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DOE OSTI2021

Population balance modeling of polyurethane foam formation with pressure‐dependent growth kernel

Abstract Polyurethane foams are widely used materials often chosen for their useful characteristics such as low thermal conductivity, ease of application, and high strength‐to‐weight ratios. Computational models are needed to predict the dynamics of the flow and expansion, and the resulting material properties, to improve manufacturing processes. In this paper, a model for PMDI, a water‐blown polyurethane foam, is presented. By extending a kinetics‐based approach by adding bubble‐scale information via a population balance equation (PBE) using the quadrature method of moments, we can track bubble size distributions during foaming. We present results from a three‐dimensional computational fluid dynamics model using arbitrary Lagrangian–Eulerian interface tracking implemented in finite element software. The model compares favorably with experimental data, including dynamics, bubble distributions measured by both camera and diffusion wave spectroscopy, and post‐test bubble size from scanning electron microscopy and density measurements from x‐ray computed tomography.

Ortiz, Weston↗

DOE OSTI2023

Characterizing pulse reverse-pulse uranium recovery in molten LiCl-KCl with intermittent electrochemical impedance spectroscopy

In this work, EIS was applied to characterize the temporal recovery of uranium from UCl 4 onto a tungsten electrode in molten LiCl-KCl salt between sets of pulse reverse-pulse (PRP) deposition steps. Impedance measurements were fitted to an equivalent circuit (EC) model of the electrode interface using Simplex optimization to calculate the double layer capacitance, charge transfer resistance, Warburg impedance, and CPE-restricted diffusion. Diffusion of uranium towards the electrode surface dominated the surface interactions for the first 80 cycles, followed by a transition to kinetic control for the remaining 520 cycles. A decrease in the Warburg impedance showed depletion of uranium from the bulk melt, which was confirmed to be a 52.5% reduction through ICP-OES. Reduction in the phasance from CPE-restricted diffusion suggested the formation of pores in the uranium deposits, which was confirmed through SEM characterization.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2022

Impact of Concurrent Solubilization and Fines Migration on Fracture Aperture Growth in Shales during Acidized Brine Injection

Acidic hydraulic fracturing fluid chemically and physically alters shale rock fabric during injection and shut-in, creating a “reaction-altered zone” along the fracture faces. To better characterize the variable thickness and composition of this reaction-altered zone under advective flow, we take a coupled experimental and modeling approach. A fluidic cell, with six fiducial markers, is first fabricated to keep the rock sample in place during the core floods and to allow image alignment of acquired images. Then, we conduct a series of reactive core floods in a clay-rich siliceous Wolfcamp shale sample with 10 wt % carbonate, using a synthetic fracturing fluid under no confining stress and at room temperature. High-resolution computed tomography (CT) scans are periodically conducted to observe the spatial alteration of the fracture network. We then perform scanning electron microscopy (SEM-EDS) on the two orthogonal surfaces (fracture surface and freshly cut profile face) to generate high-resolution elemental maps that show the change in mineralogy, both with distance along a given flow path along a fracture surface and with depth from the fracture surface into the shale matrix. These results are contrasted against a two-dimensional (2D) advection-diffusion reaction model developed previously for batch reactions between shale and synthetic fracturing fluids. The model simulates the geochemical interaction occurring at the fracture/matrix interface and penetrating into the shale matrix during the reactive core flood. Both model and experimental results show that the acidic brine is neutralized during the core flood, corresponding to an increase in fracture aperture as a function of fluid volume injected with the greatest change near the inlet. SEM-EDS scans reveal significant dissolution of carbonates on the fracture surface without pyrite oxidation. The reactive transport model indicates that carbonate depletion into the shale interior should be observable, yet SEM-EDS shows no discernible loss of carbonate in the orthogonal profile face. The combination of these observations suggests an additional fracture evolution mechanism in the reactive system, i.e., fines migration. We show that fines migration enhances the access of fracturing fluid to the matrix resulting in a more pronounced fracture widening. Finally, we conclude that coupled mineral dissolution and fines migration govern fracture aperture growth during acidized brine injection. In this work, we effectively show the underlying risk of relying solely on models that do not include an important (transport) process that can alter the system significantly and propose a combined chemomechanical mechanism for fracture evolution appropriate for this shale mineralogy.

58 GEOSCIENCES↗

DOE OSTI2024

Morphology selection in dealloying: A phase field study of the coupling among kinetic mechanisms

A phase field model is used to investigate how the corrosion rate and morphology of a dealloying metal is controlled by the kinetic rates of bulk solid diffusion, interfacial diffusivity, and interface dissolution. A specific focus is investigating the manner by which variations in these kinetic parameters synergistically influence the onset of a morphological instability at the solid-liquid interface, which is known to precede rapid dealloying corrosion towards highly topologically complex structures such as bicontinuous porous solids. This work demonstrates that this instability can be suppressed by either an increase of interdiffusion in the solid alloy, or by a decreasing rate of dissolution at the solid-liquid interface. When the instability is suppressed, the result is a relatively planar, passivated dealloying front. Importantly, however, coupled changes in kinetic parameters can also promote the morphological instability and sustain fine-scale ligament and pore formation. Finally, the relevance of the solid-liquid interfacial diffusion for determining the rate of dealloying and ligament formation is highlighted. By elucidating the mechanistic influence of bulk and interfacial kinetic factors on the dealloyed morphology, this work helps to rationalize the contrasting morphologies observed in various dealloying systems.

Diffusion↗

DOE OSTI2023

Effective Lanthanide Diffusivity through U-Zr Metallic Fuel

Fuel-cladding chemical interaction (FCCI) is one of the main concerns for the performance of U-Zr metallic fuels. Although FCCI results in complex phase transformations and morphological changes in both the fuel and cladding sides of the interface, the formation of a brittle layer in the cladding side of the interface (sometimes referred to as wastage) has one of the most significant impacts on the cladding mechanical integrity. This brittle layer is associated with the formation of intermetallic compounds between the cladding constituents Fe, Cr and the lanthanide fission product species. The formation of this cladding wastage layer has been the focus of recent efforts to develop a mechanistic modeling framework, including production of lanthanides in the fuel, transport through the fuel to the fuel-cladding interface, and phase transformation to form intermetallic phases. To calculate the rate of transport of lanthanides through the fuel, a multi-scale computational approach has been used. Atomistic calculations have been performed to determine the diffusivities of Nd, the most prevalent lanthanide species, through the solid fuel matrix and along pore surfaces. These diffusivities have been used as input parameters for a mesoscale model to determine an effective diffusion coefficient that accounts for the formation of porosity, its interconnection, and infiltration with bond sodium from the fuel-cladding gap. The effective diffusivity has been used in engineering-scale simulations using the BISON fuel performance code, and BISON simulations have been compared to representative validation cases from the EBR-II reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Fundamental study of gas species transport in the oxygen electrode of solid oxide fuel and electrolysis cells

A fundamental analysis of multicomponent gas transport models was performed in application to the oxygen electrodes of solid oxide cells. It is common practice to neglect the effect of pressure gradients within oxygen electrodes, even though a net molar flux at the electrolyte surface implies that a pressure gradient must exist. The influence of both Darcy velocity and Knudsen flux are considered in the context of ordinary (Fickian) diffusion, the dusty gas model, and the binary friction model. Comparisons between the models and different sets of assumptions are made via parametric studies on operating load, oxygen partial pressure, microstructural properties, and electrode thickness. Results show that the pressure gradient will have a significant impact on the oxygen concentration distribution and therefore the concentration overpotential. In electrolysis mode, pressure increases up to 1 atm are predicted, indicating that pressure at the electrode/electrolyte interface could contribute to electrode delamination. Additionally, it is found that Darcy's law is insufficient for calculating the pressure distribution without accounting for the flux due to Knudsen diffusion. Additionally, it is found that for the range of properties typical of oxygen electrodes, there is a negligibly small difference between the dusty gas model and binary friction model from a practical standpoint.

08 HYDROGEN↗

DOE OSTI2021

Multifidelity computing for coupling full and reduced order models

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational entities. To this end, we present a robust hybrid analysis and modeling approach combining a physics-based full order model (FOM) and a data-driven reduced order model (ROM) to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive digital twin technologies. At the interface, we introduce a long short-term memory network to bridge these high and low-fidelity models in various forms of interfacial error correction or prolongation. The proposed interface learning approaches are tested as a new way to address ROM-FOM coupling problems solving nonlinear advection-diffusion flow situations with a bifidelity setup that captures the essence of a broad class of transport processes.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Spatially Mapping the CO 2 Alkaline Sorbent Diffuse Microenvironment Using Operando Raman Spectroscopy

When designing a chemical process, the local balance of transport and kinetics, collectively referred to as the diffuse microenvironment, plays a critical role in performance but is difficult to directly observe. This work demonstrates a method of two-dimensional spatial chemical mapping of the diffuse microenvironment in the context of alkali metal hydroxide direct air capture of carbon dioxide using a custom operando gas-absorption flow cell along with confocal Raman spectroscopy. Notably, we observe the concentration boundary layer near the gas–liquid interface and elucidate the interplay of carbonate and bicarbonate ions within it while inferring local hydroxide depletion through continuum modeling. These first of their kind observations provide a technique to compare the performance of direct air capture solvents based on diffuse microenvironment dynamics while also providing metrics important for air contactor design such as boundary layer thickness. Overall, this work showcases a new experimental platform to study interfacial diffuse microenvironments in and outside of the field of direct air capture of carbon dioxide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Diffusion-Limited Kinetics in Reactive Systems

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, in this study, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term “the reactive transport effect”. We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid–surface interfaces accounting for diffusion limitations and the reactive transport effect.

Johnson, Matthew Sean↗

DOE OSTI2021

Defect-Driven Oxide Transformations and the Electrochemical Interphase

The redox reaction pathway is crucial to the sustainable production of the fuels and chemicals required for a carbon-neutral society. Our society is becoming increasingly dependent on devices using batteries and electrolyzers, all of which rely on a series of redox reactions. The overall properties of oxide materials make them very well suited for such electrochemical and catalytic applications due to their associated cationic redox properties and the static site-adsorbate interactions. As these technologies have matured, it has become apparent that defect-driven redox reactions, defect-coupled diffusion, and structural transformations that are both time- and rate-dependent are also critical materials processes. This change in focus, considering not only redox properties but also more complex, dynamic behaviors, represents a new research frontier in the molecular sciences as they are strongly linked to device operation and degradation and lie at the heart of various phenomena that take place at electrochemical interfaces. Fundamental studies of the structural, electronic, and chemical transformation mechanisms are key to the advancement of materials and technological innovations that could be implemented in various electrochemical systems. In this Account, we focus on recent studies and advances in characterizing and understanding the dynamic redox evolution and structural transformations that take place in model perovskites and layered oxides under reactive conditions and correlate them with degradation mechanisms and operations in electrolyzers and batteries. We show that the dynamic evolution of oxygen vacancies and cationic migration in the surface or bulk occurs at the solid-liquid interface, using a combination of different synchrotron-based Xray spectroscopies and scattering probes. Detailed redox-structure-reactivity correlation studies show how defects and diffusion processes can be tailored to drive various physical and chemical transformations in electrolyzers and batteries. We also highlight a strong correlation between oxygen redox reactivity and structural reorganization in both model thin films and particles, helping to bridge the gap between fundamental studies of the reaction mechanism and device applications. Finally, on the basis of these findings, we discuss strategies to probe and tune the redox reactivity and structural stability of the redox-active oxide interphase toward devising efficient pathways for energy and chemical harvesting.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Interfacial Atomistic Mechanisms of Lithium Metal Stripping and Plating in Solid–State Batteries

All-solid-state batteries based on a Li metal anode represent a promising next-generation energy storage system, but are currently limited by low current density and short cycle life. Further research to improve the Li metal anode is impeded by the lack of understanding in its failure mechanisms at lithium–solid interfaces, in particular, the fundamental atomistic processes responsible for interface failure. Here, using large-scale molecular dynamics simulations, the first atomistic modeling study of lithium stripping and plating on a solid electrolyte is performed by explicitly considering key fundamental atomistic processes and interface atomistic structures. In the simulations, the interface failure initiated with the formation of nano-sized pores, and how interface structures, lithium diffusion, adhesion energy, and applied pressure affect interface failure during Li cycling are observed. By systematically varying the parameters of solid-state lithium cells in the simulations, the parameter space of applied pressures and interfacial adhesion energies that inhibit interface failure during cycling are mapped to guide selection of solid-state cells. Furthermore, this study establishes the atomistic modeling for Li stripping and plating, and predicts optimal solid interfaces and new strategies for the future research and development of solid-state Li-metal batteries.

25 ENERGY STORAGE↗

DOE OSTI2022

Microstructural pattern formation during liquid metal dealloying: Phase-field simulations and theoretical analyses

In recent years, liquid metal dealloying has emerged as a promising material processing method to generate micro- and nanoscale bicontinuous or porous structures. Most previous studies focused on the experimental characterization of the dealloying process and on the properties of the dealloyed materials, leaving the theoretical study incomplete to fully understand the fundamental mechanisms of the liquid metal dealloying process. In this paper, we use theoretical models and phase-field simulations to clarify the kinetics and pattern formation during liquid metal dealloying. Our investigation starts from a theoretical analysis of the 1D dissolution of a binary precursor alloy, which reveals that the 1D dissolution process involves two regimes. In the first regime, due to the low solubility of one of the elements in the melt, it accumulates at the solid-liquid interface, which reduces the dissolution kinetics. In the second regime, the interface kinetics reaches a stationary regime where both elements of the precursor alloy dissolve into the melt. Previous works revealed that in the early dealloying stage, the dealloying front is destabilized by an interfacial spinodal decomposition, which triggers the formation of interconnected ligaments. Here we extend this line of work by proposing a linear stability analysis able to predict the initial length scale of the ligaments formed in the initial stage of the dealloying. Combining this analysis with the 1D dissolution model proposed here enables us to better understand the initial conditions (composition of the precursor alloy and the melt) leading to a planar dissolution without interface destabilization. Finally, we report a strong influence of solid-state diffusion on dealloying. Although the solid-state diffusivity is four to five orders of magnitude smaller than in the liquid phase, it is found to affect both dissolution kinetics and ligament morphologies.

36 MATERIALS SCIENCE↗

DOE OSTI2026

SAM Code Enhancements for Fission Product Tracking of Noble Gases and Metals in MSRs

This report documents fiscal year 2026 enhancements to the System Analysis Module (SAM) for modeling fission product transport in liquid-fueled molten salt reactors (MSRs). The work advances three principal areas: noble gas transport, noble metal deposition, and user interface improvements. The noble gas transport capability integrates drift-flux gas transport, Henry’s law two-film interphase mass transfer with pressure-based nucleation suppression, Knudsen-regime pore diffusion into porous graphite with a conjugate salt-graphite interface constraint, built-in material properties, five Sherwood-number mass transfer correlations including three derived from high-fidelity NekRS simulations, and xenon-135 reactivity feedback through SAM’s point-kinetics model. This work also presents a comprehensive verification test suite, including new analytically verified cases for pressure-dependent onset of interphase gas transfer in a stagnant vertical pipe, a postulated FLiBe-graphite Xe extraction permeator, a gravity riser with a fission-product source, and a descending pipe with gas redissolution driven by hydrostatic pressure. A machine learning framework for bubble rise velocity prediction in molten salt systems is developed and benchmarked on molten-salt and diverse aqueous bubble datasets. The best-performing fine-tuned transfer-learning networks achieve an 82% reduction in RMSE relative to the Clift correlation, and is implemented directly in SAM. The noble metal transport capability is developed, including a liquid-wall deposition model and a gas-surface flotation mechanism that transfers insoluble particles entrained by sparging gas to wetted structures. Verification tests and demonstration cases cover the surface deposition, flotation efflux, and flotation shedding. Finally, a new [SpeciesTransport] input structure replaces positional global vectors with selfcontained, order-independent, named species blocks, simplifies the specification of multiphase species and decay chains, and remains fully compatible with existing SAM input files. Together, these developments improve the physical fidelity, verification basis, and usability of SAM for system-level analyses of fissionproduct behavior in MSRs.

Mui, Travis (ORCID:0000000303736470)↗

DOE OSTI2020

Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

In this paper, we propose nonoverlapping localized exponential time differencing (ETD) methods for diffusion problems. The model time-dependent diffusion equation is first reformulated on subdomains based on the nonoverlapping domain decomposition, in which Neumann boundary conditions are imposed on the interfaces for the subdomain problems and Dirichlet type conditions are enforced to form a space-time interface problem. After spatial discretization by standard central finite differences and temporal integration with the first or second order ETD methods, the fully discrete interface problem is obtained. Such an interface problem is then solved iteratively either at each time step or over the whole time interval: the former involves the solution of stationary problems in each subdomain at each iteration while the latter involves the solution of time-dependent subdomain problems at each iteration. For both approaches, we prove that localized ETD solutions conserve mass exactly and converge in time to the exact space semidiscrete solution. Numerical experiments in two dimensions are also presented to illustrate the performance of the proposed methods.

Mass conservation↗

DOE OSTI2026

Thermodynamic Control of Interface Directs MnO 2 Nucleation Chemistry for Dense and Conformal Electrodeposition

Manganese dioxide (MnO 2 ) is widely recognized as a promising material for high-energy-density energy storage systems due to its broad applicability and facile electrodeposition. However, achieving uniform, thin, and high-mass-loading MnO 2 coatings on high-surface-area electrodes remains a significant challenge. Conventional electrodeposition methods typically yield nonuniform, thick layers with poor conductivity and limited material utilization, restricting their practical use. Here, we uncover a thermodynamically engineered vanadyl/pervanadyl (VO 2+ /VO 2 + ) interface that fundamentally reshapes MnO 2 electrodeposition chemistry, enabling highly uniform and dense coatings. Here, combining in situ AFM measurement, Classical Nucleation Theory, and Johnson–Mehl–Avrami–Kolmogorov modeling, we show that this interface reduces early-stage detectable MnO 2 island size by 35-fold and shifts the MnO 2 growth from diffusion-limited to reaction-limited progressive nucleation. This thermodynamically controlled interface yields highly dense and conformal MnO 2 films with record-high mass loading of 241 mg cm –2 (1607 mg cm –3 ) on 3D-printed graphene aerogels, without compromising porosity or inducing thickness gradient. As a prototype demonstration, the resulting MnO 2 electrodes deliver record-setting volumetric performance in both capacitors (106 F cm –3 ) and Zn//MnO 2 pouch cells (162 mAh cm –3 ). Beyond energy storage, our findings demonstrate the significance of thermodynamic interface control in MnO 2 nucleation chemistry for achieving dense and uniform coatings on various substrates, with implications for electrocatalysis, semiconductor processing, and advanced materials manufacturing.

Batteries↗

DOE OSTI2025

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗

DOE OSTI2023

Convection-Induced Compositional Patterning at Grain Boundaries in Irradiated Alloys

We consider the stability of precipitates formed at grain boundaries (GBs) by radiation-induced segregation in dilute alloys subjected to irradiation. Here, the effects of grain size and misorientation of symmetric-tilt GBs are quantified using phase field modeling. A novel regime is identified where, at long times, GBs are decorated by precipitate patterns that resist coarsening. Maps of the chemical Péclet number indicate that arrested coarsening takes place when solute advection dominates over thermal diffusion right up to the precipitate/matrix interface, preventing interfacial local equilibrium and overriding capillary effects. This contrasts with liquid-solid mixtures where convection always accelerates coarsening.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Insights into Sorption and Molecular Transport of Aqueous Glucose into Zeolite Nanopores

Liquid-phase heterogeneous catalysis using zeolites is important for biomass conversion to fuels and chemicals. There is a substantial body of work on gas-phase sorption in zeolites with different topologies; however, studies investigating the diffusion of complex molecules in liquid medium into zeolitic nanopores are scarce. Here, we present a molecular dynamics study to understand the sorption and diffusion of aqueous β-d-glucose into β-zeolite silicate at T = 395 K and P = 1 bar. Through 2-μs-long molecular dynamics trajectories, we reveal the role of the solvent, the kinetics of the pore filling, and the effect of the water model on these properties. We find that the glucose and water loading is a function of the initial glucose concentration. Although the glucose concentration increases monotonically with the initial glucose concentration, the water loading exhibits a nonmonotonic behavior. At the highest initial concentration (~20 wt %), we find that the equilibrium loading of glucose is approximately five molecules per unit cell and displays a weak dependence on the water model. Glucose molecules follow a single-file diffusion in the nanopores due to confinement. Here, the dynamics of glucose and water molecules slows significantly at the interface. The average residence time for glucose molecules is an order of magnitude larger than that in the bulk solution, while it is about twice as large for the water molecules. Our simulations reveal critical molecular details of the glucose molecule’s local environment inside the zeolite pore relevant to catalytic conversion of biomass to valuable chemicals.

09 BIOMASS FUELS↗