A versatile pressure-cell design for studying ultrafast molecular-dynamics in supercritical fluids using coherent multi-pulse x-ray scattering.

Supercritical fluids (SCFs) can be found in a variety of environmental and industrial processes. They exhibit an anomalous thermodynamic behavior, which originates from their fluctuating heterogeneous micro-structure. Characterizing the dynamics of these fluids at high temperature and high pressure with nanometer spatial and picosecond temporal resolution has been very challenging. The advent of hard x-ray free electron lasers has enabled the development of novel multi-pulse ultrafast x-ray scattering techniques, such as x-ray photon correlation spectroscopy (XPCS) and x-ray pump x-ray probe (XPXP). These techniques offer new opportunities for resolving the ultrafast microscopic behavior in SCFs at unprecedented spatiotemporal resolution, unraveling the dynamics of their micro-structure. However, harnessing these capabilities requires a bespoke high-pressure and high-temperature sample system that is optimized to maximize signal intensity and address instrument-specific challenges, such as drift in beamline components, x-ray scattering background, and multi-x-ray-beam overlap. We present a pressure cell compatible with a wide range of SCFs with built-in optical access for XPCS and XPXP and discuss critical aspects of the pressure cell design, with a particular focus on the design optimization for XPCS.

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview.

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

Evaluation of Electron Tomography Capabilities for Shale Imaging.

Despite the advantageous resolution of electron tomography (ET), reconstruction of three-dimensional (3D) images from multiple two-dimensional (2D) projections presents several challenges, including small signal-to-noise ratios, and a limited projection range. This study evaluates the capabilities of ET for thin sections of shale, a complex nanoporous medium. A numerical phantom with 1.24 nm pixel size is constructed based on the tomographic reconstruction of a Barnett shale. A dataset of 2D projection images is numerically generated from the 3D phantom and studied over a range of conditions. First, common reconstruction techniques are used to reconstruct the shale structure. The reconstruction uncertainty is quantified by comparing overall values of storage and transport metrics, as well as the misclassification of pore voxels compared to the phantom. We then select the most robust reconstruction technique and we vary the acquisition conditions to quantify the effect of artifacts. We find a strong agreement for large pores over the different acquisition workflows, while a wider variability exists for nanometer-scale features. The limited projection range and reconstruction are identified as the main experimental bottlenecks, thereby suggesting that sample thinning, advanced holders, and advanced reconstruction algorithms offer opportunities for improvement.

The Local Electronic Structure of Supercritical CO2 from X-ray Raman Spectroscopy and Atomistic-Scale Modeling.

Supercritical CO2 is encountered in several technical and natural systems related to biology, geophysics, and engineering. While the structure of gaseous CO2 has been studied extensively, the properties of supercritical CO2, particularly close to the critical point, are not well-known. In this work, we combine X-ray Raman spectroscopy, molecular dynamics simulations, and first-principles density functional theory (DFT) calculations to characterize the local electronic structure of supercritical CO2 at conditions around the critical point. The X-ray Raman oxygen K-edge spectra manifest systematic trends associated with the phase change of CO2 and the intermolecular distance. Extensive first-principles DFT calculations rationalize these observations on the basis of the 4sσ Rydberg state hybridization. X-ray Raman spectroscopy is found to be a sensitive tool for characterizing electronic properties of CO2 under challenging experimental conditions and is demonstrated to be a unique probe for studying the electronic structure of supercritical fluids.

Supercritical fluids behave as complex networks.

Supercritical fluids play a key role in environmental, geological, and celestial processes, and are of great importance to many scientific and engineering applications. They exhibit strong variations in thermodynamic response functions, which has been hypothesized to stem from the microstructural behavior. However, a direct connection between thermodynamic conditions and the microstructural behavior, as described by molecular clusters, remains an outstanding issue. By utilizing a first-principles-based criterion and self-similarity analysis, we identify energetically localized molecular clusters whose size distribution and connectivity exhibit self-similarity in the extended supercritical phase space. We show that the structural response of these clusters follows a complex network behavior whose dynamics arises from the energetics of isotropic molecular interactions. Furthermore, we demonstrate that a hidden variable network model can accurately describe the structural and dynamical response of supercritical fluids. These results highlight the need for constitutive models and provide a basis to relate the fluid microstructure to thermodynamic response functions.

Computing Thermodynamic Properties of Fluids Augmented by Nanoconfinement: Application to Pressurized Methane.

Nanoconfined fluids exhibit remarkably different thermodynamic behavior compared to the bulk phase. These confinement effects render predictions of thermodynamic quantities of nanoconfined fluids challenging. In particular, confinement creates a spatially varying density profile near the wall that is primarily responsible for adsorption and capillary condensation behavior. Significant fluctuations in thermodynamic quantities, inherent in such nanoscale systems, coupled to strong fluid-wall interactions give rise to this near-wall density profile. Empirical models have been proposed to explain and model these effects, yet no first-principles based formulation has been developed. We present a statistical mechanics framework that embeds such a coupling to describe the effect of the fluid-wall interaction in amplifying the near-wall density behavior for compressible gases at elevated pressures such as pressurized methane in confinement. We show that the proposed theory predicts accurately the adsorbed layer thickness as obtained with small-angle neutron scattering measurements. Furthermore, the predictions of density under confinement from the proposed theory are shown to be in excellent agreement with available experimental and atomistic simulations data for a range of temperatures for nanoconfined methane. While the framework is presented for evaluating the near-wall density, owing to its rigorous foundation in statistical mechanics, the proposed theory can also be generalized for predicting phase-transition and nonequilibrium transport of nanoconfined fluids.

Chemical and Reactive Transport Processes Associated with Hydraulic Fracturing of Unconventional Oil/Gas Shales.

Hydraulic fracturing of unconventional oil/gas shales has changed the energy landscape of the U.S. Recovery of hydrocarbons from tight, hydraulically fractured shales is a highly inefficient process, with estimated recoveries of <25% for natural gas and <5% for oil. This review focuses on the complex chemical interactions of additives in hydraulic fracturing fluid (HFF) with minerals and organic matter in oil/gas shales. These interactions are intended to increase hydrocarbon recovery by increasing porosities and permeabilities of tight shales. However, fluid-shale interactions result in the dissolution of shale minerals and the release and transport of chemical components. They also result in mineral precipitation in the shale matrix, which can reduce permeability, porosity, and hydrocarbon recovery. Competition between mineral dissolution and mineral precipitation processes influences the amounts of oil and gas recovered. We review the temporal/spatial origins and distribution of unconventional oil/gas shales from mudstones and shales, followed by discussion of their global and U.S. distributions and compositional differences from different U.S. sedimentary basins. We discuss the major types of chemical additives in HFF with their intended purposes, including drilling muds. Fracture distribution, porosity, permeability, and the identity and molecular-level speciation of minerals and organic matter in oil/gas shales throughout the hydraulic fracturing process are discussed. Also discussed are analysis methods used in characterizing oil/gas shales before and after hydraulic fracturing, including permeametry and porosimetry measurements, X-ray diffraction/Rietveld refinement, X-ray computed tomography, scanning/transmission electron microscopy, and laboratory- and synchrotron-based imaging/spectroscopic methods. Reactive transport and spatial scaling are discussed in some detail in order to relate fundamental molecular-scale processes to fluid transport. Our review concludes with a discussion of potential environmental impacts of hydraulic fracturing and important knowledge gaps that must be bridged to achieve improved mechanistic understanding of fluid transport in oil/gas shales.

Using adjoint-based optimization to enhance ignition in non-premixed jets.

Gradient-based optimization is used to reliably and optimally induce ignition in three examples of laminar non-premixed mixture configurations. Using time-integrated heat release as a cost functional, the non-convex optimization problem identified optimal energy source locations that coincide with the stoichiometric local mixture fraction surface for short optimization horizons, while for longer horizons, the hydrodynamics plays an increasingly important role and a balance between flow and chemistry features determines non-trivial optimal ignition locations. Rather than identifying a single optimal ignition location, the results of this study show that there may be several equally good ignition locations in a given flow configuration.

X-ray Computed Tomography for Flame-Structure Analysis of Laminar Premixed Flames.

Quantitative X-ray computed tomography (XCT) diagnostics for reacting flows are developed and demonstrated in application to premixed flames in open and optically inaccessible geometries. A laboratory X-ray scanner is employed to investigate methane/air flames that were diluted with krypton as an inert radiodense tracer gas. Effects of acquisition rate and tracer gas concentration on the signal-to-noise ratio are examined. It is shown that statistically converged three-dimensional attenuation measurements can be obtained with limited impact from the tracer gas and within an acceptable acquisition time. Specific aspects of the tomographic reconstruction and the experimental procedure are examined, with particular emphasis on the quantification of experimental uncertainties. A method is developed to determine density and temperature from the X-ray attenuation measurements. These experiments are complemented by one- and multi-dimensional calculations to quantify the influence of krypton on the flame behavior. To demonstrate the merit of XCT for optically inaccessible flames, measurements of a complex flame geometry in a tubular confinement are performed. The use of a coflow to provide a uniform tracer-gas concentration is shown to improve the quantitative temperature evaluation. These measurements demonstrate the viability of XCT for flame-structure analysis and multi-dimensional temperature measurements using laboratory X-ray systems. Further opportunities for improving this diagnostic are discussed.

Phase transitions of ordered ice in graphene nanocapillaries and carbon nanotubes.

New phase diagrams for water confined in graphene nanocapillaries and single-walled carbon nanotubes (CNTs) are proposed, identifying ice structures, their melting points and revealing the presence of a solid-liquid critical point. For quasi-2D water in nanocapillaries, we show through molecular-dynamics simulations that AA stacking in multilayer quasi-2D ice arises from interlayer hydrogen-bonding and is stable up to three layers, thereby explaining recent experimental observations. Detailed structural and energetic analyses show that quasi-2D water can freeze discontinuously through a first-order phase transition or continuously with a critical point. The first-order transition line extends to a continuous transition line, defined by a sharp transition in diffusivity between solid-like and liquid-like regimes. For quasi-1D water, confined in CNTs, we observe the existence of a similar critical point at intermediate densities. In addition, an end point is identified on the continuous-transition line, above which the solid and liquid phases deform continuously. The solid-liquid phase transition temperatures in CNTs are shown to be substantially higher than 273 K, confirming recent Raman spectroscopy measurements. We observe ultrafast proton and hydroxyl transport in quasi-1D and -2D ice at 300 K, exceeding those of bulk water up to a factor of five, thereby providing possible applications to fuel-cells and electrolyzers.

Atomistic and continuum scale modeling of functionalized graphyne membranes for water desalination.

Recent theoretical and experimental studies reported ultra-high water permeability and salt rejection in nanoporous single-layer graphene. However, creating and controlling the size and distribution of nanometer-scale pores pose significant challenges to application of these membranes for water desalination. Graphyne and hydrogenated graphyne have tremendous potential as ultra-permeable membranes for desalination and wastewater reclamation due to their uniform pore-distribution, atomic thickness and mechano-chemical stability. Using molecular dynamics (MD) simulations and upscale continuum analysis, the desalination performance of bare and hydrogenated α-graphyne and γ-{2,3,4}-graphyne membranes is evaluated as a function of pore size, pore geometry, chemical functionalization and applied pressure. MD simulations show that pores ranging from 20 to 50 Å2 reject in excess of 90% of the ions for pressures up to 1 GPa. Water permeability is found to range up to 85 L cm-2 day-1 MPa-1, which is up to three orders of magnitude larger than commercial seawater reverse osmosis (RO) membranes and up to ten times that of nanoporous graphene. Pore chemistry, functionalization and geometry are shown to play a critical role in modulating the water flux, and these observations are explained by water velocity, density, and energy barriers in the pores. The atomistic scale investigations are complemented by upscale continuum analysis to examine the performance of these membranes in application to cross-flow RO systems. This upscale analysis, however, shows that the significant increase in permeability, observed from MD simulations, does not fully translate to current RO systems due to transport limitations. Nevertheless, upscale calculations predict that the higher permeability of graphyne membranes would allow up to six times higher permeate recovery or up to 6% less energy consumption as compared to thin-film composite membranes at currently accessible operating conditions. Significantly higher energy savings and permeate recovery can be achieved if higher feed-flow rates can be realized.

Widom Lines in Binary Mixtures of Supercritical Fluids.

Recent experiments on pure fluids have identified distinct liquid-like and gas-like regimes even under supercritical conditions. The supercritical liquid-gas transition is marked by maxima in response functions that define a line emanating from the critical point, referred to as Widom line. However, the structure of analogous state transitions in mixtures of supercritical fluids has not been determined, and it is not clear whether a Widom line can be identified for binary mixtures. Here, we present first evidence for the existence of multiple Widom lines in binary mixtures from molecular dynamics simulations. By considering mixtures of noble gases, we show that, depending on the phase behavior, mixtures transition from a liquid-like to a gas-like regime via distinctly different pathways, leading to phase relationships of surprising complexity and variety. Specifically, we show that miscible binary mixtures have behavior analogous to a pure fluid and the supercritical state space is characterized by a single liquid-gas transition. In contrast, immiscible binary mixture undergo a phase separation in which the clusters transition separately at different temperatures, resulting in multiple distinct Widom lines. The presence of this unique transition behavior emphasizes the complexity of the supercritical state to be expected in high-order mixtures of practical relevance.

Effect of gravity on capillary instability of liquid jets.

The effect of gravity on the onset and growth rate of capillary instabilities in viscous liquid jets is studied. To this end, a spatial linear stability analysis of Cosserat's equations is performed using a multiscale expansion technique. A dispersion relation and expressions for the perturbation amplitude are derived to evaluate the growth rate of the most unstable axisymmetric disturbance mode. Modeling results are compared with classical results in the limit of zero Bond number, confirming the validity of this approach. Expressions for the critical Weber number, demarcating the transition between convective and absolute instability are derived as functions of capillary and Bond numbers. Parametric investigations for a range of relevant operating conditions (characterized by capillary, Weber, and Bond numbers) are performed to examine the jet breakup and the perturbation growth rate. In addition to the physical insight that is obtained from this investigation, the results that are presented in this work could also be of relevance as test cases for the algorithmic development and the verification of high-fidelity multiphase simulation codes.

Generation of optimal artificial neural networks using a pattern search algorithm: application to approximation of chemical systems.

A pattern search optimization method is applied to the generation of optimal artificial neural networks (ANNs). Optimization is performed using a mixed variable extension to the generalized pattern search method. This method offers the advantage that categorical variables, such as neural transfer functions and nodal connectivities, can be used as parameters in optimization. When used together with a surrogate, the resulting algorithm is highly efficient for expensive objective functions. Results demonstrate the effectiveness of this method in optimizing an ANN for the number of neurons, the type of transfer function, and the connectivity among neurons. The optimization method is applied to a chemistry approximation of practical relevance. In this application, temperature and a chemical source term are approximated as functions of two independent parameters using optimal ANNs. Comparison of the performance of optimal ANNs with conventional tabulation methods demonstrates equivalent accuracy by considerable savings in memory storage. The architecture of the optimal ANN for the approximation of the chemical source term consists of a fully connected feedforward network having four nonlinear hidden layers and 117 synaptic weights. An equivalent representation of the chemical source term using tabulation techniques would require a 500 x 500 grid point discretization of the parameter space.

Stochastic mixing model with power law decay of variance.

A stochastic mixing model based on the law of large numbers is presented that describes the decay of the variance of a conserved scalar in decaying turbulence as a power law, sigma2(c) proportional t(-alpha). A general Lagrangian mixing process is modeled by a stochastic difference equation where the mixing frequency and the ambient concentration are random processes. The mixing parameter lambda is introduced as a coefficient in the mixing frequency in order to account for initial length-scale ratio of the velocity and scalar field and other physical dependencies. We derive a nonlinear integral equation for the probability density function (pdf) of a conserved scalar that describes the relaxation of an arbitrary initial distribution to a delta-function. Numerical studies of this equation are conducted, and it is shown that lambda has a distinct influence on the decay rate of the scalar. Results obtained from the model for the evolution of the pdf are in a good agreement with direct numerical simulation (DNS) data.