities over 10 cm2 V-1 s-1 and electron mobilities over 1 cm2 V-1 s-1 have been reported in the past few years. However, significant non-ideal electrical characteristics, e.g., voltage-dependent mobilities, have been widely observed in both small-molecule and polymer systems. This issue makes the accurate evaluation of the electrical performance impossible and also limits the practical applications of OFETs. Here, a semiconductor-unrelated, charge-trapping-induced non-ideality in OFETs is reported, and a revised model for the non-ideal transfer characteristics is provided. The trapping process can be directly observed using scanning Kelvin probe microscopy. It is found that such trapping-induced non-ideality exists in OFETs with different types of charge carriers (p-type or n-type), different types of dielectric materials (inorganic and organic) that contain different functional groups (OH, NH2 , COOH, etc.). As fas as it is known, this is the first report for the non-ideal transport behaviors in OFETs caused by semiconductor-independent charge trapping. This work reveals the significant role of dielectric charge trapping in the non-ideal transistor characteristics and also provides guidelines for device engineering toward ideal OFETs.

Imidacloprid transport and sorption nonequilibrium in single and multilayered columns of Immokalee fine sand.

Imidacloprid (IMD) is a neonicotinoid pesticide soil-drenched to many crops to control piercing-sucking insects such as the Asian citrus psyllid (ACP). Neonicotinoids are persistent in the environment and transport analyses are helpful estimate leaching potential from soils that could result in groundwater pollution. The objective of this study was to analyze IMD breakthrough under saturated water flow in soil columns packed with three horizons (A, E, Bh) of Immokalee Fine Sand (IFS). Also, we used the dimensionless form of the convective-dispersive model (CD-Model) to compare the optimized transport parameters from each column experiment (retardation factor, R; fraction of instantaneous-to-total retardation, β; and mass transfer coefficient, ω) with the parameters obtained from sorption batch equilibria and sorption kinetics. The tracer (Cl-) breakthrough curves (BTCs) were symmetrical and properly described by the CD-Model. IMD BTCs from A, Bh, and multilayered [A+E+Bh] soil columns showed steep fronts and tailing that were well described by the one-site nonequilibrium (OSNE) model, which was an evidence of non-ideal transport due to IMD mass transfer into the soil organic matter. In general, IMD was weakly-sorbed in the A and Bh horizons (R values of 3.72 ± 0.04 and 3.08 ± 0.07, respectively), and almost no retardation was observed in the E horizon (R = 1.20 ± 0.02) due to its low organic matter content (0.3%). Using the HYDRUS-1D package, optimized parameters (R, β, ω) from the individual columns successfully simulated IMD transport in a multilayered column mimicking an IFS soil profile. These column studies and corresponding simulations agreed with previous findings from batch sorption equilibria and kinetics experiments, where IMD showed one-site kinetic mass transfer between soil surfaces and soil solution. Ideally, sandy soils should be maintained unsaturated by crop irrigation systems and rainfall monitoring during and after soil-drench application. The unsaturated soil will increase IMD retardation factors and residence time for plant uptake, lowering leaching potential from soil layers with low sorption capacity, such as the E horizon.

Characterizing and modeling of extensive atrazine elution tailing for stable manure-amended agricultural soil

Non-ideal sorption and extensive elution tailing behavior of atrazine was evaluated for an agricultural soil with and without stable manure amendment (10% by weight). A series of laboratory experiments showed that the sorption of atrazine was described by rate-limited, nonlinear reversible processes (Freundlich isotherm) for both non-amended and amended soil. Non-ideal transport of atrazine exhibited extensive low concentration elution tailing due to the most likely organic carbon fraction in the soil. This tailing behavior was more pronounced and extensive for soil with 10% stable-manure amendment. Two-site transport modeling analyses including non-linear sorption and rate-limited sorption–desorption provided a reasonably good match to the atrazine breakthrough curves but were unable to match the long-term concentration tailing, even for non-amended soil. A mathematical model incorporating nonlinear, rate-limited sorption/desorption described by a continuous-distribution function was used to successfully simulate atrazine transport early-time breakthrough and long-term concentration tailing for both non-amended and amended soil conditions.

Nonideal Transport of Contaminants in Heterogeneous Porous Media: 11. Testing the Experiment Condition Dependency of the Continuous-Distribution Rate Model for Sorption-Desorption.

A series of miscible-displacement experiments was conducted to examine the impact of experiment conditions (detection limit, input-pulse size, input concentration, pore-water velocity, contact time) on the performance of a mathematical solute-transport model incorporating nonlinear, rate-limited sorption/desorption described by a continuous-distribution reaction function. Effluent solute concentrations were monitored over a range of approximately seven orders of magnitude, allowing characterization of asymptotic tailing phenomenon. The model successfully simulated the extensive elution tailing observed for the measured data. Values for the mean desorption rate coefficient (ln k2) and the variance of ln k2 were obtained through calibration of the model to measured data. Similar parameter values were obtained for experiments with different input-pulse size, input concentration, pore-water velocity, contact time. This suggests that the model provided a robust representation of sorption-desorption for this system tested. The impact of analytical detection limit was examined by calibrating the model to subsets of the breakthrough curves wherein the extent of the elution tail was artificially reduced to mimic a poorer detection limit. The parameters varied as a function of the extent of elution tail used for the calibrations, indicating the importance of measuring as full an extent of the tail as possible.

Role of non-ideality for the ion transport in porous media: Derivation of the macroscopic equations using upscaling

This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic non-ideal effects are taken into account by an approach based on the mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. We first consider equilibrium solutions in the absence of external forces. In such a case, the velocity and diffusive fluxes vanish and the equilibrium electrostatic potential is the solution of a variant of the Poisson–Boltzmann equation coupled with algebraic equations. Contrary to the ideal case, this nonlinear equation has no monotone structure. However, based on invariant region estimates for the Poisson–Boltzmann equation and for small characteristic value of the solute packing fraction, we prove existence of at least one solution. To our knowledge this existence result is new at this level of generality. When the motion is governed by a small static electric field and a small hydrodynamic force, we generalize O’Brien’s argument to deduce a linearized model. Our second main result is the rigorous homogenization of these linearized equations and the proof that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. We eventually make numerical comparisons with the ideal case. Our numerical results show that the MSA model confirms qualitatively the conclusions obtained using the ideal model but there are quantitative differences arising that can be important at high charge or high concentrations.