Results for “thermal pressure”

DOE OSTI2022

Thermal Pressure in the Thermal Equation of State for Solid and a Proposed Substitute

Abstract The thermal equation of state (TEOS) for solids is a mathematic model among pressure, temperature and density, and is essential for geophysical, geochemical, and other high pressure–temperature (high P–T) researches. However, in the last few decades, there has been a growing concern about the accuracy of the pressure scales of the calibrants, and efforts have been made to improve it by either introducing a reference standard or building new thermal pressure models. The existing thermal equation of state, P ( V , T ) = P ( V , T 0 ) + P th ( V , T ), consists of an isothermal compression and an isochoric heating, while the thermal pressure is the pressure change in the isochoric heating. In this paper, we demonstrate that, for solids in a soft pressure medium in a diamond anvil cell, the thermal pressure can neither be determined from a single heating process, nor from the thermal pressure of its calibrant. To avoid the thermal pressure, we propose to replace the thermal pressure with a well-known thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghan-expansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghan-expansion VPT TEOS model matches the experimental pressure of zero (0) GPa very well, while the pressure prediction from the approximated Anderson PVT TEOS exhibit a big deviation and a wrong trend.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Thermal Pressure in the Laser‐Heated Diamond Anvil Cell: A Quantitative Study and Implications for the Density Versus Mineralogy Correlation of the Mantle

Abstract Thermal pressure is an inevitable thermodynamic consequence of heating a volumetrically constrained sample in the diamond anvil cell. Its possible influences on experimentally determined density‐mineralogy correlations are widely appreciated, yet the effect itself has never been experimentally measured. We present here the first quantitative measurements of the spatial distribution of thermal pressure in a laser‐heated diamond anvil cell (LHDAC) in both olivine and AgI. The observed thermal pressure is strongly localized and closely follows the distribution of the laser hotspot. The magnitude of the thermal pressure is of the order of the thermodynamic thermal pressure ( αK T Δ T ) with gradients between 0.5 and 1.0 GPa/10 μm. Remarkably, we measure a steep gradient in thermal pressure even in a sample that is heated close to its melting line. This generates consequences for pressure determinations in pressure‐volume‐temperature (PVT) equation of state measurements when using an LHDAC. We show that an incomplete account of thermal pressure in PVT experiments can lead to biases in the coveted depth versus mineralogy correlation. However, the ability to spatially resolve thermal pressure in an LHDAC opens avenues to measure difficult‐to‐constrain thermodynamic derivative properties, which are important for comprehensive thermodynamic descriptions of the interior of planets.

Yen, Connor Ethan↗

DOE OSTI2025

Constraining gas motion and non-thermal pressure beyond the core of the Abell 2029 galaxy cluster with XRISM

We report on a detailed spectroscopic study of the gas dynamics and hydrostatic mass bias of the galaxy cluster Abell 2029, utilizing high-resolution observations from XRISM Resolve. Abell 2029, known for its cool core and relaxed X-ray morphology, provides an excellent opportunity to investigate the influence of gas motions beyond the central region. Expanding upon prior studies that revealed low turbulence and bulk motions within the core, our analysis covers regions out to the scale radius $R_{2500}$ (670 kpc) based on three radial pointings extending from the cluster center toward the northern side. We obtain accurate measurements of bulk and turbulent velocities along the line of sight. The results indicate that non-thermal pressure accounts for no more than 2% of the total pressure at all radii, with a gradual decrease outward. The observed radial trend differs from many numerical simulations, which often predict an increase in non-thermal pressure fraction at larger radii. These findings suggest that deviations from hydrostatic equilibrium are small, leading to a hydrostatic mass bias of around 2% across the observed area.

X-rays: galaxies: clusters↗

DOE OSTI2021

Demonstration of CFD to support the coupled analysis of a reactor pressure vessel subjected to pressurized thermal shock

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended duration or under accident condition. As one of the most significant components of a reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Aging degradation mechanisms (e.g. thermo-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The prediction of the temperature field is achieved by using computational fluid dynamics (CFD) simulation. In this report, a demonstration CFD standalone simulation is performed to support coupled analysis for Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS). The study use a simplified computational domain to represents a real RPV. The purpose of the study is to demonstrate the transient temperature response of RPV to ECC injection. The CFD model is built in a robust and efficient way for further coupled calculation. The next steps of this work, including the coupled thermal and tensor mechanics capabilities using Cardinal are expected to be complete by the end of FY21 for the demo problem. After this, into FY22, the capability will be demonstrated for a realistic RPV.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Modeling of thermal pressurization in tight claystone using sequential THM coupling: Benchmarking and validation against in-situ heating experiments in COx claystone

We apply thermoporoelasticity and a sequentially coupling technique for modeling thermally-driven coupled Thermo-Hydro-Mechanical (THM) processes in tight claystone. A THM benchmark case with a corresponding analytic solution for thermoporoelasticity under a constant heat loading verifies the model. Thereafter, two in situ heating experiments are simulated for model validation: a smaller-scale heating experiment (TED experiment) and a larger-scale experiment (ALC experiment) in Callovo-Oxfordian (COx) claystone at the Meuse/Haute-Marne underground research laboratory in France. The model exhibits good performance to match the observed temperature and pore pressure evolution for the smaller-scale TED experiment. For the larger-scale ALC experiment, general trends of thermal-pressurization are captured in the modeling, but pressure is underestimated at some monitoring points during cool-down. This indicates that the THM response in the field may be affected by the variability of rock's properties or irreversible or time-dependent mechanical processes that are not included in the current thermoporoelastic model. The main contributions of this work are as follows: (1) we verify and validate the numerical simulator, TOUGH-FLAC, to be a valuable coupled THM modeling tool; (2) prove that the laboratory determined material parameters can be used as reference values for upscaling experiments. However, to better identify and quantify THM processes with modeling of in situ tests, more emphasize should be dedicated to obtaining high-quality mechanical deformation data.

58 GEOSCIENCES↗

DOE OSTI2023

Sizing and Selection of Pressure Relief Valves for High-Pressure Thermal–Hydraulic Systems

This study covers the critical concerns related to the sizing, selection, installation, maintenance, and testing of pressure safety valves (PSVs). The aim is to ensure the safety of pressurized systems, hydrostatic transmission systems, and hydraulic plants, including process plants, thermal power plants, and nuclear reactor systems. PSVs are devices that ensure the safety and reliability of pressurized vessels, lines, and systems during overpressure events. The task of selecting which PSV features are of greatest value for a specific purpose is complex—especially in the design of a high-pressure experimental thermal–hydraulic facility for hydrostatic and transient testing of the reactor system—when the systems are in the design and development phases and require qualification and demonstration to prove that they have reached a given level of technological readiness. The present study highlights the required steps for users to follow the associated rules, guidelines, and recommendations. As a part of this research, case studies are presented to help readers better understand the applicable strategy and standards. A discussion and a review of PSV performance degradation and failure are summarized to provide a better understanding of varied process applications and conditions, including fluid flow dynamics, boundary-layer formation and pressure drops, gas bubble formation and collapse, geometric configurations, inlet/outlet piping, abrupt pressure fluctuations, and acoustic resonance. Moreover, this study discusses the servicing and testing of PSVs in a multiphase pressurized system. Overall, it provides a basic overview of how PSVs ensure the safety of pressurized systems, supported by case studies and industrial practices.

02 PETROLEUM↗

DOE OSTI2020

A study of thermal pressurization and potential for hydro-fracturing associated with nuclear waste disposal in argillaceous claystone

Not Available

58 GEOSCIENCES↗

DOE OSTI2022

Multi physics simulation on Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS) by using Cardinal

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended durations or under accident condition. As one of the most significant components of a Reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Ageing degradation mechanisms (e.g. thermo-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Simulation and Analysis on Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS) under SBLOCA scenario by using Cardinal to support the fracture mechanics analyses

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended durations or under accident condition. As one of the most significant components of a Reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Ageing degradation mechanisms (e.g. thermos-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The multi-physics simulations are performed using Cardinal, a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and other multi-physics sub-modules within the MOOSE framework. Cardinal now fully supports MOOSE stochastic perturbations of NekRS models with varying boundary conditions, initial conditions, material properties, and any other quantity which is defined by a kernel (such as coefficients in a momentum source model). The implementation is designed in a flexible manner so that scalar values are sent from MOOSE into a user scratch space in NekRS, which can then be applied for any purpose within the NekRS case files (both on the host and device). When modeling PTS, several factors can impact the results significantly. In this report, the impacts of the geometry of the model, Reynolds number and buoyancy effect are investigated. Two geometry, i.e., a simplified model and a realistic RPV model, with both laminar and turbulent flow condition are adopted for the PTS simulation with and without buoyancy effect. The purpose of the investigation is to understand the impact of these factors on the prediction of temperature history of RPV. The accurate prediction on the temperature evolution, which will be exported to Grizzly code for further analyses on the progression of aging mechanisms and their effects on the integrity of RPV structures, is very crucial. Based on the understanding of these factors, a more sophisticated model is built to analysis the PTS under SBLOCA scenario. A literature survey is conducted to pick the SBLOCA scenario for the multi-physics simulation. The analysis helps to explain the form and the transformation of the cold plum when the ECC is activated under SBLOCA. This model can be can be applied to study the PTS effect for different RPV configurations. The results can help to assess structural component degradation for advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Effects of rejuvenation modes on the microstructures and mechanical properties of metallic glasses

This study systematically investigates the effects of three rejuvenation modes, namely biaxial loading, thermal pressure loading, and cryogenic thermal cycling, on the microstructures and mechanical properties of Cu 64 Zr 36 metallic glasses (MGs) using molecular dynamics (MD) simulations. The simulation results demonstrate that biaxial tension application during loading results in a rejuvenated glassy state with high strength. Specifically, we find that the yield stress, Young's modulus, and shear modulus of the rejuvenated glass obtained by biaxial tensile loading decreased by 2.8%, 2.1%, and 2.7%, respectively, compared to an as-cast MG reference. We also find that MGs achieve the greatest degree of rejuvenation, at the expense of strength, with the use of thermal pressure loading. Interestingly, the application of cryogenic thermal cycling results in a rejuvenated state with a lower strength drop compared to thermal pressure loading. Furthermore, analysis of the potential energy and medium-range-order (MRO) size indicates that the microstructures of MGs achieves a high-energy ordered glass state after thermal pressure loading, but a high-energy disordered glass state after biaxial tensile loading and cryogenic thermal cycling. Furthermore, these findings provide meaningful insights into the effect of rejuvenation modes on the microstructures and mechanical properties of MGs, as well as useful guidelines for designing MGs with high strength and superior plasticity for prospective applications in industry.

36 MATERIALS SCIENCE↗

DOE OSTI2023

P-V-T equation of state of boron carbide

We report the P-V-T equation of state measurements of B 4 C to 50 GPa and approximately 2500 K in laser-heated diamond anvil cells. We obtain an ambient temperature, third-order Birch–Murnaghan fit to the P-V data that yields a bulk modulus K 0 of 221(2) GPa and derivative, (dK/dP) 0 of 3.3(1). These were used in fits with both a Mie–Grüneisen–Debye model and a temperature-dependent, Birch–Murnaghan equation of state that includes thermal pressure estimated by thermal expansion (α) and a temperature-dependent bulk modulus (dK 0 /dT). The ambient pressure thermal expansion coefficient (α 0 + α 1 T), Grüneisen γ(V) = γ 0 (V/V 0 ) q and volume-dependent Debye temperature, were used as input parameters for these fits and found to be sufficient to describe the data in the whole P-T range of this study.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Pressure-Dependent Thermal Expansion Coefficient by a Diamond Anvil Cell

A thermal expansion coefficient (αp) is an essential thermophysical quantity for high-pressure research. The thermal expansion coefficient is the volume change over the temperature in an isobaric heating process. Although isobaric heating processes for diamond anvil cell (DAC) have been conducted by keeping the pressure constant during heating, pressure determination at high-temperature high pressure is debatable for decades long. In this paper, a revertible heating/cooling approach is presented, while its pressure determination at high-temperature high pressure is not required. We report a pressure-dependent thermal expansion coefficient of MgO at 9.5 GPa by reversible heating/cooling was determined by a DAC and its result matches the one collected by a large volume press, whose isobaric heating was conducted by manually adjusting its load/pressure.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Metrology for femtosecond pulsed x-ray heating in diamond anvil cell experiments at the European XFEL: Revisiting the iron phase diagram up to 150 GPa

The development of pulsed intense x-ray sources, such as free electron laser, offers new avenues for high pressure experiments. Here, we study the feasibility and metrology of x-ray heating in diamond anvil cells at the European x-ray free electron laser. This method enables one to volumetrically heat the sample while inhibiting chemical migration and probing the crystallographic structure of the sample throughout the heating with a high repetition rate. We focus our study on iron, whose phase diagram is well established up to 100 GPa, to explore the possibilities and limitations of this technique. We volumetrically heat iron samples at starting pressures ranging from 10 to 138 GPa, using the x-ray beam pulsed at 4.5 MHz in a serial pump-and-probe experimental design. Experimental challenges arise from temperature gradients within the sample, changes in temperature at the 100 ns timescale, the difficulty of direct temperature estimates, the effect of thermal pressure, and the presence of metastable crystallites due to rapid cycles of heating and cooling. Hence, we develop a multi-crystal-like data processing method that allows us to account for sample heterogeneity in probed conditions. We then calibrate our measurements using known physical properties of iron under pressure. Thermal pressure in our experiments increases from 4% of the isochoric prediction at 10 GPa to 23% at 138 GPa, and we show that our data are in agreement with most previous observations of iron in this pressure range. The method can now be implemented at higher pressures and temperatures and on materials with unknown phase diagrams.

Materials science↗

DOE OSTI2022

Effects of doping, hydrostatic pressure, and thermal quenching on the phase transitions and magnetocaloric properties in Mn 1– x Co x NiGe

The effects of doping, hydrostatic pressure, and thermal quenching on the phase transitions and magnetocaloric properties of the Mn 1–x Co x NiGe system have been investigated. Cobalt doping on the Mn site shifted the martensitic structural transition toward lower temperature until it was ultimately absent, leaving only a magnetic transition from a ferromagnetic (FM) to a paramagnetic (PM) state in the high-temperature hexagonal phase. Co-occurrence of the magnetic and structural transitions to form a first-order magnetostructural transition (MST) from the FM orthorhombic to the PM hexagonal phase was observed in samples with 0.05 < x < 0.20. An additional antiferromagnetic–ferromagnetic-like transition was observed in the martensite phase for 0.05 < x < 0.10, which gradually vanished with increasing Co concentration (x > 0.10) or magnetic field (H > 0.5 T). The application of external hydrostatic pressure shifted the structural transition to lower temperature until an MST was formed in samples with x = 0.03 and 0.05, inducing large magnetic entropy changes up to –80.3 J kg –1 K –1 (x = 0.03) for a 7-T field change under 10.6-kbar pressure. Similar to the effects of the application of hydrostatic pressure, an MST was formed near room temperature in the sample with x = 0.03 by annealing at high temperature (1200 °C) followed by quenching, resulting in a large magnetic entropy change of –56.2 J kg –1 K –1 . Furthermore, these experimental results show that the application of pressure and thermal quenching, in addition to compositional variations, are effective methods to create magnetostructural transitions in the MnNiGe system, resulting in large magnetocaloric effects.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Properties of molecular clumps and cores in colliding magnetized flows

ABSTRACT We simulate the formation of molecular clouds in colliding flows of warm neutral medium with the adaptive mesh refinement code flash in eight simulations with varying initial magnetic field strength, between 0.01–5 μG. We include a chemical network to treat heating and cooling and to follow the formation of molecular gas. The initial magnetic field strength influences the fragmentation of the forming cloud because it prohibits motions perpendicular to the field direction and hence impacts the formation of large-scale filamentary structures. Molecular clump and core formation occurs anyhow. We identify 3D clumps and 3D cores, which are defined as connected, CO-rich regions. Additionally, 3D cores are heavily shielded. While we do not claim those 3D objects to be directly comparable to observations, this enables us to analyse their full virial state. With increasing field strength, we find more fragments with a smaller average mass; yet the dynamics of the forming clumps and cores only weakly depends on the initial magnetic field strength. The molecular clumps are mostly unbound, probably transient objects, which are weakly confined by ram pressure or thermal pressure, indicating that they are swept up by the turbulent flow. They experience significant fluctuations in the mass flux through their surface, such that the Eulerian reference frame shows a dominant time-dependent term due to their indistinct nature. We define the cores to encompass highly shielded molecular gas. Most cores are in gravitational-kinetic equipartition and are well described by the common virial parameter $\alpha _\mathrm{vir}$, while some undergo minor dispersion by kinetic surface effects.

Weis, M. (ORCID:0000000256838860)↗

DOE OSTI2021

Pressure-assisted thermal sterilization of avocado puree in high barrier polymeric packaging

The aim of this study was to examine the influence of pressure-assisted thermal sterilization (PATS) on properties of polymeric packaging and packaged avocado puree. High pressure of 600 MPa and initial vessel temperature of 90 °C were used over 5 min processing time. We used two high barrier film pouches: Film A-(PE/PA6//EVOH//PA6/PE) and film B-(AlO x -coated PET//AlO x -coated PET//PA//CPP). Oxygen transmission rates (OTR) changed from 0.16 ± 0.07 to 3.24 ± 0.52 cm 3 /m 2 .day for film A after processing while OTRs were not detected for film B. Water vapor transmission rates (WVTR) changed from 3.72 ± 0.06 to 4.97 ± 0.14 g/m 2 .day for film A and 0.11 ± 0.02 to 0.62 ± 0.0.6 g/m 2 .day for film B. The dissolved oxygen in packaged avocado puree reduced from 21% to 3% after PATS for both films. Reduced oxygen level in packaged avocado may help extend its shelf life. Dielectric properties and X-ray diffraction helped explain PATS induced changes in film barrier properties. The total chlorophyll, greenness, and lightness decreased significantly (p < 0.05) after PATS. The thiobarbituric acid activity reduced after PATS. PATS showed potential to produced shelf-stable avocado puree; however, shelf-life studies are needed to further develop PATS process.

42 ENGINEERING↗

DOE OSTI2021

Pressure and thermal annealing effects on the photoconversion efficiency of polymer solar cells

This paper presents the results of experimental and theoretical studies of the effects of pressure and thermal annealing on the photo-conversion efficiencies (PCEs) of polymer solar cells with active layers that consist of a mixture of poly(3-hexylthiophene-2,5-diyl) and fullerene derivative (6,6)-phenyl-C 61 -butyric acid methyl ester. The PCEs of the solar cells increased from ~2.3% (for the unannealed devices) to ~3.7% for devices annealed at ~150 °C. A further increase in thermal annealing temperatures (beyond 150 °C) resulted in lower PCEs. Further improvements in the PCEs (from ~3.7% to ~5.4%) were observed with pressure application between 0 and 8 MPa. However, a decrease in PCEs was observed for pressure application beyond 8 MPa. The improved performance associated with thermal annealing is attributed to changes in the active layer microstructure and texture, which also enhance the optical absorption, mobility, and lifetime of the optically excited charge carriers. The beneficial effects of applied pressure are attributed to the decreased interfacial surface contacts that are associated with pressure application. The implications of the results are then discussed for the design and fabrication of organic solar cells with improved PCEs.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Figuring Out Gas & Galaxies in Enzo (FOGGIE). VI. The Circumgalactic Medium of L * Galaxies Is Supported in an Emergent, Nonhydrostatic Equilibrium

The circumgalactic medium (CGM) is often assumed to exist in or near hydrostatic equilibrium, with the regulation of accretion and the effects of feedback treated as perturbations to a stable balance between gravity and thermal pressure. We investigate global hydrostatic equilibrium in the CGM using four highly resolved L* galaxies from the Figuring Out Gas & Galaxies in Enzo (FOGGIE) project. The FOGGIE simulations were specifically targeted at fine spatial and mass resolution in the CGM (Δx ≲ 1 kpc h –1 and M ≃ 200M ⊙ ). We develop a new analysis framework that calculates the forces provided by thermal pressure gradients, turbulent pressure gradients, ram pressure gradients of large-scale radial bulk flows, centrifugal rotation, and gravity acting on the gas in the CGM. Thermal and turbulent pressure gradients vary strongly on scales of ≲5 kpc throughout the CGM. Thermal pressure gradients provide the main supporting force only beyond ~0.25R 200 , or ~50 kpc at z = 0. Within ~0.25R 200 , turbulent pressure gradients and rotational support provide stronger forces than thermal pressure. More generally, we find that global equilibrium models are neither appropriate nor predictive for the small scales probed by absorption line observations of the CGM. Local conditions generally cannot be derived by assuming a global equilibrium, but an emergent global equilibrium balancing radially inward and outward forces is obtained when averaging over the nonequilibrium local conditions on large scales in space and time. Approximate hydrostatic equilibrium holds only at large distances from galaxies, even when averaging out small-scale variations.

79 ASTRONOMY AND ASTROPHYSICS↗