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Results for “Diffusion in heterogeneous media”

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

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Effects of Gas-Phase Radiation and Detailed Kinetics on the Burning and Extinction of a Solid Fuel

This is the first attempt to analyze both radiation and detailed kinetics on the burning and extinction of a solid fuel in a stagnation-point diffusion flame. We present a detailed and comparatively accurate computational model of a solid fuel flame along with a quantitative study of the kinetics mechanism, radiation interactions, and the extinction limits of the flame. A detailed kinetics model for the burning of solid trioxane (a trimer of formaldehyde) is coupled with a narrowband radiation model, with carbon dioxide, carbon monoxide, and water vapor as the gas-phase participating media. The solution of the solid trioxane diffusion flame over the flammable regime is presented in some detail, as this is the first solution of a heterogeneous trioxane flame. We identify high-temperature and low-temperature reaction paths for the heterogeneous trioxane flame. We then compare the adiabatic solution to solutions that include Surface radiation only and gas-phase and surface radiation using a black surface model. The analysis includes discussion of detailed flame chemistry over the flammable regime and, in particular, at the low stretch extinction limit. We emphasize the low stretch regime of the radiatively participating flame, since this is the region representative of microgravity flames. When only surface radiation is included, two extinction limits exist (the blow-off limit, and the low stretch radiative limit), and the burning rate and maximum flame temperatures are lower, as expected. With the inclusion of surface and gas-phase radiation, results show that, while flame temperatures are lower, the burning rate of the trioxane diffusion flame may actually increase at low stretch rate due to radiative feedback from the flame to the surface.

Rhatigan, Jennifer L.↗
DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications

This study presents a physics-informed neural network (PINN) framework for reactive transport modeling for simulating fast bimolecular reactions in porous media. Accurate characterization of cAhemical interactions and product formation in surface and subsurface environments is essential for advancing critical mineral extraction and related geoscience applications. The proposed methodology sequentially addresses the flow and diffusion–reaction subproblems. The flow field is computed using a mixed formulation, while the diffusion–reaction system is modeled via two uncoupled tensorial diffusion equations reformulated in terms of chemical invariants. PINNs are employed to solve the governing equations, enabling data-efficient, mesh-free prediction of chemical concentration fields. The framework is validated through a series of benchmark problems involving flow in heterogeneous porous media. Initial verification is conducted using patch tests for the flow field, followed by validation of the transport problem with emphasis on preserving non-negativity of concentrations. The complete fast bimolecular reaction scenario is then solved, yielding spatial distributions of reactants and product species. Results demonstrate that the PINNs-based approach effectively captures sharp, mixing-limited reaction fronts and dispersive mixing behavior, offering reliable predictions of reactive plume evolution. These capabilities are crucial for evaluating long-term subsurface behavior in applications such as fluid storage, energy extraction, and efficient extraction of critical minerals.

42 ENGINEERING↗
DOE OSTI2022

Macrovoid resolved simulations of transport through HPRO relevant membrane geometries

Modeling the transport properties such as diffusivity and permeability of high pressure reverse osmosis (HPRO) membranes is critical for the selection and manufacture of membranes suitable for operation under high pressure. These properties can be significantly affected by the changes in heterogeneous pore structures due to compaction. Here, the modeling platform presented in this work resolves the two scale porosity in HPRO relevant membranes. A synthetic membrane geometry is constructed based on available experimental visualizations of pore structures. The simulations directly capture the flow channeling that results from a combination of material properties and geometric features of the macrovoids. A parametric study is presented to account for the transition of flow characteristics from a material governed regime to a macrovoid governed regime. Permeability of the membrane is evaluated using the simulation data and compared with an existing model that scales with the square of tortuosity over a range of material properties. The model is found to perform well under a narrow range of tortuosity while deviating from the calculated permeabilities at extreme conditions. The effective permeability of the membrane is found to vary by at least two orders of magnitude between the two flow regimes. It is also observed that tortuosity is a bounded property with its upper limit determined by the macrovoid geometry. Consequently, the tortuosity based correlations fail near a flow regime that is mainly governed by the macrovoids. The modeled permeability can be more than an order of magnitude smaller than the simulation result. A new model based on flux-weighted porosity of a membrane is introduced and its correlation with tortuosity is studied. The model agrees with the simulated data as, in addition to tortuosity, it also accounts for the flux partition within and outside the flow channels. Such correlations enable extending the existing understanding of flow characteristics to enhance predictability of porous media models.

42 ENGINEERING↗
DOE OSTI2022

An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our previous work on nonlinear multigrid for heterogeneous diffusion problems. The coarse spaces in the multigrid hierarchy are constructed by first aggregating degrees of freedom, and then solving some local flow problems. The mixed formulation and the choice of coarse spaces allow us to assemble the coarse problems without visiting finer levels during the solving phase, which is crucial for the scalability of multigrid methods. Specifically, a natural generalization of the upwind flux can be evaluated directly on coarse levels using the precomputed coarse flux basis vectors. We find that the resulting solver is applicable to problems discretized on general unstructured grids. The performance of the proposed nonlinear multigrid solver in comparison with the standard single level Newton's method is demonstrated through challenging numerical examples. It is observed that the proposed solver is robust for highly nonlinear problems and clearly outperforms Newton's method in the case of high Courant-Friedrichs-Lewy (CFL) numbers.

58 GEOSCIENCES↗
DOE OSTI2020

Grain detachment and transport clogging during mineral dissolution in carbonate rocks with permeable grain boundaries

In this paper, we explore the effect of permeable grain boundaries on carbonate rock dissolution in order to improve our understanding of grain detachment and migration during reactive flow. To do so we investigated the effects of grain size and enhanced reactivity along grain boundaries on global dissolution kinetics. Variations of permeability and porosity were calculated, and exponential relationships were observed in fractured rocks. Our model employed a reactive transport framework based on the Darcy-Brinkman equation to simulate calcite dissolution in carbonate rocks composed of microporous grains and, included fluid transport along grain boundaries. The model includes fluid flow, solute transport by advection–diffusion, heterogeneous reaction between fluid and minerals and grain detachment with subsequent grain transport in macropores. The migration of solid particles due to dissolution was based on cluster analysis and local movement, and the results show that grain detachment can lead to significant decreases in permeability due to the clogging of transport pathways. Microporous media with smaller grain sizes (fine grains in this study) showed a higher average reaction rate than those with coarser grains. In addition, as the overall rates of geochemical processes are commonly affected by the presence of texture heterogeneities such as fractures, a single fracture (macropore) introduced into a microporous matrix composed of permeable grains and grain boundaries was modelled as a large channel connecting the inlet and outlet of the simulation domain. It was found that macropore clogging by grain detachment temporary decreased permeability, lowering the long-term global reaction rates. Lastly, we observed that increases in flow rate can reduce detachment and fracture clogging by reducing local dissolution along grain boundaries.

58 GEOSCIENCES↗
NASA NTRS1998

Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media

The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.

NASA Discipline Cardiopulmonary↗
DOE OSTI2020

Connecting Hindered Transport in Porous Media across Length Scales: From Single-Pore to Macroscopic

Hindered mass transport is widely observed in various porous media, including filtration membranes and porous rocks. However, there is no universal model capable of predicting transport in porous media due to the heterogeneity of porous structures and the complexity of the underlying microscopic mechanisms, including electrostatic and hydrodynamic effects. Here, we used a highly ordered porous medium (i.e. a silica inverse opal film) as a model system to directly explore the effects of geometric parameters (i.e. pore size, pore throat size and tracer particle size) and microscopic interaction parameters (e.g. controlled by ionic strength) on nanoparticle transport in porous environments using three-dimensional single-particle tracking. We found a linear scaling relation between the macroscopic diffusion coefficient and microscopic diffusion behaviors and a combination of parameters associated with microscopic features and phenomena, including both geometric effects and particle-level interactions. The proportionality coefficient relating micro and macro behaviors was complex and related to the connectivity of the matrix and pore-size variation, which could lead to tortuous diffusion pathways, hindering macroscopic transport. Furthermore, these findings provide important insights into nanoparticles and macromolecules transport in various porous media.

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

Microstructure, Transport, and Mechanics of Compacted Clay Simulated at the 0.1 μm Scale (1400 Smectite Clay Particles) Using a Coarse-Grained Model with Explicit Counterions

Clay-rich geomaterials play a critical role in many subsurface systems. The macroscale properties of these materials (low permeability, high ionic conductivity, high swelling pressure, etc.) are sensitive to molecular-level adsorption and hydration interactions at clay−water interfaces. Efforts to develop multiscale simulation approaches to predict these properties reveal a scale gap between atomistic simulations (typically limited to systems smaller than 10 nm) and continuum-scale models (which use computational grid elements with dimensions ≳ 10 μm). In this study, we present a coarse-grained (CG) framework that partly bridges this gap by simulating compacted smectite clay assemblages with dimensions of 0.1 μm containing 1,400 clay particles across a range of dry densities (1,050 to 1,850 kg·m −3 ) and Na/Ca counterion compositions (Na fraction ranging from 0.2 to 1). The simulated systems, along with their reconstructed binary three-dimensional pore networks, are used to evaluate the microstructure, pore size distribution, tortuosity, ion diffusivity, and swelling pressure of compacted smectite clay. Results show that our approach captures important features of the mesoscale heterogeneity of compacted clays, including tactoid formation, hierarchical porosity, and anisotropic pore networks. Results also reveal how compaction and counterion composition govern emergent behaviors, including dominant pore sizes, directional transport, and electrochemical response. This work highlights the potential of CG simulations to bridge molecular and continuum scales and to advance geotechnical and environmental applications involving clay-rich materials as well as related nanoporous media such as geopolymers and calcium-silicate-hydrate. However, the results also suggest that accurate prediction of certain microstructural and mechanical properties (e.g., swelling pressure) may require even larger-scale systems on the order of 1 μm.

02 PETROLEUM↗
DOE OSTI2021

Fluorescence Microscopic Investigations of Molecular Dynamics in Self–Assembled Nanostructures

Many analytical methods employ self-assembled nanostructured materials as chemical recognition media. Molecular permeation through these materials exhibits unique selectivity owing to nanoconfinement-induced enhancement of permeant–nanostructure interactions. This Personal Account introduces our efforts to investigate the detailed dynamics of single or a small number of molecules in nanostructured materials. Here, we developed new experimental and analysis approaches built upon laser-based fluorescence microscopy to measure the detailed translational and orientational dynamics of molecules diffusing in horizontally-oriented, cylindrical nanostructures, including surfactant micelles, silica mesopores, block copolymer microdomains, and bolaamphiphile-based organic nanotubes. Our studies clarified nanoscale details on the structural/chemical heterogeneity of the nanostructures, and their impacts on molecular mass transport dynamics.

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

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Discrete Fracture Network Modeling to Estimate Upscaled Parameters for the Topopah Spring, Lava Flow, and Tiva Canyon Aquifers at Pahute Mesa, Nevada National Security Site

This report describes the results of Discrete Fracture Network (DFN) simulations for the Topopah Spring Aquifer (TSA), Lava Flow Aquifer, and Tiva Canyon Aquifer (TCA), at Pahute Mesa on the Nevada National Security Site (NNSS), formerly the Nevada Test Site. The research focuses on calculating upscaled groundwater flow and contaminant transport parameters using DFNs generated according to fracture characteristics observed in the TSA, LFA and TCA at Pahute Mesa. The highly fractured and heterogeneous nature of these aquifers makes them candidates for stochastic DFN modeling of radionuclide transport on a small scale with subsequent upscaling. One hundred independent DFN realizations are generated for each aquifer, and the upscaled parameters for continuum simulations of subsurface flow and transport in fractured media at Pahute Mesa are calculated. Our goal is to implement a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, such as channelization of flow and transport along a few well connected, large fractures. Additionally, to simulate advective and advective-diffusive transport through the fracture networks, the Time Domain Random Walk (TDRW) approach is applied to account for matrix diffusion into a finite half-space. Moreover, a novel approach to calculate dynamic (active) fracture surface area to reflect flow channeling is implemented. This work will improve the representation of radionuclide transport processes in largescale, regulatory-focused models by providing estimates of hard-to-measure flow and contaminant transport parameters at large scales. In this report, we (1) show recent results of flow and transport simulations on multiple DFN realizations of the TSA, LFA, TCA; (2) discuss the resulting distributions of estimated upscaled parameters; (3) describe the estimation of upscaled parameters for an equivalent parallel-plate continuum model and (4) present a comparison between simulated transport from the equivalent continuum model and an actual DFN.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Nanoparticle Tracking to Probe Transport in Porous Media

From the granular and fractured subsurface environment to highly engineered polymer membranes used in pharmaceutical purification, porous materials are ubiquitous in nature and industrial applications. In particular, porous media are used extensively in processes including water treatment, pharmaceutical sterilization, food/beverage processing and heterogeneous catalysis, where hindered mass transport is either essential to the process or a necessary, but undesirable limitation. Unfortunately, there are currently no universal models capable of predicting mass transport based on a description of the porous material because real porous materials are complex, and because many coupled dynamic mechanisms (e.g. adsorption, steric effects, hydrodynamic effects, electrostatic interactions, etc.) give rise to the observed macroscopic transport phenomena. While classical techniques, like nuclear magnetic resonance and dynamic light scattering, provide useful information about mass transport in porous media at the ensemble level, they provide limited insight into the microscopic mechanisms that give rise to complex phenomena such as anomalous diffusion, hindered pore-space accessibility, and unexpected retention under flow, among many others. To address this issue, we have developed refractive index matching imaging systems, combined with single-particle tracking methods, allowing the direct visualization of single particle motion within a variety of porous materials. Here, we summarize our recent efforts to advance the understanding of nanoparticle transport in porous media using single-particle tracking methods in both fundamental and applied scenarios. First, we describe the basic principles for two-dimensional and three-dimensional single-particle tracking in porous materials. Then, we describe concrete examples of nanoparticle transport in porous materials from two perspectives: (1) understanding fundamental elementary particle transport processes in porous media, including pore accessibility and cavity escape, which limit transport in porous media; (2) facilitating applications in industrial processes, e.g. by understanding the mechanisms of particle fouling and remobilization in filtration membranes. Finally, we provide an outlook of opportunities associated with investigating other types of mass transport in confined environments using single-particle tracking methods, including electrophoretic and self-propelled motion.

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

Quantification of the Crack Evolution Process by Extracting Relevant Signal Components from Wave Propagation and Diffusive Transport Front Measurements

Wave propagation and diffusive transport phenomena in a geological rock sample undergoing crack evolution process are expected to interact with the mechanical discontinuities in the medium. The measurements of the signals associated with these phenomena can be used to assess and monitor the crack-driven micromechanical alterations in the rock. Different wave/diffusion phenomena, such as sonic propagation, pressure diffusion, and acoustic emission (AE), are sensitive to different elements of the mechanical discontinuities generated during the evolution of the crack clusters from initiation to coalescence. Sonic propagation, AE, and pressure diffusion monitoring have the potential to map the crack evolution because the transmitter-receiver arrays can be designed, arranged and tuned to (1) achieve maximum recovery of the scattered waveforms and travel times, (2) capture the later arrivals and multiple reflections, and (3) illuminate large rock volume. However, the structural/topological complexities of the mechanical discontinuities, complex distribution of the stress fields, complex mechanical alterations in media, and fluid redistribution in the crack system pose serious challenges for the detection and modeling of the crack evolution process (from here on, we will use the term ‘crack evolution process’ to mean that the crack evolution occurred under shallow crustal conditions). For purposes of accurately accounting such complexities and heterogeneities in the absence of reliable physical laws, simulation methods, and signal processing techniques, my early-career research proposal will develop and apply novel data-driven machine learning methods to: (1) extract signal components relevant to the various phases of crack evolution and (2) generate a 2D visual map of the crack evolution process.

58 GEOSCIENCES↗
DOE OSTI2025

Hydrodynamic characterization of the redox chemistry of crown-encapsulated uranyl complexes

The redox properties of actinide-containing species strongly influence their reactivity, speciation, and interfacial behavior, but the experimental quantification of the electrochemical characteristics of molecular actinide complexes in nonaqueous media has not received the attention it deserves. Here, results from hydrodynamic methods and electrochemical simulations of U(VI)/U(V) redox are reported, including quantification of heterogeneous electron-transfer kinetics and estimation of chemical reversibility of U(VI)/U(V) interconversion at electrodes in acetonitrile-based electrolyte. The complexes investigated are recently reported U(VI) and U(V) complexes in which the uranyl ion (UO 2 n+ ) is encapsulated in a macrocyclic 18-crown-6-like moiety templated by a Pt(II) center. These complexes feature the most positive value U VI /U V reduction potential yet reported and are thus particularly relevant to study of facile U(V) generation from U(VI) precursors as well as uranium electroanalysis. Rotating disk electrode (RDE) studies have been used to quantify the diffusion coefficients of the U(VI) and U(V) complexes, and standard heterogeneous electron transfer rate constants ( k 0 ) for the redox have been determined using a conventional Koutecký-Levich analysis. Rotating ring-disk electrode (RRDE) studies have been used to directly interrogate the chemical reversibility of U(VI)-U(V) interconversion, confirming that reduction of the U(VI) complex at an Au disk is associated with formation of the U(V) analogue that can be readily re-oxidized at a Pt ring under hydrodynamic (rotating) conditions. Because measurements of the type reported here are generally associated with current flows that are larger than those found in corresponding quiescent (unstirred) conditions, our findings suggest that hydrodynamic methods could be advantageous for design of electroanalytical approaches to detection of actinide species and study of their redox properties.

actinides↗
DOE OSTI2023

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Abstract. Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics.

58 GEOSCIENCES↗
DOE OSTI2020

A higher-order finite element reactive transport model for unstructured and fractured grids

Abstract This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method, which provides smooth velocity fields even in highly heterogenous formations with discrete fractures. A multilinear Discontinuous Galerkin FE method is used to solve the multicomponent transport problem. This method is locally mass conserving and its second order convergence significantly reduces numerical dispersion. In terms of thermodynamics, the aqueous phase is considered as a compressible fluid and its properties are derived from a Cubic Plus Association (CPA) equation of state. The new simulator is validated against several benchmark problems (involving, e.g., Fickian and Nernst-Planck diffusion, isotope fractionation, advection-dispersion transport, and rock-fluid reactions) before demonstrating the expanded capabilities offered by the underlying FE foundation, such as high computational efficiency, parallelizability, low numerical dispersion, unstructured 3D gridding, and discrete fraction modeling.

58 GEOSCIENCES↗
DOE OSTI2024

Significance of Low‐Velocity Zones on Solute Retention in Rough Fractures

Natural fractures are characterized by high internal heterogeneity. This internal variability is the cause of flow channeling, which in turn leads to contaminant transport taking place primarily along the high-velocity channels. Mass exchange between the high-velocity channels and the low-velocity zones has the potential to enhance contaminant retention, due to solute diffusion into the low-velocity zones and subsequent exposure to additional surface area for diffusion into the bordering rock matrix. Here, we derive a random walk particle tracking method for heterogeneous fractures, which includes an additional term to account for the aperture gradient. The method takes into account advection, diffusion in the fracture and matrix diffusion. The developed numerical framework is applied to assess the effect of low-velocity zones in rough self-affine fractures. The results show that diffusion into low-velocity zones has a visible but modest impact on contaminant retention. The magnitude of this impact does not change considerably, regardless of whether diffusion into the rock matrix is considered in the model, and increases for a decreasing average Péclet number of the fracture.

58 GEOSCIENCES↗