Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “DISPERSIONS”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Chemical upgrade of carbon monoxide to acetate on an atomically dispersed copper catalyst via CO-insertion

Electrochemical conversion of small molecules such as carbon dioxide (CO 2 ) and carbon monoxide (CO) to high-value multi-carbon products (C 2+ ) offers a chemical upgrade approach for fuels and chemical feedstock production using renewable energy, in the possible absence of the petrochemical industry under the new energy system such as hydrogen economy. Identifying robust and efficient electrocatalysts to selectively produce C 2+ products remains a challenge. In this study, we report a synthetic strategy of atomically dispersing copper atoms on nitrogen-rich porous carbon (Cu–N–C) through pyrolysis of a supramolecular assembly. Benefitting from the unsaturated coordination structure, in KOH electrolyte, the Cu–N–C with a Cu content of 6.9 wt% exhibits a maximum acetate Faradaic efficiency (FE) of 30% with an acetate partial current density as high as 48 mA cm –2 in electrochemical CO reduction. Different from the C–C coupling mechanism on metallic copper, we propose a CO insertion mechanism for the acetate production on the single site copper catalyst.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A strategy for automated core design to increase economic viability and minimize fuel fragmentation, relocation, and dispersal susceptibility in high-burnup cores

The nuclear industry aims to increase the cycle length of pressurized water reactors from 18 to 24 months to increase power plant capacity factors and economic viability. These cycle length extensions will inherently require fuel rods to exceed the current peak rod average burnup limit of 62 GWd/MTU. A chief concern of operating beyond the current burnup limit is the fuel fragmentation, relocation, and dispersal (FFRD) phenomenon in which pulverized fuel fragments can axially relocate and escape through a burst in the cladding formed during a loss-of-coolant accident. In this work, we demonstrate an approach for automating core design employing an optimization tool based on a penalty-free, parallel simulated annealing algorithm to produce pressurized water reactor core designs with two different optimization objectives. The two objectives were to produce core designs with (1) mitigated FFRD susceptibility while achieving 24-month cycle lengths (2) maximum cycle length with no regard for the likelihood of FFRD. Batch size was considered in tandem with both cases to maximize economic viability. The PARCS nodal model was the primary reactor physics tool used in the optimizations and used nuclear cross sections calculated with 2D Polaris lattice physics models. Reactor performance and safety characteristics of the optimized cores were verified using high-fidelity Virtual Environment for Reactor Applications models. The core designs produced by the optimization tool are compared with each other and to a high-burnup core design produced and analyzed in previous works to highlight the fuel management strategies that may enhance high-burnup reactor safety and economic viability. The optimized cores satisfied their respective objective functions, producing a maximum cycle length of 720 effective full-power days in one core design and one that may reduce FFRD susceptibility by up to 50% based on the first-order approximation to FFRD risk formulated in this work. The optimized cores met most constraints but exceeded the hot channel factor limit, especially in FFRD cases where fresh fuel carried more power. Furthermore, this highlights the need for future lattice-level optimizations and broader assembly options.

Cycle length↗
DOE OSTI2025

Investigating the weak charge of 48 Ca using a dispersive optical model

A new nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in 48 Ca that reproduces the weak-form-factor measurement of CREX. In addition to elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution, the CREX-measured weak form factor has been fit to extract the neutron and proton self-energies both above and below the Fermi energy. The resulting single-particle propagators yield a weak form factor of F w = 0.125 ± 0.05 and a neutron skin of R skin = 0.152 ± 0.05 fm, in good agreement with CREX. The rearrangement of the neutron distribution to accommodate such a thin neutron skin results in the high-momentum content of the neutrons exceeding that of the protons, in contrast to what is expected from high-energy two-nucleon knockout measurements by the CLAS collaboration and ab initio asymmetric matter calculations. The present analysis also emphasizes the importance of neutron experimental data in constraining weak charge observables necessary for a precise description of neutron densities. Notably, the neutron reaction cross section and further parity-violating experiments weak form factor measurements are essential to generate a unique way to determine the 48 Ca neutron distribution in this framework.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Benchmark of interfacial area concentration approaches for the two-fluid model in gas-dispersed condensing flow

Accurate predictions of interfacial area concentration (IAC) are required for closure of the condensation phase change term. The interfacial area transport equation (IATE) can dynamically predict interfacial area concentration and is increasingly being used in the benchmarking of phase change flows over static based correlations which require a flow regime map. For higher flow regimes, the two-group two-fluid IATE model can separately model the transport of spherical bubbles and cap/slug bubbles. Recently, a modified formulation of the one-group and two-group two-fluid model with interfacial area transport equation was proposed for gas-dispersed condensing flows. Three datasets have been used for validation consisting of condensing two-phase flow data in the unheated section of a vertical annulus with conditions spanning a range of pressures, inlet subcoolings and mass fluxes for benchmarking the various IAC approaches. For bubbly flows, the coupled void transport - IATE simulation results in good agreement in the predictions of the void fraction and the interfacial area concentration under nearly all sixty conditions. Considering the proposed two-group two-fluid IATE model formulation, the group-2 Nusselt number correlation is investigated to account for the appropriate heat transfer length scale for group-2 bubbles. Validation of the proposed two-group two-fluid model against the new dataset shows good agreement with experimental data with significant improvement over the one-group IATE model for conditions with substantial group-2 void fraction throughout the simulation domain.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

ENERGY DISPERSIVE DIFFRACTION TOMOGRAPHY OF SHARK VERTEBRAL CENTRA

Shark vertebrae and their centra (vertebral bodies) are high-performance structures able to survive millions of cycles of high amplitude strain despite lacking a repair mechanism for accumulating damage. Shark centra consist of mineralized cartilage, a biocomposite of bioapatite (bAp), and collagen, and the nanocrystalline bAp's contribution to functionality remains largely uninvestigated. Using the multiple detector energy-dispersive diffraction (EDD) system at 6-BM-B, the Advanced Photon Source, and 3D tomographic sampling, the 3D functionality of entire centra were probed. Immersion in ethanol vs phosphate-buffered saline produces only small changes in bAp d-spacing within a great hammerhead centrum. EDD mapping under in situ loading was performed an entire blue shark centrum, and 3D maps of bAp strain showed the two structural zones of the centrum, the corpus calcareum and intermedialia, contained opposite-signed strains approaching 0.5%, and application of similar to 8% nominal strain did not alter these strain magnitudes and their spatial distribution.

Park, Jun-Sang↗
DOE OSTI2021

High-Performance Catalytic Four-Channel Hollow Fibers with Highly Dispersed Nickel Nanoparticles Prepared by Atomic Layer Deposition for Dry Reforming of Methane

In this study, highly dispersed nickel (Ni) nanoparticles (NPs) with an average particle size of 4.3 nm were uniformly deposited on the outer surface, the inner channel surface, and inside the pores of 20-cm long 4-channel α-Al 2 O 3 hollow fibers (HFs) by atomic layer deposition (ALD) for dry reforming of methane (DRM). Cerium oxide (CeO 2 ) was added to promote the catalytic performance of Ni/Al 2 O 3 -HF catalysts. Rationally designed filling methods, by tuning the reactor size and inert fillings, can reduce the catalyst bed voidage in a fixed bed reactor for better reactant gas distribution, effectively utilize the Ni reactive sites, and achieve excellent catalytic performance. It was found that the CeO 2 -promoted Ni/Al 2 O 3 -HF catalyst was highly active and highly stable without deactivation during an overall 400-hr DRM test at 850 ºC. CeO 2 with reversible valence states could participate in surface reactions; especially, the formation of CeAlO 3 provided sufficient surface Ce 3+ for CO 2 activation and enhanced the stability and reusability of the HF catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Anharmonic phonon dispersion in polyethylene

The second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. Here, the calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Adsorption and Catalytic Activity of Gold Nanoparticles in Mesoporous Silica: Effect of Pore Size and Dispersion Salinity

The assembled state of nanoparticles (NPs) within porous matrices plays a governing role in directing their biological, electronic, and catalytic properties. However, the effects of the spatial confinement and environmental factors, such as salinity, on the NP assemblies within the pores are poorly understood. In this study, we use adsorption isotherms, spectrophotometry, and small-angle neutron scattering to develop a better understanding of the effect of spatial confinement on the assembled state and catalytic performance of gold (Au) NPs in propylamine-functionalized SBA-15 and MCM-41 mesoporous silica materials (mSiO 2 ). We carry out a detailed investigation of the effect of pore diameter and ionic strength on the packing and spatial distribution of AuNPs within mSiO 2 to get a comprehensive insight into the structure, functioning, and activity of these NPs. We demonstrate the ability of the adsorbed AuNPs to withstand aggregation under high salinity conditions. We attribute the observed preservation of the adsorbed state of AuNPs to the strong electrostatic attraction between oppositely charged pore walls and AuNPs. The preservation of the structure allows the AuNPs to retain their catalytic activity for a model reaction in high salinity aqueous solution, here, the reduction of p-nitrophenol to p-aminophenol, which otherwise is significantly diminished due to bulk aggregation of the AuNPs. This fundamental study demonstrates the critical role of confinement and dispersion salinity on the adsorption and catalytic performance of NPs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Effect of Dispersion Medium Composition and Ionomer Concentration on the Microstructure and Rheology of Fe–N–C Platinum Group Metal-free Catalyst Inks for Polymer Electrolyte Membrane Fuel Cells

In this paper, we present an investigation of the microstructure and rheological behavior of catalyst inks consisting of Fe–N–C platinum group metal-free catalysts and a perfluorosulfonic acid ionomer in a dispersion medium (DM) of water and 1-propanol ( n PA). The effects of the ionomer-to-catalyst (I/C) ratio and weight percentage of water (H 2 O %) in the DM on the ink microstructure were studied. Steady-shear and dynamic-oscillatory-shear rheology, in combination with synchrotron X-ray scattering, was utilized to understand interparticle interactions and the level of agglomeration of the inks. In the absence of the ionomer, the inks were significantly agglomerated, approaching a gel-like microstructure for catalyst concentrations as low as 2 wt %. The effect of H 2 O % in the DM on particle agglomeration was found to vary with particle concentration. In concentrated inks (≥2 wt % catalyst), increasing H 2 O % was found to increase agglomeration because of the hydrophobic nature of the catalysts. In dilute inks (<1 wt % catalyst), the trend was reversed with increasing H 2 O %, suggesting that electrostatic interactions are dominating the behavior. In inks with 5 wt % catalyst, the addition of an ionomer was found to significantly stabilize the catalyst against agglomeration. Maximum stability was observed at 0.35 I/C for all DM H 2 O % studied. At high ionomer concentrations (I/C > 0.35), interesting differences were observed between n PA-rich inks (H 2 O % ≤ 50%) and H 2 O-rich (82% H 2 O) inks. The n PA-rich inks remained predominantly stable—ink viscosity only weakly increased with I/C and the Newtonian behavior was maintained for I/C up to 0.9. In contrast, the H 2 O-rich inks exhibited a significant increase in viscoelasticity with increasing I/C, suggesting flocculation of the catalyst by the ionomer. These differences suggest that the nature of the interactions between the ionomer and catalyst is highly dependent on the H 2 O % in the DM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Probing High-Pressure Structural Evolution in Polyurea with In Situ Energy-Dispersive X-ray Diffraction and Molecular Dynamics Simulations

Polyurea, an elastomer with a phase-segregated microstructure, has been proven as an effective coating in defense applications. To gain a more complete understanding of the high-pressure atomic-level morphology of these phases and to validate molecular dynamics (MD) simulations, multi-angle energy-dispersive X-ray diffraction experiments were performed in situ up to pressures of ~6 GPa at room temperature. Structure factors were obtained and compared to MD simulations with an average error of less than 5% between major peak positions. The first sharp diffraction peak shifted from 4.56 Å to lower d-spacing with pressure, indicating compression between hard segments. This was further supported by the behavior of a peak at ~3.86 Å from the pair distribution function (PDF), suspected to represent π-stacking and separation between soft segments. Compression within the hard segments themselves is minimal as low-r peaks in the PDF are not greatly affected by pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantifying Atomically Dispersed Catalysts Using Deep Learning Assisted Microscopy

The catalytic performance of atomically dispersed catalysts (ADCs) is greatly influenced by their atomic configurations, such as atom–atom distances, clustering of atoms into dimers and trimers, and their distributions. Scanning transmission electron microscopy (STEM) is a powerful technique for imaging ADCs at the atomic scale; however, most STEM analyses of ADCs thus far have relied on human labeling, making it difficult to analyze large data sets. Here, we introduce a convolutional neural network (CNN)-based algorithm capable of quantifying the spatial arrangement of different adatom configurations. The algorithm was tested on different ADCs with varying support crystallinity and homogeneity. Results show that our algorithm can accurately identify atom positions and effectively analyze large data sets. Here, this work provides a robust method to overcome a major bottleneck in STEM analysis for ADC catalyst research. We highlight the potential of this method to serve as an on-the-fly analysis tool for catalysts in future in situ microscopy experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A Focused Ion Beam-Scanning Transmission Electron Microscopy with Energy-Dispersive X-ray Spectroscopy Study on Technetium Incorporation within Iron Oxides through Fe(OH) 2 (s) Mineral Transformation

Incorporation of Tc(IV) into iron oxide/hydroxide minerals has been explored and proposed as a promising pathway to preventing Tc(IV) reoxidation to environmentally mobile pertechnetate (TcO 4 - ) and improving long-term immobilization of radioactive technetium-99 (Tc). However, visual evidence evaluating the distribution of Tc(IV) incorporated within iron oxide/hydroxide phases has not been available, until now, despite potential implications on Tc(IV) stability within the host phase. For the purpose of this study Tc(IV) incorporation into iron oxide/hydroxide phases was facilitated via Fe(OH) 2 (s) oxidation and mineral transformation to magnetite (Fe 3 O 4 ). Focused ion beam - scanning transmission electron microscopy equipped with energy-dispersive X-ray spectroscopy (FIB/STEM-EDS) methods were then combined with X-ray diffraction and absorption spectroscopy techniques to characterize and visually demonstrate that, for the first time, Tc(IV) is heterogeneously incorporated into different iron oxide/hydroxide phases as Tc(IV)-incorporated magnetite and/or TcO 2 ·2H 2 O(s) via different incorporation mechanisms. Heterogeneous distribution of Tc(IV) in magnetite suggests either (i) TcO4- is reduced quickly at the magnetite surface and then encapsulated into magnetite during continued octahedral crystal growth, or (ii) Tc(IV) alternatively partitioned into multiple layers of a blocky, plate-like morphological magnetite structure showing stratified Tc. With limited Tc-hematite (Fe 2 O 3 ) incorporation, the results suggest that TcO 2 ·2H 2 O(s) is formed and mainly associated/embedded in fibrous nanometer-sized polycrystalline hematite. This work highlights the power of modern state-of-the-art FIB/STEM-EDS approach to provide essential visual insights of the Tc-iron oxide/hydroxide incorporation and generate reliable mechanism-informed designs for waste forms relying on Tc mineral incorporation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Atomically Dispersed Iron–Nitrogen Sites on Hierarchically Mesoporous Carbon Nanotube and Graphene Nanoribbon Networks for CO 2 Reduction

Atomically dispersed metal and nitrogen co-doped carbon (M-N/C) catalysts hold great promise for electrochemical CO 2 conversion. However, there is a lack of cost-effective synthesis approaches to meet the goal of economic mass production of single-atom M-N/C with desirable carbon support architecture for efficient CO 2 reduction. Herein, we report facile transformation of commercial carbon nanotube (CNT) into isolated Fe-N 4 sites anchored on carbon nanotube and graphene nanoribbon (GNR) networks (Fe-N/CNT@GNR). The oxidization-induced partial unzipping of CNT results in the generation of GNR nanolayers attached to the remaining fibrous CNT frameworks, which reticulates a hierarchically mesoporous complex and thus enables a high electrochemical active surface area and smooth mass transport. The Fe residues originating from CNT growth seeds serve as Fe sources to form isolated Fe-N-4 moieties located at the CNT and GNR basal plane and edges with high intrinsic capability of activating CO 2 and suppressing hydrogen evolution. The Fe-N/CNT@GNR delivers a stable CO Faradaic efficiency of 96% with a partial current density of 22.6 mA cm -2 at a low overpotential of 650 mV, making it one of the most active M-N/C catalysts reported. This work presents an effective strategy to fabricate advanced atomistic catalysts and highlights the key roles of support architecture in single-atom electrocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Molecular Catalyst Synthesis Strategies to Prepare Atomically Dispersed Fe-N-C Heterogeneous Catalysts

We report a strategy to integrate atomically dispersed iron within a heterogeneous nitrogen-doped carbon (N-C) support, inspired by routes for metalation of molecular macrocyclic iron complexes. The N-C support, derived from pyrolysis of a ZIF-8 metal–organic framework, is metalated via solution-phase reaction with FeCl 2 and tributyl amine, as a Brønsted base, at 150 °C. Fe active sites are characterized by 57 Fe Mössbauer spectroscopy and aberration-corrected scanning transmission electron microscopy. The site density can be increased by selective removal of Zn 2+ ions from the N-C support prior to metalation, resembling the transmetalation strategy commonly employed for the preparation of molecular Fe-macrocycles. As a result, the utility of this approach is validated by the higher catalytic rates (per total Fe) of these materials relative to established Fe-N-C catalysts, benchmarked using an aerobic oxidation reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Cooperative Atomically Dispersed Fe–N 4 and Sn–N x Moieties for Durable and More Active Oxygen Electroreduction in Fuel Cells

One grand challenge for deploying porous carbons with embedded metal–nitrogen–carbon (M–N–C) moieties as platinum group metal (PGM)-free electrocatalysts in proton-exchange membrane fuel cells is their fast degradation and inferior activity. Here, we report the modulation of the local environment at Fe–N 4 sites via the application of atomic Sn–N x sites for simultaneously improved durability and activity. We discovered that Sn–N x sites not only promote the formation of the more stable D2 FeN 4 C 10 sites but also invoke a unique D3 SnN x –Fe II N 4 site that is characterized by having atomically dispersed bridged Sn–N x and Fe–N 4 . This new D3 site exhibits significantly improved stability against demetalation and several times higher turnover frequency for the oxygen reduction reaction (ORR) due to the shift of the reaction pathway from a single-site associative mechanism to a dual-site dissociative mechanism with the adjacent Sn site facilitating a lower overpotential cleavage of the O–O bond. This mechanism bypasses the formation of the otherwise inevitable intermediate that is responsible for demetalation, where two hydroxyl intermediates bind to one Fe site. Lastly, a mesoporous Fe/Sn-PNC catalyst exhibits a positively shifted ORR half-wave potential and more than 50% lower peroxide formation. This, in combination with the stable D3 site and enriched D2 Fe sites, significantly enhanced the catalyst’s durability as demonstrated in membrane electrode assemblies using complementary accelerated durability testing protocols.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Low-Temperature Non-Oxidative Coupling of Methane on Atomically Dispersed Titanium–Aluminum–Boron Nanopowder

Nonoxidative coupling of methane represents a long-standing challenge in heterogeneous catalysis, as it requires activation of the carbon–hydrogen (C–H) bond, controlled carbon–carbon (C–C) bond formation, and effective hydrogen management without relying on oxidants. Here, we report a low-temperature C–H activation and nonoxidative C–C coupling of methane over atomically dispersed titanium–aluminum–boron nanopowder (Ti–Al–B NP) utilizing a catalytic microreactor coupled to synchrotron single-photon photoionization reflectron time-of-flight mass spectrometry. The soft-ionization, in situ probing method detects the nascent reaction products and radical intermediates under operando conditions, including methyl radical, C2 hydrocarbons, and molecular hydrogen. Methane activation is initiated at 800 K, approximately 700 K below the gas-phase decomposition threshold, leading predominantly to ethylene formation with selectivity reaching up to 78% among the C–C coupled products. Electronic structure calculations on model Ti–Al–B clusters elucidate a cooperative catalytic mechanism in which titanium enables methane adsorption and C–H activation, boron acts as a reversible hydrogen reservoir, and aluminum stabilizes methylene intermediates, thereby facilitating selective C–C coupling and dehydrogenation. These findings establish a distinct catalyst architecture for nonoxidative methane coupling based on earth abundant elements alternative to expensive platinum and other noble metal-containing conventional catalysts and provide molecular-level design principles for controlling dehydrogenation and subsequent C–C bond formation in challenging light alkane conversions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Single-Atom Nickel Dispersed on Mo 2 TiC 2 T x MXene for Upcycling of Polyolefins via Catalytic Hydropyrolysis for Fuels and Lubricants

Plastic waste has been a major social and environmental problem. Chemical upcycling of plastic waste into transportation fuels or lubricant oil has emerged as an attractive and promising approach to convert plastic waste into valuable products. However, conventional catalyst systems often require high-pressure hydrogen, prolonged residence time, and the use of noble metal catalysts. Here, we present zero-valent nickel single atoms on Mo-based MXenes (Ni/Mo 2 TiC 2 T x ) for effective hydrogenation of polyolefins. In situ spectroscopic and microscopic characterizations demonstrate the formation of Ni–Mo and Ni–C bonds at a low Ni loading, resulting in the formation of dispersed intercalated Ni atoms. The catalysts were then employed to convert polyethylene into fuels and lubricant molecules under atmospheric hydrogen pressure, short vapor residence time (τ < 1 s), and mild reaction temperature (300 °C). We further demonstrated the possibility of tuning the Ni structure by changing the Ni loading, attributed to the strong metal–support interactions (MSIs) with the Mo 2 TiC 2 T x support. Under optimized conditions, 22.5 C% gasoline, 12.0 C% diesel, 19.2 C% jet fuel (JP-8), and 37.4 C% lubricant were produced over 0.5% Ni/Mo 2 TiC 2 T x . This work highlights the potential of utilizing MSIs of Mo 2 TiC 2 T x MXenes to synthesize single-atom catalysts (SACs) for upcycling plastic waste into higher-value products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗