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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13

Multi-Scale Modeling of Hydrogen Transport in a Porous Fuel Cell Anode

Proton-exchange-membrane fuel cells (PEMFC) are a clean energy conversion alternative to traditional fossil-fuel combustion; however, transport resistances in the electrode pose a lower-limit to catalyst loading and commercialization of PEMFCs. PEMFCs consist of simultaneous hydrogen (H 2 ) oxidation and oxygen (O 2 ) reduction at the anode and cathode, respectively. Here, while oxygen transport resistances in PEMFCs have been widely studied both experimentally and analytically, hydrogen transport resistances are less understood. Herein, we present a physics-based model that encompasses multi-scale transport within the anode side of the PEMFC. The O 2 in the cathode here is omitted and replaced with H 2 to deconvolute O 2 transport resistance contributions, similar to that of a hydrogen pump. Replication of the hydrogen pump setup allows for comparison of the model against experimental analysis of H 2 gas-transport resistance in H 2 limiting-current experiments, which can also inform gas transport (including oxygen) in general. Herein, we present a multi-scale analytical model of the porous anode catalyst layers and individual catalyst agglomerates that enables determination of the effects of electrode morphology such as agglomerate size, catalyst loading, etc. on H 2 transport resistance through the porous electrode to complement and better understand H 2 limiting current experiments and deconvolute local H 2 transport resistances.

Zhang, Rosa↗

RadSim: Particle Transport Wrapper

RadSim is being developed to provide the capability to simulate radiation source emissions, interpolate results from radiation transport tools into a common format to prepare incident flux, and model radiation detector response. This software package includes wrapper API code which is utilized in the development of the second (transport) task of the RadSim project. This software package only contains tools to interface RadSim with radiation transport tools (GEANT4 and MCNP) and does not include any part of the transport source code itself. The users will need prior access to the transport tools (GEANT4 and MCNP), and can use this software package to interface with the transport tool of their choice. This software package takes the geometry file for a radiation transport problem and converts it into an input deck for the transport tools (GEANT4 and MCNP). Additionally, it also contains filters that convert the output of the transport tools to a common flux format.

Cheung, Hoi Sing↗

Understanding and controlling water-organic co-transport in amorphous microporous materials

The transport of molecules in microporous material is a significant and active area of research in separation applications. The movement of vapor/liquid molecules in a high-loading condition in microporous spaces is especially challenging to interrogate. This project aims to understand and control the transport of complex water and organic solvent mixtures in varying structures of microporous carbon molecular sieve (CMS) and activated carbon membranes. Modeling of transport behavior in such carbonaceous samples using computational modeling is difficult due to their amorphous structure. Therefore, this research intends to study the transport mechanism of water-organic mixtures by experimentally revealing fundamental transport properties, such as guest sorption amounts as well as diffusion and permeation rates. Considering the different size and guest-host affinity of water and organic solvent molecules, the objective of this research is to understand the structural conditions within the ultramicropores and micropores that generate different types of molecular transport and selection mechanisms within such complex systems. Carbonaceous materials are developed using tailored pyrolysis techniques to pyrolyze polymeric precursors, including polyvinylidene chloride (PVDC),polyvinylidene fluoride (PVDF), polymer of intrinsic microporosity (PIM) -1, and fully aromatic polyamide. The initial stage of the research will focus on the microscopic diffusion and sorption studies of pure component water, xylene isomers, and n,n- dimethylformamide within various carbons. Additional structural investigation on CMS, such as gas physisorption and neutron scattering studies, will be executed to gain deeper insight into these structure-transport relationships. Scanning electron microscopy and X-ray photoelectron microscopy are also used to further characterize these materials. The research will progress to probe mutual diffusion of complex water-organic mixtures within various CMS microstructures. Competitive sorption and permeation studies of the binary mixtures in different microstructural CMS will be followed. The obtained binary mixture transport parameters were used to predict binary water-organic mixtures transport.

36 MATERIALS SCIENCE↗

Development of PFLOTRAN Transport Capability for Use in the Waste Isolation Pilot Plant Performance Assessment - 20545

Waste Isolation Pilot Plant (WIPP) performance assessment (PA) calculations estimate the probability of radionuclide release from the repository to the land surface and across the land withdrawal boundary for a regulatory period of 10,000 years after facility closure. Simulations of flow and transport in the repository and the surrounding Salado Formation are foundational to the PA. Because proposed additional waste emplacement panels would result in an asymmetric repository layout, the US Department of Energy (DOE) is preparing to transition to use of a three-dimensional (3-D) model domain for simulation of flow and transport instead of the two-dimensional (2-D) flared grid domain currently used. DOE has charged Sandia National Laboratories with developing the capability necessary to simulate processes affecting flow and transport in the WIPP in PFLOTRAN, an open-source massively parallel multi-phase flow and reactive transport code. The new flow and transport capabilities developed in PFLOTRAN incorporate WIPP-specific process models and will replace the 2-D simulators (BRAGFLO and NUTS) that are currently utilized for Salado flow and transport calculations in WIPP PA. The focus of this paper is on the development of a new Nuclear Waste Transport (NWT) mode in PFLOTRAN that has all of the capabilities necessary for Salado transport simulations, including the ability to handle complete dry-out (100% gas saturation) of arbitrary cells in the model domain, radionuclide mass conservation at step changes in porosity associated with borehole intrusion, and the ability to calculate fluxes on a flared grid. The new PFLOTRAN transport capability and a suite of verification tests were designed around a list of functional requirements for WIPP PA calculations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Understanding, inhibiting, and engineering membrane transporters with high-throughput mutational screens

Promiscuous membrane transporters play vital roles across domains of life, mediating the uptake and efflux of structurally and chemically diverse substrates. Although many transporter structures have been solved, the fundamental rules of polyspecific transport remain inscrutable. In recent years, high-throughput genetic screens have solidified as powerful tools for comprehensive, unbiased measurements of variant function and hypothesis generation, but have had infrequent application and limited impact in the transporter field. In this primer, we describe the principles of high-throughput screening methods available for studying polyspecific transporters and comment on the necessity and potential of high-throughput methods for deciphering these transporters in particular. We present several screening approaches which could provide a fundamental understanding of the molecular basis of function and promiscuity in transporters. Here, we further posit how this knowledge can be leveraged to design inhibitors that combat multidrug resistance and engineer transporters as needed tools for synthetic biology and biotechnology applications.

EPIs↗

Ion Transport in Carbon Nanotube Porins with a pH-Switchable Entrance Gate

Molecular transport in nanofluidic channels often differs drastically from conventional bulk transport. Strong confinement in those channels amplifies the roles of surface transport, surface defects, and molecular gates. Here, in this study, we introduce a chemical functionality at the nanotube rim that acts as a pH-triggered molecular gate by forming a movable lid that blocks the pore entrance. We use ion and proton transport measurements to show that these sub-1 nm diameter fluorescent ultrashort carbon nanotube porins (FUNPs) modulate ion transport by switching between the “open” and “closed” conformations of this gate. Specifically, at neutral pH the channel lid is open, allowing unimpeded ion transport through the gate, whereas at acidic pH values the lid forms a “closed” conformation that blocks transport through the nanotube. We also report first-principles MD simulations that confirm this gating mechanism and reveal molecular details of the ion and proton transport processes in these functional nanopores.

Carbon nanotubes↗

Response of thermal and fast-ion transport to beam ion population, rotation and T e / T i in the DIII-D steady state hybrid scenario

The thermal and fast-ion transport properties of DIII-D steady-state hybrid discharges with normalized beta β N ≳ 3 are studied at low injected torque and an increased electron to ion temperature ratio T e / T i . Linear stability analysis performed with the TGLF turbulent code indicates that a high-k mode is usually dominant at smaller radii, whereas a low-k mode is usually dominant at larger radii in these plasmas. A reduction in the net injected torque from 8.6 to 4.3 N-m leads to reduced E × B shear and hence, an enhanced turbulence that was observed on the Doppler backscattering diagnostic and was also computed with TGLF. As T e / T i in the core was increased from 0.57 to 0.66 by adding electron cyclotron current drive (ECCD) to these plasmas, higher levels of transport are observed with increased high-k modes indicated by TGLF. The fast-ion transport level varied over an order of magnitude in these discharges depending on whether Alfvén eigenmodes, fishbones, or no instabilities were observed. Hybrid plasmas with fishbones have decreased fast-ion transport, compared to plasmas with Alfvén eigenmodes, since they are resonant with a smaller portion of phase space and their resonance is farther from the wall. This reduction in fast-ion transport with ECCD mitigates the increase in turbulent transport, resulting in higher performance than expected during strong electron heating. Similarly, the lowest fast-ion transport was observed in the low torque plasma, which also led to better than expected performance at this torque value. Finally, the thermal and fast-ion transport changes observed as the torque/rotation and T e / T i are varied indicate possible methods for transferring this scenario to a reactor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

COG User's Manual: A Multiparticle Monte Carlo Transport Code (Sixth Edition)

COG is a high-resolution code for the Monte Carlo simulation of coupled particle transport in arbitrary 3-D geometry. COG will transport neutrons, protons, deuterons, alpha particles with energies up to hundreds of GeV, and photons with energy ranges limited by the available cross section sets and physics models. Electrons can be transported via the EGS5 electron transport kernel, electrons can also be transported. The COG code is a significant upgrade from earlier Monte Carlo transport codes and has been written specifically to make it more versatile, accurate, and easy to use. COG has provisions for calculating deep penetration (shielding) problems, criticality problems, and neutron activation problems while retains all of the standard capabilities found in other Monte Carlo transport codes. COG uses high-resolution pointwise cross-section databases and makes no compromises in the transport physics, so that the results of a COG run are limited only by the accuracy of the databases used. COG runs primarily on Linux Operating System workstations with MPICH software installed – currently, Red Hat 7 & 8, Windows 10 (Windows Subsystem for Linux –WSL), Ubuntu 16, 18 & 20, OpenSUSE Leap 15.2, Fedora 32, Apple Power Mac with Intel CPU (with MacPorts installed) workstations, and LLNL LC supercomputer CTS-1 cluster with TOSS 3 are supported.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Editorial: Structure and mechanism of microbial membrane active transporters

Membrane active transporters play essential roles in microbial physiology. They couple energy transduction to conformational changes that drive translocation of nutrients, substrates and ions, as well as molecular communication. The structure and function of microbial membrane active transporters are highly diverse. Typical examples include the primary active transporters in the ATP-binding cassette (ABC) superfamily (Thomas and Tampé, 2020; Davidson et al., 2008; Locher et al., 2002), the secondary active transporters in the Major Facilitator Superfamily (MFS) (Drew et al., 2021; Kaback and Guan, 2019), and the ligand-gated porins in the TonB-dependent transporter (TBDT) family (Klebba et al., 2021). As structural, proteogenomic, and computational methods advance, active transporters are increasingly recognized as dynamic molecular machines whose mechanisms can now be visualized and modeled with remarkable precision, building on decades of biochemical and biophysical discovery that established the foundations of this field. The transporter studies recruited in this Research Topic provide us with new insights into the field including structure-function of sugar transporters in yeast, structural prediction and classification of ABC complexes in Bacillus subtilis, Type VI Secretion System (T6SS) in Bacteroides fragilis, amino acids uptake in Escherichia coli and bacterial spore germination.

mechanism↗

Conservative solute transport processes and associated transient storage mechanisms: Comparing streams with contrasting channel morphologies, land use and land cover

Abstract Land use within a watershed impacts stream channel morphology and hydrology and, therefore, in‐stream solute transport processes and associated transient storage mechanisms. This study evaluated transport processes in two contrasting stream sites where channel morphology was influenced by the surrounding land use, land cover, climate and geologic controls: Como Creek, CO, a relatively undisturbed, high gradient, forested stream with a gravel bed and complex channel morphology, and Clear Creek, IA, an incised, low‐gradient stream with low‐permeability substrate draining an agricultural landscape. We performed conservative stream tracer injections at these sites to address the following questions: (1) How does solute transport vary between streams with differing morphologies? and (2) How does solute transport at each stream site change as a function of discharge? We analysed in‐stream tracer time series data and compared results quantifying solute attenuation in surface and subsurface transient storage zones. Significant trends were observed in these metrics with varying discharge conditions at the forested site but not at the agricultural site. There was a broad range of transport mechanisms and evidence of substantial exchange with both surface and hyporheic transient storage in the relatively undisturbed, forested stream. Changing discharge conditions activated or deactivated different solute transport mechanisms in the forested site and greatly impacted advective travel time. Conversely in the simplified agricultural stream, there was a narrow range of solute transport behaviour across flows and predominantly surface transient storage at all measured discharge conditions. These results demonstrate how channel simplification inhibits available solute transport mechanisms across varying discharge conditions.

54 ENVIRONMENTAL SCIENCES↗

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗

Colloid-facilitated transport of 238 Pu, 233 U and 137 Cs through fractured chalk: Laboratory experiments, modelling, and implications for nuclear waste disposal

The influence of montmorillonite colloids on the mobility of 238 Pu, 233 U and 137 Cs through a chalk fracture was investigated to assess the transport potential for radioactive waste. Radioisotopes of each element, along with the conservative tracer tritium, were injected in the presence and absence of montmorillonite colloids into a naturally fractured chalk core. In parallel, batch experiments were conducted to obtain experimental sorption coefficients (K d , mL/g) for both montmorillonite colloids and the chalk fracture material. Breakthrough curves were modelled to determine diffusivity and sorption of each radionuclide to the chalk and the colloids under advective conditions. Uranium sorbed sparingly to chalk (log K d = 0.7 ± 0.2) in batch sorption experiments. 233 U(VI) breakthrough was controlled primarily by the matrix diffusion and sorption to chalk (15 and 25% recovery with and without colloids, respectively). Cesium, in contrast, sorbed strongly to both the montmorillonite colloids and chalk (batch log K d = 3.2 ± 0.01 and 3.9 ± 0.01, respectively). The high affinity to chalk and low colloid concentrations overwhelmed any colloidal Cs transport, resulting in very low 137 Cs breakthrough (1.1–5.5% mass recovery). Batch and fracture transport results, and the associated modelling revealed that Pu migrates both as Pu (IV) sorbed to montmorillonite colloids and as dissolved Pu(V) (7% recovery). Transport experiments revealed differences in Pu(IV) and Pu(V) transport behavior that could not be quantified in simple batch experiments but are critical to effectively predict transport behavior of redox-sensitive radionuclides. Finally, a brackish groundwater solution was injected after completion of the fracture flow experiments and resulted in remobilization and recovery of 2.2% of the total sorbed radionuclides which remained in the core from previous experiments. In general, our study demonstrates consistency in sorption behavior between batch and advective fracture transport. Finally, the results suggest that colloid-facilitated radionuclide transport will enhance radionuclide migration in fractured chalk for those radionuclides with exceedingly high affinity for colloids.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Are enzymes transported in soils by water fluxes?

Transport of extracellular hydrolytic enzymes in soils has always been a subject of doubt. The considerations against its importance are that (i) enzymes benefit their producers the most when they remain in close proximity; and (ii) enzymes are large molecules with low mobility due to high affinity to fine soil particles and organic matter. However, soil mineral colloids (SMC), to which extracellular enzymes also have an affinity and which are known to facilitate transport of a broad variety of chemicals and microorganisms in soils, can serve as vehicles for enzyme transport as well. Since current literature lacks information on enzyme transport in soils, our goal was to determine whether enzymes are transported and, if so, whether they are transported in a free- or in a colloid-associated form. We conducted column transport experiments with four hydrolytic enzymes, namely, β-glucosidase, acid-phosphatase, cellobiohydrolase, and xylosidase, in soils with contrasting textures. The eluents containing enzymes were applied on top of soil columns, while enzyme activities, SMC, and electrical conductivity were measured in the effluents from the columns. Our results provided evidence of joint enzyme transport with soil colloids. The enzymes associated with the coarse SMC (1 μm < Ø) contributed 52–88% of the total enzyme activity in the effluents. The remaining enzyme activity was attributed to the enzymes associated with organic colloids, fine SMC (Ø < 1 μm) and free enzymes in solution. Furthermore, this study suggested a dual effect of ionic strength in the soil suspension on enzyme activity and their release from soils with soil colloids.

59 BASIC BIOLOGICAL SCIENCES↗

Efficient Intermolecular Charge Transport in π-Stacked Pyridinium Dimers Using Cucurbit[8]uril Supramolecular Complexes

Intermolecular charge transport through π-conjugated molecules plays an essential role in biochemical redox processes and energy storage applications. In this work, we observe highly efficient intermolecular charge transport upon dimerization of pyridinium molecules in the cavity of a synthetic host (cucurbit[8]uril, CB[8]). Stable, homoternary complexes are formed between pyridinium molecules and CB[8] with high binding affinity, resulting in an offset stacked geometry of two pyridiniums inside the host cavity. The charge transport properties of free and dimerized pyridiniums are characterized using a scanning tunneling microscope-break junction (STM-BJ) technique. Our results show that π-stacked pyridinium dimers exhibit comparable molecular conductance to isolated, single pyridinium molecules, despite a longer transport pathway and a switch from intra- to intermolecular charge transport. Control experiments using a CB[8] homologue (cucurbit[7]uril, CB[7]) show that the synthetic host primarily serves to facilitate dimer formation and plays a minimal role on molecular conductance. Molecular modeling using density functional theory (DFT) reveals that pyridinium molecules are planarized upon dimerization inside the host cavity, which facilitates charge transport. In addition, the π-stacked pyridinium dimers possess large intermolecular LUMO–LUMO couplings, leading to enhanced intermolecular charge transport. Altogether, this work demonstrates that supramolecular assembly can be used to control intermolecular charge transport in π-stacked molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulated Dust Transport in the Convective Boundary Layer

Soil dusts are an important source of aerosol in agricultural regions and can affect the Earth's radiation budget through the modification of cloud properties, and in particular, through their ability to act as ice nucleating particles. In order to impact cloud properties, agricultural soil dusts need to be transported from the point of emission to cloud–relevant altitudes. Vertical transport within the planetary boundary layer is strongly controlled by turbulence and is challenging to represent accurately in regional and global models. Large–eddy simulations (LES) are run at resolutions capable of resolving most of the turbulent energy directly and can thus better simulate vertical transport. In this study, we leverage the LES ARM Symbiotic Simulation and Observation (LASSO) large–eddy simulations to simulate vertical transport of agricultural dust within the turbulent boundary layer using a modified version of the stochastic dispersion model FLEXPART–WRF. We find that the modified model is better capable of simulating particle transport due to turbulence, and that particle size was the greatest factor in determining particle lifetime. Individual meteorology and particle density had intermediate effects upon particle transport, while release height had little effect upon simulation results. Finally, we utilize a quasi–single column model (QSCM) approach to determine how our results compare to a parameterized treatment of turbulence. The QSCM simulations led to greater tracer transport out of the boundary layer, with ramifications for any studies utilizing a Lagrangian stochastic model to understand tracer dispersion. Furthermore, these results highlight the importance of accurately simulating turbulence for understanding particle transport.

54 ENVIRONMENTAL SCIENCES↗

Fully consistent Eulerian Monte Carlo fields method for solving probability density function transport equations in turbulence modeling

The probability density function (PDF) transport equation method is a sophisticated model for the closure of turbulent mixing and turbulent reactive flows. An efficient solution approach for solving the PDF transport equation has been vital for the method to be widely used in applications. The Eulerian Monte Carlo fields (EMCF) method has been developed to solve the PDF transport equation efficiently for decades. A recent work by Wang et al. revealed a serious issue of the EMCF method for not being fully consistent with the PDF transport equation for which the method is designed to solve. This work advances the state of the art by introducing fully consistent EMCF methods for solving the PDF transport equation. The fully consistent EMCF formulations are derived for two different PDF equation forms. The consistency of the EMCF formulations is mathematically confirmed by examining the derived moment transport equations from the EMCF formulations and from the PDF transport equation. The method of manufactured solutions is employed to further verify the consistency and convergence of the different EMCF formulations numerically. The newly introduced EMCF formulations bring the EMCF method to full consistency with the PDF transport equations for the first time.

42 ENGINEERING↗

Mesoscopic finite-size effects of unconventional electron transport in PdCoO 2

A wide range of unconventional transport phenomena has recently been observed in single-crystal delafossite metals. Here, we present a theoretical framework to elucidate electron transport using a combination of first-principles calculations and numerical modeling of the anisotropic Boltzmann transport equation. Using PdCoO 2 as a model system, we study different microscopic electron and phonon scattering mechanisms and establish the mean free path hierarchy of quasiparticles at different temperatures. We treat the anisotropic Fermi surface explicitly to numerically obtain experimentally-accessible transport observables, which bridge between the “diffusive,” “ballistic,” and “hydrodynamic” transport regime limits. Further, we illustrate that the distinction between the “quasiballistic” and “quasihydrodynamic” regimes is challenging and often needs to be quantitative in nature. From first-principles calculations, we populate the resulting transport regime plots and demonstrate how the Fermi surface orientation adds complexity to the observed transport signatures in micrometer-scale devices. Our work provides key insights into microscopic interaction mechanisms on open hexagonal Fermi surfaces and establishes their connection to the macroscopic electron transport in finite-size channels.

36 MATERIALS SCIENCE↗

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗