Full Thermodynamic Equilibrium Research Articles

Helium as a signature of the double detonation in Type Ia supernovae

ABSTRACT The double detonation is a widely discussed mechanism to explain Type Ia supernovae from explosions of sub-Chandrasekhar mass white dwarfs. In this scenario, a helium detonation is ignited in a surface helium shell on a carbon/oxygen white dwarf, which leads to a secondary carbon detonation. Explosion simulations predict high abundances of unburnt helium in the ejecta, however, radiative transfer simulations have not been able to fully address whether helium spectral features would form. This is because helium can not be sufficiently excited to form spectral features by thermal processes, but can be excited by collisions with non-thermal electrons, which most studies have neglected. We carry out a full non-local thermodynamic equilibrium radiative transfer simulation for an instance of a double detonation explosion model, and include a non-thermal treatment of fast electrons. We find a clear He i λ10830 feature which is strongest in the first few days after explosion and becomes weaker with time. Initially this feature is blended with the Mg ii λ10927 feature but over time separates to form a secondary feature to the blue wing of the Mg ii λ10927 feature. We compare our simulation to observations of iPTF13ebh, which showed a similar feature to the blue wing of the Mg ii λ10927 feature, previously identified as C i. Our simulation shows a good match to the evolution of this feature and we identify it as high velocity He i λ10830. This suggests that He i λ10830 could be a signature of the double detonation scenario.

Discovery of an extended G giant chromosphere in the 2019 eclipse of γ Per

The November 2019 eclipse of γ Per was a rare opportunity to seek evidence for a chromosphere of the G8 giant, hitherto suspected but not detected. Twenty-nine years after the only other observed eclipse, we aim to find chromospheric absorption in the strong Ca II H&K lines, and to determine its column densities and scale height. Using the Telescopio Internacional de Guanajuato Robótico-Espectroscópico (TIGRE) in Guanajuato (central Mexico) before, during and after the 8 days of total eclipse, we obtained good S/N spectra of the G8 giant alone and composite spectra of the partial phases, near eclipse and far from eclipse. In the near UV of the Ca II H&K and Hϵ lines, the G giant spectrum that was adequately scaled was subtracted from the composite spectra in partial phases, near and far from eclipse, to obtain the A3 companion spectra with and without traces of chromospheric absorption. In addition, we used PHOENIX full non-local thermodynamic equilibrium model atmospheres on the blue A star spectrum, iSpec spectral analysis of the red G giant spectrum, and evolution tracks to study both components of γ Per. For the first time, we present evidence for this rare type of a not very extended G giant chromosphere, reaching out about half of an A-star radius (~1.5 Gm) with a scale height of only 0.17 Gm. By its location in the Hertzsprung-Russell diagram, the γ Per G8 giant is very close to the onset of more extended chromospheres. Furthermore, we show that this giant has a rather inactive chromosphere, and a recent 5 ksec XMM pointing reveals only a very faint, low-energy corona. While the γ Per primary has a mass of ~3.6 M⊙, and its A3 companion has one of ~2.4 M⊙, the latter is too cool (8400 ± 300 K), which is too evolved on the main sequence to be the same age as the primary. The high eccentricity of the 5329.08 days long-period orbit may therefore be reminiscent of a rare capture event. Using the eclipse method, we resolve a pivotal case of a G giant chromosphere, which seems to represent a low-gravity analogue of the inactive Sun. A systematic change of giant chromospheric extent by Hertzsprung-Russell diagram position is confirmed. Compared to the solar chromosphere, the density scale height increases with gravity by ∝ ɡ−1.5.

Full non-LTE spectral line formation

In this article we discuss a method for obtaining a numerical solution to the so-called full nonlocal thermodynamic equilibrium (non-LTE) radiation transfer problem. More specifically, the usual numerical iterative methods for non-LTE radiation transfer are coupled with that formalism and new numerical additions are explained in detail. We benchmarked the whole process with the standard non-LTE transfer problem for a two-level atom with Hummer’s RI − A partial frequency redistribution function. Finally, we present new quantities, such as the spatial distribution of the velocity distribution function of excited atoms, which can only be accessed by adopting a more general frame for non-LTE radiation transfer, such as the one we propose here.

The Problem of Stability of Gas-Condensate Mixture at Pore-Scale: The Study by Density Functional Hydrodynamics

The method of the density functional hydrodynamics (DFH) is used to model compositional gas-condensate systems in natural cores at pore-scale. In previous publications, it has been demonstrated by the authors that DFH covers many diverse multiphase pore-scale phenomena, including fluid transport in RCA and SCAL measurements and complex EOR processes. The pore-scale modeling of multiphase flow scenarios is performed by means of the direct hydrodynamic (DHD) simulator, which is a numerical implementation of the DFH. In the present work, we consider the problem of pore-scale numerical modeling of three-phase system: residual water, hydrocarbon gas and hydrocarbon liquid with phase transitions between the two latter phases. Such situations happen in case of gas-condensate or volatile oil deposits, in oil deposits with gas caps or in EOR methods with gas injection. The corresponding field development modeling by the conventional reservoir simulators rely on phase permeabilities and capillary pressures, which are provided by laboratory core analysis experiments. But the problem with gas-liquid hydrocarbon mixtures is that in laboratory procedures it may be difficult or even impossible to achieve full thermodynamic equilibrium between phases as it must be under the reservoir conditions of the initial reservoir state. However, reaching the said equilibrium is quite possible in numerical simulation. In this work, the gas-liquid mixture, after being injected into core sample, would slowly undergo the rearrangement of the phases and chemical components in pores converging to the minimum of the Helmholtz energy functional. This process is adequately described by DFH with consequent impact on phase permeabilities and capillary pressure. We give pore-scale numerical examples of the described phenomena in a micro-CT porous rock model for a realistic gas-condensate mixture with quantitative characterization of phase transition kinetic effects.

Electrochemically deposited molybdenum disulfide surfaces enable polymer adsorption studies using quartz crystal microbalance with dissipation monitoring (QCM-D)

Polymer and small molecules are often used to modify the wettability of mineral surfaces which facilitates the separation of valuable minerals such as molybdenum disulfide (MoS2) from gangue material through the process of froth flotation. By design, traditional methods used in the field for evaluating the separation efficacy of these additives fail to give proper access to adsorption kinetics and molecule conformation, crucial aspects of flotation where contact times may not allow for full thermodynamic equilibrium. Thus, there is a need for alternative methods for evaluating additives that accurately capture these features during the adsorption of additives at the solid/liquid interface. Here, we present a novel method for preparing MoS2 films on quartz crystals used for Quartz Crystal Microbalance with Dissipation (QCM-D) measurements through an electrochemical deposition process. The resulting films exhibit well-controlled structure, composition, and thickness and therefore are ideal for quantifying polymer adsorption. After deposition, the sensors can be annealed without damaging the quartz crystal, resulting in a phase transition of the MoS2 from the as-deposited, amorphous phase to the 2H semiconducting phase. Furthermore, we demonstrate the application of these sensors to study the interactions of additives at the solid/liquid interface by investigating the adsorption of a model polymer, dextran, onto both the amorphous and crystalline MoS2 surfaces. We find that the adsorption rate of dextran onto the amorphous surface is approximately twice as fast as the adsorption onto the annealed surface. These studies demonstrate the ability to gain insight into the short-term kinetics of interaction between molecules and mineral surface, behavior that is key to designing additives with superior separation efficiency.

New predictions for radiation-driven, steady-state mass-loss and wind-momentum from hot, massive stars

Context. Reliable predictions of mass-loss rates are important for massive-star evolution computations. Aims. We aim to provide predictions for mass-loss rates and wind-momentum rates of O-type stars, while carefully studying the behaviour of these winds as functions of stellar parameters, such as luminosity and metallicity. Methods. We used newly developed steady-state models of radiation-driven winds to compute the global properties of a grid of O-stars. The self-consistent models were calculated by means of an iterative solution to the equation of motion using full non-local thermodynamic equilibrium radiative transfer in the co-moving frame to compute the radiative acceleration. In order to study winds in different galactic environments, the grid covers main-sequence stars, giants, and supergiants in the Galaxy and both Magellanic Clouds. Results. We find a strong dependence of mass-loss on both luminosity and metallicity. Mean values across the grid are Ṁ~L*2.2 and Ṁ~L*0.95; however, we also find a somewhat stronger dependence on metallicity for lower luminosities. Similarly, the mass loss-luminosity relation is somewhat steeper for the Small Magellanic Cloud (SMC) than for the Galaxy. In addition, the computed rates are systematically lower (by a factor 2 and more) than those commonly used in stellar-evolution calculations. Overall, our results are in good agreement with observations in the Galaxy that properly account for wind-clumping, with empirical Ṁ versus Z* scaling relations and with observations of O-dwarfs in the SMC. Conclusions. Our results provide simple fit relations for mass-loss rates and wind momenta of massive O-stars stars as functions of luminosity and metallicity, which are valid in the range Teff = 28 000–45 000 K. Due to the systematically lower values for Ṁ, our new models suggest that new rates might be needed in evolution simulations of massive stars.

Improving the Understanding of CrIS Full Spectral Resolution Nonlocal Thermodynamic Equilibrium Radiances Using Spectral Correlation

AbstractIn recent years, significant progress has been made in fast radiative transfer model (RTM) simulation of daytime nonlocal thermodynamic equilibrium (NLTE) emission. However, NLTE remains as one important reason that prevents the hyperspectral shortwave infrared (SWIR) radiance observations from being assimilated into numerical weather prediction (NWP) models. To better understand the limitations of existing RTM‐based NLTE simulation, this study introduces a new statistical method, called Spectral Correlations to Estimate Non‐Local Thermal Equilibrium (SCENTE), to estimate the NLTE radiances in the Cross‐track Infrared Sounder (CrIS) SWIR radiance observations. SCENTE is applied to four typical season days, including spring equinox, summer solstice, fall equinox, and winter solstice. By analyzing calculation/background minus observation (BMO) of CrIS SWIR brightness temperature (BT), results show that SCENTE characterizes the NLTE well with standard deviation of differences (STD) comparable to observation noise for both daytime and nighttime, while the community RTM (CRTM) has substantially larger STD at night, mainly due to the lack of daytime NLTE just beyond the day/night terminator and the lack of aurora‐related NLTE. Detailed investigation of the biases of BMO shows that CRTM underestimates daytime SWIR NLTE effects by 0.76 K, while SCENTE overestimates SWIR NLTE effects by 0.70 K. The overestimation is because SCENTE uses CRTM‐simulated SWIR local thermodynamic equilibrium (LTE) radiances in the training, which is underestimated by 0.70 K in BT. SCENTE, complementary to RTM‐based simulations, can be used for quality control of SWIR radiances for assimilation and retrieval of atmospheric soundings.

Sunquake with a second bounce, other sunquakes, and emission associated with the X9.3 flare of 6 September 2017

In this paper we present the interpretation of the observations of the flare from 6 September 2017 reported in Paper I. These include gamma-ray (GR), hard X-ray (HXR), soft X-rays, Lyαline, extreme ultraviolet (EUV), Hα, and white light (WL) emission, which were recorded during the two flaring events 1 (FE1) and 2 (FE2) that occurred at 11:55:37 UT (FE1) and 12:06:40 UT (FE2). Paper I also reported the first detection of the sunquake with first and second bounces of seismic waves combined with four other sunquakes in different locations supported with the observations of HXR, GR, EUV, Hα, and WL emission with strongly varying spatial resolution and temporal coverage. In the current paper, we propose some likely scenarios for heating of flaring atmospheres in the footpoints with sunquakes which were supported with EUV and Hαemission. We used a range of parameters derived from the HXR, EUV, and Hαline observations to generate hydrodynamic models, which can account for the blueshifts derived from the EUV emission and the redshifts observed with the EUV Imaging Spectrometer in the He II line and by the CRisp Imaging Spectro-Polarimeter in the Swedish Solar Telescope in Hαline emission. The parameters of hydrodynamic shocks produced by different beams in flaring atmospheres were used as the initial conditions for another type of hydrodynamic models that were developed for acoustic wave propagation in the solar interior. These models simulate the sets of acoustic waves produced in the interior by the hydrodynamic shocks from atmospheres above deposited in different footpoints of magnetic loops. The Hαline profiles with large redshifts in three kernels (two in FE1 and one in FE2) were interpreted with the full non-local thermodynamic equilibrium radiative simulations in all optically thick transitions (Lyman lines and continuum Hα, Hβ, and Pα) applied for flaring atmospheres with fast downward motions while considering thermal and non-thermal excitation and ionisation of hydrogen atoms by energetic power-law electron beams. The observed Hαline profiles in three kernels were fit with the simulate blue wing emission of the Hαline profiles shifted significantly (by 4–6 Å) towards the line red wings, because of strong downward motions with velocities about 300 km s−1by the shocks generated in flaring atmospheres by powerful beams. The flaring atmosphere associated with the largest sunquake (seismic source 2 in FE1) is found consistent with being induced by a strong hydrodynamic shock produced by a mixed beam deposited at an angle of −30° from the local vertical. We explain the occurrence of a second bounce in the largest sunquake by a stronger momentum delivered by the shock generated in the flaring atmosphere by a mixed beam and deeper depths of the interior where this shock was deposited. Indeed, the shock with mixed beam parameters is found deposited deeply into the interior beneath the flaring atmosphere under the angle to the local vertical that would allow the acoustic waves generated in the direction closer to the surface to conserve enough energy for the second bounces from the interior layers and from the photosphere. The wave characteristics of seismic sources 1 and 3 (in FE1) were consistent with those produced by the shocks generated by similar mixed beams deposited at the angles −(0 − 10)° (seismic source 1) and +30° (seismic source 3) to the local vertical. The differences of seismic signatures produced in the flares of 6 September 2011 and 2017 are also discussed.

The 3D non-LTE solar nitrogen abundance from atomic lines

Nitrogen is an important element in various fields of stellar and Galactic astronomy, and the solar nitrogen abundance is crucial as a yardstick for comparing different objects in the cosmos. In order to obtain a precise and accurate value for this abundance, we carried out N I line formation calculations in a 3D radiative-hydrodynamic STAGGER model solar atmosphere in full 3D non-local thermodynamic equilibrium (non-LTE). We used a model atom that includes physically motivated descriptions for the inelastic collisions of N I with free electrons and with neutral hydrogen. We selected five N I lines of high excitation energy to study in detail, based on their strengths and on their being relatively free of blends. We found that these lines are slightly strengthened from non-LTE photon losses and from 3D granulation effects, resulting in negative abundance corrections of around − 0.01 dex and − 0.04 dex, respectively. Our advocated solar nitrogen abundance is log ɛN = 7.77, with the systematic 1σ uncertainty estimated to be 0.05 dex. This result is consistent with earlier studies after correcting for differences in line selections and equivalent widths.

Crystallization of the outer crust of a non-accreting neutron star

Context. The interior of a neutron star is usually assumed to be made of cold catalyzed matter. However, the outer layers are unlikely to remain in full thermodynamic equilibrium during the formation of the star and its subsequent cooling, especially after crystallization occurs. Aims. We study the cooling and the equilibrium composition of the outer layers of a non-accreting neutron star down to crystallization. Here the impurity parameter, generally taken as a free parameter in cooling simulations, is calculated self-consistently using a microscopic nuclear model for which a unified equation of state has recently been determined. Methods. We follow the evolution of the nuclear distributions of the multi-component Coulomb liquid plasma fully self-consistently, adapting a general formalism originally developed for the description of supernova cores. We calculate the impurity parameter at the crystallization temperature as determined in the one-component plasma approximation. Results. Our analysis shows that the sharp changes in composition obtained in the one-component plasma approximation are smoothed out when a full nuclear distribution is allowed. The Coulomb coupling parameter at melting is found to be reasonably close to the canonical value of 175, except for specific values of the pressure for which supercooling occurs in the one-component plasma approximation. Our multi-component treatment leads to non-monotonic variations of the impurity parameter with pressure. Its values can change by several orders of magnitude reaching about 50, suggesting that the crust may be composed of an alternation of pure (highly conductive) and impure (highly resistive) layers. The results presented here complement the recent unified equation of state obtained within the same nuclear model. Conclusions. Our self-consistent approach to hot dense multi-component plasma shows that the presence of impurities in the outer crust of a neutron star is non-negligible and may have a sizeable impact on transport properties. In turn, this may have important implications not only for the cooling of neutron stars, but also for their magneto-rotational evolution.

New predictions for radiation-driven, steady-state mass-loss and wind-momentum from hot, massive stars

Context. Radiation-driven mass loss plays a key role in the life cycles of massive stars. However, basic predictions of such mass loss still suffer from significant quantitative uncertainties. Aims. We develop new radiation-driven, steady-state wind models for massive stars with hot surfaces, suitable for quantitative predictions of global parameters like mass-loss and wind-momentum rates. Methods. The simulations presented here are based on a self-consistent, iterative grid solution to the spherically symmetric, steady-state equation of motion, using full non-local thermodynamic equilibrium radiative transfer solutions in the co-moving frame to derive the radiative acceleration. We do not rely on any distribution functions or parametrization for computation of the line force responsible for the wind driving. The models start deep in the subsonic and optically thick atmosphere and extend up to a large radius at which the terminal wind speed has been reached. Results. In this first paper, we present models representing two prototypical O-stars in the Galaxy, one with a higher stellar mass M*∕M⊙ = 59 and luminosity log10L*∕L⊙ = 5.87 (spectroscopically an early O supergiant) and one with a lower M*∕M⊙ = 27 and log10L*∕L⊙ = 5.1 (a late O dwarf). For these simulations, basic predictions for global mass-loss rates, velocity laws, and wind momentum are given, and the influence from additional parameters like wind clumping and microturbulent speeds is discussed. A key result is that although our mass-loss rates agree rather well with alternative models using co-moving frame radiative transfer, they are significantly lower than those predicted by the mass-loss recipes normally included in models of massive-star evolution. Conclusions. Our results support previous suggestions that Galactic O-star mass-loss rates may be overestimated in present-day stellar evolution models, and that new rates might therefore be needed. Indeed, future papers in this series will incorporate our new models into such simulations of stellar evolution, extending the very first simulations presented here toward larger grids covering a range of metallicities, B supergiants across the bistability jump, and possibly also Wolf-Rayet stars.

Equations of state for polyethylene and its shock-driven decomposition products

We construct new equations of state (EOS) for high density and ultrahigh molecular weight polyethylene and their chemical decomposition products under shock loading. The former were built using the SESAME framework, based in part on new specific heat and thermal expansion data reported here. The products EOS was based on thermochemical modeling under the assumption of full thermodynamic and chemical equilibrium. The products are represented as the ideal mixture of bulk carbon in the form of diamond, H2, H, and CH4. In the process of building a new EOS for the products, we recalibrated our exponential-6 pair potential for methane in order to better agree with data that have appeared since its original parameterization. The polyethylene EOS were calibrated to thermal, thermomechanical, and shock data, and their performance was evaluated in hydrodynamic modeling of deep release experiments reported previously.

Two-step procedure for trace element analysis in food via calibration-free laser-induced breakdown spectroscopy

Elemental analyses via calibration-free laser-induced breakdown spectroscopy (LIBS) usually suffer low sensitivity due to continuum emission generated by the plasma in local thermodynamic equilibrium. Here we propose a two-step measurement procedure that enables improved sensitivity of calibration-free LIBS. The method consists of recording two emission spectra with different delays between the laser pulse and the detector gate. The short delay is used to probe the plasma in conditions of full local thermodynamic equilibrium in order to measure major and minor element concentrations. To evaluate the concentrations of trace elements, a second measurement with improved limits of detection is performed with a larger gate delay. In that condition, the partial equilibrium state of the plasma enables the quantification of minor and trace elements. Demonstrated via analyses of lyophilized seafood samples, the presented method is suitable for all types of food, and more general for organic materials and all materials that include elements such as carbon, oxygen, nitrogen and hydrogen, for which the equilibrium state is hardly achieved.

Temporal variations of electron density and temperature in Kr/Ne/H2 photoionized plasma induced by nanosecond pulses from extreme ultraviolet source

Spectral investigations of low-temperature photoionized plasmas created in a Kr/Ne/H2 gas mixture were performed. The low-temperature plasmas were generated by gas mixture irradiation using extreme ultraviolet pulses from a laser-plasma source. Emission spectra in the ultraviolet/visible range from the photoionized plasmas contained lines that mainly corresponded to neutral atoms and singly charged ions. Temporal variations in the plasma electron temperature and electron density were studied using different characteristic emission lines at various delay times. Results, based on Kr II lines, showed that the electron temperature decreased from 1.7 to 0.9 eV. The electron densities were estimated using different spectral lines at each delay time. In general, except for the Hβ line, in which the electron density decreased from 3.78 × 1016 cm−3 at 200 ns to 5.77 × 1015 cm−3 at 2000 ns, most of the electron density values measured from the different lines were of the order of 1015 cm−3 and decreased slightly while maintaining the same order when the delay time increased. The time dependences of the measured and simulated intensities of a spectral line of interest were also investigated. The validity of the partial or full local thermodynamic equilibrium (LTE) conditions in plasma was explained based on time-resolved electron density measurements. The partial LTE condition was satisfied for delay times in the 200 ns to 1500 ns range. The results are summarized, and the dominant basic atomic processes in the gas mixture photoionized plasma are discussed.

Ripping RNA by Force Using Gaussian Network Models

Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict, studies in the context of proteins have shown that topology is the major determinant of the unfolding landscapes. By building on this finding we study the responses of RNA molecules to force by adapting Gaussian network model (GNM) that represents RNAs using a bead-spring network with isotropic interactions. Cross-correlation matrices of residue fluctuations, which are analytically calculated using GNM even upon application of mechanical force, show distinct allosteric communication as RNAs rupture. The model is used to calculate the force-extension curves at full thermodynamic equilibrium, and the corresponding unfolding pathways of four RNA molecules subject to a quasi-statically increased force. Our study finds that the analysis using GNM captures qualitatively the unfolding pathway of T. ribozyme elucidated by the optical tweezers measurement. However, the simple model cannot capture features, such as bifurcation in the unfolding pathways or the ion effects, in the forced-unfolding of RNAs.

Neutral Hydrogen and Its Emission Lines in the Solar Corona

Since the Lalpha rocket observations of (Gabriel, Solar Phys. 21, 392, 1971), it has been realized that the hydrogen (H) lines could be observed in the corona and offer an interesting diagnostic for the temperature, density, and radial velocity of the coronal plasma. Moreover, various space missions have been proposed to measure the coronal magnetic and velocity fields through polarimetry in H lines. A necessary condition for such measurements is to benefit from a sufficient signal-to-noise ratio. The aim of this article is to evaluate the emission in three representative lines of H for three different coronal structures. The computations have been performed with a full non-local thermodynamic equilibrium (non-LTE) code and its simplified version without radiative transfer. Since all collisionnal and radiative quantities (including incident ionizing and exciting radiation) are taken into account, the ionization is treated exactly. Profiles are presented at two heights (1.05 and 1.9 solar radii, from Sun center) in the corona, and the integrated intensities are computed at heights up to five solar radii.We compare our results with previous computations and observations (e.g. Lalpha from UVCS) and find a rough (model-dependent) agreement. Since the Halpha line is a possible candidate for ground-based polarimetry, we show that in order to detect its emission in various coronal structures, it is necessary to use a very narrow (less than 2 A wide) bandpass filter.

Shadowgraph visualization of condensing R134a flow through ejectors

Accurate simulation of ejector flows has been challenging due to the difficulties in modeling two-phase supersonic flows of fluids other than air or steam at high temperature and pressure conditions. Such modeling is necessary for ejector optimization, but the models currently available have yet to be validated. A transparent ejector test section is designed, fabricated, and operated in an ejector-based chiller loop using R134a as the working fluid. Undistorted visual access allows for detailed shadowgraph visualization of the motive jet in the mixing section at various degrees of condensation. High-speed imaging is used with measured temperatures and pressures at the ejector inlets to validate available analytical and CFD models. It is found that the best modeling techniques assume that the motive flow exits the motive nozzle at full thermodynamic equilibrium, and that the k-ε RNG turbulence model in ANSYS FLUENT captures these equilibrium conditions sufficiently.

Replacement of barite by a (Ba,Ra)SO4 solid solution at close-to-equilibrium conditions: A combined experimental and theoretical study

Solid solution formation between RaSO4 and BaSO4 has long been recognized as a process which potentially controls the Ra concentration in the environment. Here, we have systematically studied the replacement of pure barite by a (Ba,Ra)SO4 solid solution in 0.1M NaCl through batch experiments extending up to 883days at close-to-equilibrium (CTE) conditions, which are relevant to disposal of nuclear waste in a deep geological repository. Kinetic and thermodynamic models were applied to support the interpretation of the experiments, which were carried out at room temperature and at two distinct solid/liquid ratio (0.5 or 5g/L). Different stages of recrystallization were observed, based on the rate of removal of Ra from aqueous solution. After a first slow kinetic step, a change in the slope of the aqueous Ra concentration vs. time is observed, suggesting nucleation of a new (Ba,Ra)SO4 phase from supersaturation. If this stage was considered to reflect equilibrium between aqueous and solid solution, one would infer ideality or even negative interaction parameters (a0⩽0). After this fast nucleation step, in the 0.5g/L experiments the Ra concentrations in the aqueous solution slowly increase, approaching a concentration close to that required for equilibrium with a regular (Ba,Ra)SO4 solid solution with an interaction parameter a0=1.0. Therefore, these data suggest a non-equilibrium Ra entrapment during the nucleation phase of the replacement, followed by slow recrystallization toward true thermodynamic solid solution equilibrium. Moreover, an interaction parameter value of a0=1.0 was inferred from our experiments, which is in good agreement with theoretical predictions from atomistic simulations.A key result from this study is that aqueous solution and binary (Ba,Ra)SO4 approach full thermodynamic equilibrium within laboratory time scales (2.5years). This justifies assuming complete thermodynamic equilibrium for this system in geochemical calculations of processes occurring on geological time scales. This finding is of direct relevance for the safety assessment of radioactive waste disposal, since it may constrain the solubility and thus the mobility of Ra in such environments.

A method for simulating two-phase pipe flow with real equations of state

Common two-fluid models for pipe flow assume local non-equilibrium regarding phase transfer. To solve the two-fluid models together with accurate equations of state for real fluids will in most cases require mechanical, thermal and chemical equilibrium between the phases. The reason is that reference equations of state for real substances typically describe full thermodynamic equilibrium. In this paper, we present a method for numerically solving an equilibrium model analysed by Morin and Flåtten in the paper A two-fluid four-equation model with instantaneous thermodynamical equilibrium, 2013.The four-equation two-fluid model with instantaneous thermodynamical equilibrium is derived from a five-equation two-fluid model with instantaneous thermal equilibrium. The four-equation model has one mass equation common for both phases, but allows for separate phasic velocities. For comparison, the five-equation two-fluid model is numerically solved, using source terms to impose thermodynamical equilibrium. These source terms are solved using a fractional-step method.We employ the highly accurate Span–Wagner equation of state for CO2, and use the simple and robust FORCE scheme with MUSCL slope limiting. We demonstrate that second-order accuracy may be achieved for smooth solutions, whereas the first-order version of the scheme even allows for a robust transition to single-phase flow, also in the presence of instantaneous phase equilibrium.

The effect of energetic particle beams on the chromospheric emission of the 2004 July 25 flare

In this paper the role of particle beams in the generation of a close spatial and temporal correlation between hard X-ray (HXR) energy and Hα line emission bursts in the solar flare of 2004 July 25 is discussed. The light curves in the HXR emission and Hα line reveal that the pre-flare and main flare events are correlated with the variations of line-of-sight (LOS) magnetic flux. The HXR emission shows three main bursts during the main flare phase, which are accompanied by Hα intensity increases. The latter appear in 10 locations (kernels) at different times in succession; the kernel locations are associated with strong magnetic sources situated on the opposite side from the magnetic neutral line (MNL). The appearance of Hα kernels in the pre-flare event and those at the start of the main event ia correlated very closely (within a few seconds) with the HXR emission observed by the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) (HXR+Hα kernels), while the appearance of some others, not associated with HXR emission, was delayed by tens of seconds. Electron-beam parameters were derived from the RHESSI spectra in which the observed HXR photon flux was corrected for the self-induced electric field effect. Possible implications of this electric field on the production of transient magnetic fields observed during the flare are discussed. The Hα emission observed during the first burst was simulated in a hydrodynamic atmosphere for 5 levels plus a continuum hydrogen atom with the full non-local thermodynamic equilibrium (non-LTE) approach combining radiative, thermal and non-thermal excitation and ionization by an electron beam with the derived parameters. The simulated temporal profiles of Hα emission produced by non-thermal hydrogen excitation revealed a very good fit to the observed ones in the HXR+Hα kernels and 10–20 s delays in the other kernels. This allows us to speculate that Hα emission is caused mainly by electrons in the HXR+Hα kernels and mainly by protons in the others.