Transport Model Research Articles

Transport properties of high Mach number hypersonic air plasmas

Abstract The collisional and transport properties of hypersonic plasmas have been simulated by an air plasma chemistry model, which includes collisions with electrons, ions and neutral species, elastic scattering, vibrational relaxation and a transport model. Species and thermal fluxes at the surface of the vehicle have been investigated as a function of post-shock gas temperature and species sticking coefficient for a fixed altitude of 50 km. At temperatures below about 5000 K, the leading species are vibrationally excited nitrogen molecules, while at higher temperatures the atomic oxygen and nitrogen dominate. Large fluxes of oxygen atoms have been observed in the simulations, on the order of 1020 cm − 2 s − 1, which may lead to high rates of surface oxidation. Another subject of this study is temperature equilibration. For electrons, equilibration takes tens of microseconds, while the vibrational temperature equilibration time vary widely; from a few microseconds to hundreds of microseconds, depending on the gas temperature. Finally, the adiabatic parameter γ was calculated for post-shock gas temperatures 5000 K and 10 000 K and total gas density 1.2 × 10 17 c m − 3 . For post-shock gas temperature 5000 K, only a slight reduction of γ from the ideal gas value of γ = 1.4 is observed, while for 10 000 K it drops to γ ≅ 1.26, which has a considerable impact on plasma properties. It was further established that the vibrational kinetics plays a leading role. While a single excited vibrational level of the N2 molecule captures the salient properties of the plasma, a detailed vibration kinetics is required for high-fidelity simulations.

Surface Flux Transport Modeling Using Physics-informed Neural Networks

Studying the magnetic field properties on the solar surface is crucial for understanding the solar and heliospheric activities, which in turn shape space weather in the solar system. Surface flux transport (SFT) modeling helps us to simulate and analyze the transport and evolution of magnetic flux on the solar surface, providing valuable insights into the mechanisms responsible for solar activity. In this work, we demonstrate the use of machine learning techniques in solving magnetic flux transport, making it accurate. We have developed a novel physics-informed neural network (PINN)-based model to study the evolution of bipolar magnetic regions using SFT in one-dimensional azimuthally averaged and also in two dimensions. We demonstrate the efficiency and computational feasibility of our PINN-based model by comparing its performance and accuracy with that of a numerical model implemented using the Runge–Kutta implicit–explicit scheme. The mesh-independent PINN method can be used to reproduce the observed polar magnetic field with better flux conservation. This advancement is important for accurately reproducing observed polar magnetic fields, thereby providing insights into the strength of future solar cycles. This work paves the way for more efficient and accurate simulations of solar magnetic flux transport and showcases the applicability of PINNs in solving advection–diffusion equations with a particular focus on heliophysics.

An experimental investigation of boundary layer over permeable interfaces in Hele-Shaw micromodels

This study experimentally investigates boundary layer development over permeable interfaces using Hele-Shaw micromodels and high-resolution micro-particle image velocimetry (micro-PIV). Velocity vectors, captured at a 5 μm scale, reveal the flow behavior at the interface between free-flow and porous media with ordered structures and porosities ranging from 50% to 85%. The results show that the boundary layer streamline alignment decreases with increasing porosity, while lower permeability fosters more uniform and parallel flow near the interface. Flow channeling occurs along paths of the least resistance, with more flow directed through the Hele-Shaw free-flow region as the solid fraction of the porous material increases. The Reynolds number (0.14–0.94), based on the Hele-Shaw hydraulic diameter, has a minimal effect on the normalized velocity distribution. Furthermore, an analytical solution for the external boundary layer thickness exhibited good agreement with experimental data, confirming a thickness of 2–4 times the square root of the free-flow Hele-Shaw permeability. Additionally, a Q-criterion analysis identified, for the first time, distinct zones within the external boundary layer, capturing the balance between rotational and deformation components as a function of permeability. These findings offer insight into flow dynamics in porous media systems, with implications for both natural and industrial applications, and contribute to the improved modeling of fluid dynamics and momentum transport in coupled free-flow and porous media environments.

Using Rainfall‐Induced Groundwater Temperature Response to Estimate Lateral Flow Velocity

AbstractThis study introduces a novel heat tracing method for estimating lateral groundwater flow velocity induced and sustained by heavy rainfall events in lowland areas, leveraging the distinct temperature difference between rainfall and groundwater. The method is motivated by the observation that the rainfall‐induced groundwater temperature signal dissipates along the flow path. To explain the observed temperature anomaly and then estimate the lateral flow velocity, we develop a semi‐analytical model for heat transport in the aquifer, accounting for conduction losses to adjacent layers. Our findings reveal that interactions between the aquifer, vadose zone, and bedrock significantly influence the temperature signal, thereby affecting velocity estimation. Inaccuracies in measured aquifer properties, such as thickness, porosity, and thermal conductivity of surrounding layers, increase the uncertainty of velocity estimates. However, variations in aquifer thermal conductivity have a minimal effect on the method's overall accuracy. When estimating multiple parameters, velocity estimates tend to be less reliable, especially if aquifer porosity remains uncertain. This is due to the challenges of simultaneously inverting both velocity and porosity. Overall, this work underscores the potential of using heat as a tracer for assessing lateral groundwater flow following rainfall, offering a practical, low‐cost solution applicable in a wide range of settings.

Numerical Modelling of Carrier Transport in Organic Field Effect Transistors

Background: Organic field effect transistors (OFETs), used in the fabrication of nanosensors, are one of the most promising devices in organic electronics because of their lightweight, flexibility, and low fabrication cost. However, the optimization of such OFETs is still in an early stage due to the minimal analytical and numerical models presented in the literature. Objective: This research presses to demonstrate a numerical carrier transport model based on the finite element method (FEM) to investigate the I-V characteristic of OFETs. Methods: Two various organic semiconductor materials have been included in the study, polyaniline and pentacene, where micro-scale, as well as nano-scale models have been presented. OFETs regarding channel length, dielectric thickness, and doping level impact have been studied. We nominated the threshold voltage, the on/off current ratio, the sub-threshold swing, and the field effect mobilities as the primary output evaluating parameters. Results: The numerical model has shown the criticality of the doping effect on tuning the device flowing drain current to exceed 300 μA saturation current, along with a threshold voltage of -0.1 V under a channel length of 30 nm. Conclusion: The study highlights the effectiveness of polyaniline over pentacene as nano-channel length OFET due to the boosted conductivity of polyaniline concerning pentacene.

Biofilm Growth in Porous Media Well Approximated by Fractal Multirate Mass Transfer With Advective‐Diffusive Solute Exchange

AbstractBiofilm growth in porous media changes not only the hydrodynamic properties of the medium (reduction in porosity and permeability, and increase in dispersivity), but also the transport itself (breakthrough curves display increasingly fast first arrivals and long tails). These features are well reproduced by multicontinuum models (Multi‐Rate Mass Transfer, MRMT) which can be used to describe reactive transport in heterogeneous porous media and facilitate the simulation of reactions that are localized within biofilms. Here, we present a conceptual and numerical model of biochemical reactive transport with dynamic biofilm growth based on MRMT formulations. Mass exchange between mobile water and immobile biofilm aggregates is represented by a memory function, which simplifies definition of MRMT parameters. We successfully tested this model on two sets of laboratory data and found that (a) a basic model based on the growth of uniformly sized biofilm aggregates fails to reproduce laboratory tracer tests and rate of biofilm growth, while a fractal growth model, which we obtain by integrating the memory functions of biofilm aggregates with a power law distribution, does; (b) the biofilm memory function evolves as the biofilm grows; and (c) the early time portion of eluted volume tracer breakthrough curves are independent of flow rate, whereas the tail becomes heavier when the flow rate is decreased, which implies that both advection controlled and diffusion controlled mass exchange coexist in biofilms. These findings imply that porous media biofilms are essentially different from those developing in human tissues or open spaces.

Evaluating the role of sex-related structure-function differences on airway aerosol transport and deposition.

Several experimental studies have found that females have higher particle deposition in the airways than males. This has implications for the delivery of aerosolized therapeutics and for understanding sex differences in respiratory system response to environmental exposures. This study evaluates several factors that potentially contribute to sex differences in particle deposition, using scale-specific structure-function models of one-dimensional (1-D) ventilation distribution, particle transport, and deposition. The impact of gravity, inhalation flow rate, and dead space are evaluated in 12 structure-based models (7 females; 5 males). Females were found to have significantly higher total, bronchial, and alveolar deposition than males across a particle size range from 0.01 to 10 μm. Results suggest that higher deposition fraction in females is due to higher alveolar deposition for smaller particle sizes and higher bronchial deposition for larger particles. Females had higher alveolar deposition in the lower lobes and slightly lower particle concentration in the left upper lobe. Males were found to be more sensitive to changes due to gravity, showing greater reduction in bronchial deposition fraction. Males were also more sensitive to change in inhalation flow rate and to scaling of dead space due to the larger male baseline airway size. Predictions of sex differences in particle deposition-that are consistent with the literature-suggest that sex-based characteristics of lung and airway size interacting with particle size gives rise to differences in regional deposition.NEW & NOTEWORTHY Sex differences in airway tract particle deposition are analyzed using computational models that account for scale-specific structure and function. We show that sex-related differences in lung and airway size can explain experimental observations of increased deposition fraction in females, with females tending toward enhanced fine particle deposition in the alveolar airways and enhanced bronchial deposition for larger particles.

Conjugate heat transfer simulations of a radially cooled gas turbine blade leading edge using a vortex-based fluidic oscillator for sweeping jet impingement

The turbine blades of aero engines are subjected to extremely high temperatures, particularly at the leading edge, where temperatures can reach approximately 1800–2000 K. Therefore, effective heat load management is crucial. A vortex-based fluidic oscillator for sweeping jet impingement was proposed as an innovative cooling method to enhance heat transfer at leading edge of high-pressure gas turbine blades. This numerical investigation evaluates the cooling performance of a vortex-based sweeping jet compared to steady and conventional sweeping jets in a radially cooled high-pressure turbine blade. In this study, a conjugate heat transfer model based on three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) equations is employed. The shear stress transport (SST k–ω) model is specifically selected to predict the flow field and heat transfer characteristics of a vortex-based fluidic oscillator applied to the leading edge. To verify the accuracy of numerical calculations, two sets of experimental data were used as benchmark. The results demonstrated strong qualitative and quantitative agreement with experimental data. Various parameters, including coolant mass flow rates (0.171, 0.514, and 0.857 g/s), aspect ratios (0.5, 0.65, and 1), jet-to-wall spacings (H/D = 2, 4, and 6), and pressure drop, were examined to assess overall cooling effectiveness and heat transfer performance. Time-averaged and time-resolved flow field measurements revealed that vortex-based fluidic oscillator significantly enhanced cooling effects and covered a larger impinging area compared to a steady jet. Notably, the vortex-based fluidic oscillator achieved a 24.3% higher heat transfer performance than the steady jet at H/D = 2, with an average temperature decrease in approximately 21 K at leading edge.

Development of a Generalizable Data-Driven Turbulence Model: Conditioned Field Inversion and Symbolic Regression

This paper addresses the issue of predicting separated flows with Reynolds-averaged Navier–Stokes (RANS) turbulence models, which are essential for many engineering tasks. Traditional RANS models usually struggle with this task, so recent efforts have focused on data-driven methods such as field inversion and machine learning (FIML) to correct this issue by adjusting the baseline equations. However, these FIML methods often reduce accuracy in attached boundary layers. To address this issue, we developed a “conditioned field inversion” technique. This method adjusts the corrective factor β (used by FIML) in the shear-stress transport (SST) model. It multiplies β with a shield function fd that is off in the boundary layer and on elsewhere. This maintains the accuracy of the baseline model for the attached flows. We applied both conditioned and classic field inversion to the NASA hump and a curved backward-facing step, creating two datasets. These datasets were used to train two models: SR-CND (symbolic regression-conditioned, from our new method) and SR-CLS (symbolic regression-classic, from the traditional method). The SR-CND model matches the SR-CLS model in predicting separated flows in various scenarios, such as periodic hills, the NLR7301 airfoil, the 3D SAE (Society of Automotive Engineers) car model, and the 3D Ahmed body, and outperforms the baseline SST model in the cases presented in the paper. Importantly, the SR-CND model maintains accuracy in the attached boundary layers, whereas the SR-CLS model does not. Therefore, the proposed method improves separated flow predictions while maintaining the accuracy of the original model for attached flows, offering a better way to create data-driven turbulence models.

Ensemble Kalman Filter Data Assimilation into the Surface Flux Transport Model to Infer Surface Flows: An Observing System Simulation Experiment

Knowledge of the global magnetic field distribution and its evolution on the Sun’s surface is crucial for modeling the coronal magnetic field, understanding the solar wind dynamics, computing the heliospheric open flux distribution, and predicting the solar cycle strength. As the far side of the Sun cannot be observed directly and high-latitude observations always suffer from projection effects, we often rely on surface flux transport (SFT) simulations to model the long-term global magnetic field distribution. Meridional circulation, the large-scale north–south component of the surface flow profile, is one of the key components of the SFT simulation that requires further constraints near high latitudes. Prediction of the photospheric magnetic field distribution requires knowledge of the flow profile in the future, which demands reconstruction of that same flow at the current time so that it can be estimated at a later time. By performing Observing System Simulation Experiments, we demonstrate how the ensemble Kalman filter technique, when used with an SFT model, can be utilized to make “posterior” estimates of flow profiles into the future that can be used to drive the model forward to forecast the photospheric magnetic field distribution.

Daily high-resolution surface PM2.5 estimation over Europe by ML-based downscaling of the CAMS regional forecast.

Fine particulate matter (PM2.5) is a key air quality indicator due to its adverse health impacts. Accurate PM2.5 assessment requires high-resolution (e.g., atleast 1 km) daily data, yet current methods face challenges in balancing accuracy, coverage, and resolution. Chemical transport models such as those from the Copernicus Atmosphere Monitoring Service (CAMS) offer continuous data but their relatively coarse resolution can introduce uncertainties. Here we present a synergistic Machine Learning (ML)-based approach called S-MESH (Satellite and ML-based Estimation of Surface air quality at High resolution) for estimating daily surface PM2.5 over Europe at 1 km spatial resolution and demonstrate its performance for the years 2021 and 2022. The approach enhances and downscales the CAMS regional ensemble 24h PM2.5 forecast by training a stacked XGBoost model against station observations, effectively integrating satellite-derived data and modeled meteorological variables. Overall, against station observations, S-MESH (mean absolute error (MAE) of 3.54 μg/m3) shows higher accuracy than the CAMS forecast (MAE of 4.18 μg/m3) and is approaching the accuracy of the CAMS regional interim reanalysis (MAE of 3.21 μg/m3), while exhibiting a significantly reduced mean bias (MB of -0.3 μg/m3 vs. -1.5 μg/m3 for the reanalysis). At the same time, S-MESH requires substantially less computational resources and processing time. At concentrations >20 μg/m3, S-MESH outperforms the reanalysis (MB of -7.3 μg/m3 and -10.3 μg/m3 respectively), and reliably captures high pollution events in both space and time. In the eastern study area, where the reanalysis often underestimates, S-MESH better captures high levels of PM2.5 mostly from residential heating. S-MESH effectively tracks day-to-day variability, with a temporal relative absolute error of 5% (reanalysis 10%). Exhibiting good performance at high pollution events coupled with its high spatial resolution and rapid estimation speed, S-MESH can be highly relevant for air quality assessments where both resolution and timeliness are critical.

Methods for Quantifying Source-Specific Air Pollution Exposure to Serve Epidemiology, Risk Assessment, and Environmental Justice.

Identifying sources of air pollution exposure is crucial for addressing their health impacts and associated inequities. Researchers have developed modeling approaches to resolve source-specific exposure for application in exposure assessments, epidemiology, risk assessments, and environmental justice. We explore six source-specific air pollution exposure assessment approaches: Photochemical Grid Models (PGMs), Data-Driven Statistical Models, Dispersion Models, Reduced Complexity chemical transport Models (RCMs), Receptor Models, and Proximity Exposure Estimation Models. These models have been applied to estimate exposure from sources such as on-road vehicles, power plants, industrial sources, and wildfires. We categorize these models based on their approaches for assessing emissions and atmospheric processes (e.g., statistical or first principles), their exposure units (direct physical measures or indirect measures/scaled indices), and their temporal and spatial scales. While most of the studies we discuss are from the United States, the methodologies and models are applicable to other countries and regions. We recommend identifying the key physical processes that determine exposure from a given source and using a model that sufficiently accounts for these processes. For instance, PGMs use first principles parameterizations of atmospheric processes and provide source impacts exposure variability in concentration units, although approaches within PGMs for source attribution introduce uncertainties relative to the base model and are difficult to evaluate. Evaluation is important but difficult-since source-specific exposure is difficult to observe, the most direct evaluation methods involve comparisons with alternative models.

IMPACT OF SOURCE (DRAIN) DOPING PROFILES AND CHANNEL DOPING LEVEL ON SELF-HEATING EFFECT IN FinFET

In this work the impact of the doping profile in the source and drain areas on the self-heating effect in SOI FinFET is simulated at different doping levels in the channel. Constant profile as well as two types of analytical profiles are considered. The impact of the doping profile on the threshold voltage and on the ratio Ion/Ioff at different doping levels of the channel is also considered. To consider the self-heating effect the thermodynamic transport model in TCAD Sentaurus software is used for simulation. The results of simulation show that self-heating effect, threshold voltage, and Ion/Ioff ratio considerably depend on the doping profile in source and drain areas.

Multiphase flow and reactive transport benchmark for radioactive waste disposal

AbstractCompacted bentonite is part of the multi-barrier system of radioactive waste repositories. The assessment of the long-term performance of the barrier requires using reactive transport models. Here we present a multiphase flow and reactive transport benchmark for radioactive waste disposal. The numerical model deals with a 1D column of unsaturated bentonite through which water, dry air and $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) may flow and with the following reactions; aqueous complexation, calcite and gypsum dissolution/precipitation, cation exchange and gas dissolution. INVERSE-FADES-CORE V2, $$\hbox {DuMu}^X$$ DuMu X , TOUGHREACT and iCP were benchmarked with 6 test cases of increasing complexity, starting with conservative tracer transport under variably unsaturated conditions and ending with water flow, gas diffusion, minerals and cation exchange. The solutions of all codes exhibit similar trends. Small discrepancies are found in conservative tracer transport due to differences in hydrodynamic dispersion. Computed $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) pressures agree when a sufficiently refined grid is used. Small discrepancies in $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) and pH are found near the no-flow boundary at early times which vanish later. Discrepancies are due differences in the formulations used for gas flow at nearly water-saturated conditions. Computed $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) pressures show a fluctuation between $$10^{-4}$$ 10 - 4 and $$10^{-3}$$ 10 - 3 years which slows down the in-diffusion of $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) . This fluctuation is associated with chemical reactions involving $${\hbox {CO}_{2}}$$ CO 2 . There are discrepancies in solute concentrations due to differences in the Debye–Hückel (DH) formulation. They are overcome when all codes use the same DH formulation. The results of this benchmark will contribute to increase the confidence on multiphase reactive transport models for radioactive waste disposal.

Analysis and prediction of denitration performance of Mn1Co0.5Cr0.5Ox catalyst based on CFD and BP-GA method

Based on the experimental data of Mn1Co0.5Cr0.5Ox catalysts and the component transport model in Computational Fluid Dynamics (CFD), a kinetic model for the standard NH3-SCR (NH3 selective catalytic reduction) process was effectively established. The objective of the model development was to predict the denitrification reaction rate of the catalyst, which incorporates various factors such as the Arrhenius parameters (Pre-exponential factor and activation energy), inertial resistance, viscous resistance, and surface-to-volume ratio. To verify the practicability of the model, simulation results were compared with actual experimental data. The effects of NH3, NO, O2 concentrations, and gas hourly space velocity (GHSV) on NO conversion were simulated and analyzed. Subsequently, the NO conversion prediction model was trained and established using a combination of numerical simulation results, back-propagation neural network, and genetic algorithm (BP-GA). Furthermore, the significance of the impact that various factors had on the denitrification activity of the catalyst was determined.

On the 3D Transport of Low-energy Galactic Cosmic-ray and Jovian Electrons in the Inner Heliosphere in the Presence of a Fisk-type Heliospheric Magnetic Field

Modeling the transport of low-energy (1−10 MeV) cosmic-ray electrons can lead to valuable insights as to the behavior of the heliospheric magnetic field (HMF), due to the fact that the mean free path (MFP) of these particles parallel to the HMF is significantly larger than their perpendicular MFP, and that these particles experience little in the way of drift due to gradients/curvatures in the HMF and along the heliospheric current sheet. Jovian electrons are particularly suitable for such an endeavour, as they originate from a decentral source in the inner heliosphere. To this end, the transport of these electrons is studied using a 3D, ab initio particle transport code that incorporates theoretical expressions for electron diffusion coefficients, and utilizes as inputs for these transport coefficients turbulence quantities calculated using a two-component turbulence transport model. The effects of a novel Fisk-type field on the transport of these Jovian electrons are investigated and compared with the effects of a standard Parker field.

A Tale of Two Storms: Inter‐Storm Variability of Stable Water Isotopes in a Solute Transport Model

ABSTRACTStable isotopic methods in hydroclimate monitoring are powerful for improving water resources management, but applications are limited, especially in semi‐arid regions where such management is needed most. Here, we show that we can address shortcomings related to the lack of a seasonal signal using stable water isotopic signatures measured in precipitation over the East San Francisco Bay area, California, during two contrasting events sampled at more than 20 locations in the winter of 2023. The observed range in δ18O in the rain samples is similar for both storms. However, the distributions do not overlap—the mean air temperature and δ18O during Winter Storm Olive (February 2023) were 2°C and − 12‰, respectively, while a warm atmospheric river event (March 2023) had a mean temperature of 9°C and δ18O of −6‰, close to the long‐term average δ18O measured in local precipitation. The Winter Storm showed expected trends in δ18O related to geography (i.e., lower with greater distance inland and elevation), while the atmospheric river δ18O pattern was more spatially uniform. We use hydrometric data from a gaged watershed in the study area and isotopic signatures of rain sampled during the two storm events and apply a solute transport model (StorAge selection) with a travel‐time approach to examine predicted watershed responses and potential water tracing applications. In this virtual experiment, we find that event size exerts a strong control on the relative amounts of runoff versus pre‐event water in the stream, while uncertainty in stream hydrograph separation is related to the degree of contrast between precipitation/runoff and pre‐event water. Key to flood prediction, adaptation, and mitigation, especially in coastal urban areas, is knowledge of the contributing water sources and timing of stream flow. The strong contrast in stable isotopes between these two events, close in time and over the same area, illustrates the potential to use stable isotope signatures to track the transport and mixing of events through natural and engineered watersheds that are threatened by climate whiplash events.

Effects of rotor squealer tip with non-uniform heights on heat transfer characteristic and flow structure of turbine stage

Squealer tip has a significant influence on both aerodynamic and heat transfer characteristics of the high-pressure turbine. Among the geometric parameters of the squealer, squealer height is one of the essential parameters in the tip design. However, due to the complexity of parameterization and meshing of the squealer, the related research is usually carried out on the squealer with a constant height. In this paper, a parameterization strategy generates squealer of assigned heights at four key positions of the blade, the leading edge-pressure side, the leading edge-suction side, the trailing edge-pressure side, and the trailing edge-suction side. An in-house mesh generation platform (NuFlux) is adopted to automatically generate the structured meshes. The aerothermal performance of a transonic turbine stage is assessed using steady Reynolds-averaged Navier–Stokes simulations with the k−ω shear stress transport model for the turbulence closure. The main purpose is to obtain the squealer tip configuration with the lowest heat transfer coefficient. The results show that non-uniform squealer further reduces the cavity floor heat transfer on the basis of uniform squealer by changing the interaction process between the asymmetric vortex pair (the pressure-side corner vortex and the casing-driven scraping vortex), which provides a valuable reference for the design of the squealer tip of advanced high-pressure turbines.

Direct calculation of the eddy viscosity operator in turbulent channel flow at Re τ = 180

This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method (Mani & Park, Phys. Rev. Fluids, 2021, 054607) to direct numerical simulation (DNS) of a turbulent channel flow at $Re_\tau =180$ using two different forcing strategies that are designed to separately assess the anisotropy and non-locality of momentum mixing. In the first strategy, the leading term of the Kramers–Moyal expansion of the eddy viscosity is quantified, revealing all 81 tensorial coefficients that essentially characterise the local-limit eddy viscosity. The results indicate the following: (1) the eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both the mean strain rate and mean rotation rate tensors associated with the momentum field and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity is quantified as an integration kernel revealing the non-local influence of the mean momentum gradient at each wall-normal coordinate on all nine components of the Reynolds stresses over the channel width. Our results indicate that while the shear component of the Reynolds stress is reasonably reproduced by the local mean gradients, other components of the Reynolds stress are highly non-local. These results provide an understanding of anisotropy and non-locality requirements for closure modelling of momentum transport in attached wall-bounded turbulent flows.

Transport and competitive interfacial adsorption of PFOA and PFOS in unsaturated porous media: Experiments and modeling

Among emerging contaminants, per- and polyfluoroalkyl substances (PFAS) have captured public attention based upon their environmental ubiquity and potential risks to human health. Due to their typical surface release conditions and amphiphilic properties, PFAS tend to sorb to soil and accumulate at the air-water interface within the vadose zone. These processes can result in substantial plume attenuation. Although there is a growing body of literature on vadose zone transport, few studies have explored PFAS mixture transport, particularly under conditions where nonlinear sorption processes are important. The present study aims to advance our understanding of PFAS transport in variably saturated porous media through integration of experiments and mathematical modeling. Experiments include batch studies to quantify sorption to the solid phase, interfacial tension (IFT) measurements to estimate adsorption at the air-water interface (AWI), and column studies with F-70 Ottawa sand at 100 % and ca. 50 % water saturation to explore transport mechanisms. Employed PFAS solutions encompass individual solutes and binary mixtures of perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS) at concentration levels spanning four orders of magnitude to assess competitive and nonlinear sorption at the AWI. Observations demonstrate that concentration levels and competitive effects substantially influence PFAS transport in unsaturated systems. In the presence of PFOS, PFOA experienced less retention than would be anticipated based on single-solute behavior, and effluent breakthrough curves exhibited chromatographic peaking. The presented mathematical model for simultaneous flow and transport of PFAS was able to capture experimental observations with a consistent set of parameters and minimal curve fitting. These results demonstrate the robustness of the model formulation that included rate-limited interfacial mass transfer, an extended Langmuir-Szyszkowski model for adsorption at the AWI, and a scaled Leverett thermodynamic model to predict the AWI specific area. Overall, the results of this work underscore the importance of the AWI in PFAS transport and highlight the relevance of competition effects in adsorption formulations.