Full Chemical Equilibrium Research Articles

Origin of Li brine-type deposits in the Cretaceous gypsum-bearing formation of the Jitai Basin, South China: Constraints from geochemistry and H, O, Li, B, and Sr isotopes

Li brine-type deposits have recently been discovered in the Upper Cretaceous gypsum-bearing formation of the Jitai Basin, South China. The source and enrichment mechanism of Li in brines, however, are still unclear. To define the origin of lithium and evaluate the water-rock interaction process, this work presents chemical and multi-isotope data for Li-rich brines from the Jitai Basin. Seven brine samples collected from Meigang boreholes contain high salinities of 190–339 g/L, lithium concentrations of 60.6–106.0 mg/L, and low magnesium/lithium ratios of ∼11. The good correlation between δD and δ18O values suggests that the primary brine has been diluted by meteoric water, while contributions from halite dissolution or secondary brines having dissolved solid halite are also indicated by the high Na/Cl (0.58–0.63) and Cl/Br (average of ∼26987) mass ratios, the Na deficit and Ca excess, and the fact that high-salinity brines have lower δD, δ18O and δ34SSO4 values. Among the chemical geothermometers commonly used in the literature, only the SiO2-chalcedony, Na/K/Ca and K/Mg thermometric relationships give concordant temperature values of 120 ± 15 °C for the deep reservoir of these brines, suggesting that the latter are not in full chemical equilibrium with the reservoir rocks (excess of sodium due to halite dissolution), but this temperature can be considered as representative of their deep reservoir. Moreover, most of the chemical geothermometers yield close temperature values of 115 ± 15 °C for the deep reservoir of three neighboring dilute thermal waters. The homogeneous 87Sr/86Sr ratios (0.713865–0.713915) and δ11B (+1.8‰–+3.4‰) and δ7Li (+13.1‰–+14.2‰) values show a close affinity to the continental crust, possibly implying a fluid signature involving the interactions between clastic host rocks and brines. X-ray diffraction and scanning electron microscopy analyses and Li contents of reservoir rocks reveal the presence of dominant lithian muscovites of clastic origin, probably originating from weathering of Li-enriched igneous rocks, which contribute to most of the lithium input in the hydrologic system of the basin. Thus, it is proposed that lithium enrichment in brines from the Upper Cretaceous gypsum-bearing clastic aquifers of the Jitai Basin was generated by water-rock interactions involving lithian muscovites.

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.

Analysis of the back-to-back correlation function of kaonsat different evolution temperatures

In the high temperature and high density in-medium system formed by high energy heavy ion collisions, the interaction between particles and the medium system can be squeezed into quasi-particles by the Bogoliubov transformation. The mass of quasi-particles is different from the mass of free particles received by the detector, thus producing the back-to-back correlation between two particles. In this paper, the effective mass of quasi-particle model is used as a variable to analyze the back-to-back correlation function of the kaons. With the expansion and evolution of the high temperature and high density in-medium system, it has to undergo four different stages of temperature of the quark-gluon plasma phase transition, full chemical equilibrium, partial chemical equilibrium, thermal equilibrium. Analysis of the back-to-back correlation function of kaons was based on four different temperature values given theoretically and experimentally. The results show that the partial chemical equilibrium model marked by the frozen-out temperature T pch =140 MeV is an ideal particle frozen-out model for calculating large momentum meson correlation.

Thermal model description of p\u2013Pb collisions at sqrt{s_{NN}} = 5.02\xa0TeV

The ALICE data on light flavor hadron production obtained in p–Pb collisions at sqrt{s_{NN}} = 5.02 TeV are studied in the thermal model using the canonical approach with exact strangeness conservation. The chemical freeze-out temperature is independent of centrality except for the lowest multiplicity bin, with values close to 160 MeV but consistent with those obtained in Pb–Pb collisions at sqrt{s_{NN}} = 2.76 TeV. The value of the strangeness non-equilibrium factor gamma _s is slowly increasing with multiplicity from 0.9 to 0.96, i.e. it is always very close to full chemical equilibrium.

(3+1)D Quasiparticle Anisotropic Hydrodynamics for Ultrarelativistic Heavy-Ion Collisions.

We present the first comparisons of experimental data with phenomenological results from (3+1)D quasiparticle anisotropic hydrodynamics (aHydroQP). We compare particle spectra, average transverse momentum, and elliptic flow. The dynamical equations used for the hydrodynamic stage utilize aHydroQP, which naturally includes both shear and bulk viscous effects. The (3+1)D aHydroQP evolution obtained is self-consistently converted to hadrons using anisotropic Cooper-Frye freeze-out. Hadron production and decays are modeled using a customized version of therminator 2. In this first study, we utilized smooth Glauber-type initial conditions and a single effective freeze-out temperature T_{FO}=130 MeV with all hadronic species in full chemical equilibrium. With this rather simple setup, we find a very good description of many heavy-ion observables.

Surprisingly large uncertainties in temperature extraction from thermal fits to hadron yield data at LHC

The conventional hadron-resonance gas (HRG) model with the Particle Data Group hadron input, full chemical equilibrium, and the hadron-type dependent eigenvolume interactions, is employed to fit the hadron midrapidity yield data of the ALICE collaboration for the most central Pb+Pb collisions. For the case of point-like hadrons, the well-known fit result is reproduced. However, the situation changes if the hadrons have different eigenvolumes. In the case when all the mesons are point-like while all the baryons have an effective hardcore radius of 0.3 fm, the temperature dependence of has a broad minimum in the temperature range of 155−210 MeV, with a fit quality comparable to the minimum in the point-particle case. A very similar result is obtained when only baryon–baryon eigenvolume interactions are considered, with the eigenvolume parameter taken from the previous fit to the ground state of nuclear matter. Finally, when we apply the eigenvolume corrections with a mass-proportional eigenvolume , fixed to a particular hardcore proton radius rp, we observe a second minimum in the temperature dependence of , located at significantly higher temperatures. For instance, at rp = 0.5 fm, the fit quality is better than in the point-particle HRG case in a very wide temperature range of 170−320 MeV, which creates uncertainty in the temperature determination from the fit to the data of 150 MeV. These results show that thermal fits to the heavy-ion hadron yield data are very sensitive to the modeling of the short-range repulsion eigenvolume between hadrons, and that the chemical freeze-out temperature can only be extracted from the LHC hadron yield data with sizable uncertainty.

Strangeness production in AA and pp collisions

Boost-invariant hadron production in high energy collisions occurs in causally disconnected regions of finite space-time size. As a result, globally conserved quantum numbers (charge, strangeness, baryon number) are conserved locally in spatially restricted correlation clusters. Their size is determined by two time scales: the equilibration time specifying the formation of a quark-gluon plasma, and the hadronization time, specifying the onset of confinement. The expected values for these scales provide the theoretical basis for the suppression observed for strangeness production in elementary interactions ($pp$, $e^+e^-$) below LHC energies. In contrast, the space-time superposition of individual collisions in high energy heavy ion interactions leads to higher energy densities, resulting in much later hadronization and hence much larger hadronization volumes. This largely removes the causality constraints and results in an ideal hadronic resonance gas in full chemical equilibrium. In the present paper, we determine the collision energies needed for that; we also estimate when $pp$ collisions reach comparable hadronization volumes and thus determine when strangeness suppression should disappear there as well.

A two-fluid four-equation model with instantaneous thermodynamical equilibrium

We consider an equilibrium version of a common two-fluid model for pipe flow, containing one mixture mass equation and one mixture energy equation. This model can be derived from a five-equation model with instantaneous thermal equilibrium, to which additional phase relaxation terms are added. An original contribution of this paper is a quasilinear formulation of the instantaneous phase relaxation limit. From this, the mixture sound speed intrinsic to the model can be extracted. This allows us to directly prove some subcharacteristic conditions with respect to a previously established model hierarchy of different relaxation processes. These subcharacteristic conditions reveal the fundamental insight of this paper; in the hierarchy, thermodynamic versus velocity relaxation both reduce the mixture sound velocity with a factor that is independent of whether the other type of relaxation has been performed.

Evolution of transverse flow and effective temperatures in the parton phase from a multiphase transport model

I study the space-time evolution of transverse flow and effective temperatures in the dense parton phase with the string melting version of a multi-phase transport model. Parameters of the model are first constrained to reproduce the bulk data on the rapidity density, $p_{\rm T}$ spectrum and elliptic flow at low $p_{\rm T}$ for central and mid-central Au+Au collisions at $200A$ GeV and Pb+Pb collisions at $2760A$ GeV. I then calculate the transverse flow and effective temperatures in volume cells within mid-spacetime-rapidity $|\eta|<1/2$. I find that the effective temperatures extracted from different variables, which are all evaluated in the rest frame of a volume cell, can be very different; this indicates that the parton system in the model is not in full chemical or thermal equilibrium locally, even after averaging over many events. In particular, the effective temperatures extracted from the parton energy density or number density are often quite different than those extracted from the parton mean $p_{\rm T}$ or mean energy. For these collisions in general, effective temperatures extracted from the parton energy density or number density are higher than those extracted from the parton mean $p_{\rm T}$ in the inner part of the overlap volume, while the opposite occurs in the outer part of the overlap volume. I argue that this indicates that the dense parton matter in the inner part of the overlap volume is over-populated; I also find that all cells with energy density above 1 GeV/fm$^3$ are over-populated after a couple of fm/$c$.

Shear viscosity in a perturbative quark–gluon plasma

Among the key features of hot and dense QCD matter produced in ultra-relativistic heavy-ion collisions at RHIC is its very low shear viscosity, indicative of the properties of a near-ideal fluid, and a large opacity demonstrated by jet energy loss measurements. In this work, we utilize a microscopic transport model based on the Boltzmann equation with quark and gluon degrees of freedom and cross sections calculated from perturbative quantum chromodynamics to simulate an ideal quark–gluon plasma in full thermal and chemical equilibrium. We then use the Kubo formalism to calculate the shear viscosity to entropy-density ratio of the medium as a function of temperature and system composition. One of our key results is that the shear viscosity over entropy-density ratio η/s becomes invariant to the chemical composition of the system when plotted as a function of energy-density instead of temperature.

Centrality dependence of strangeness production in heavy-ion collisions as a geometrical effect of core–corona superposition

It is shown that data on strange particle production as a function of centrality in Au–Au collisions at sNN=200 GeV can be explained with a superposition of emission from a hadron gas at full chemical equilibrium (core) and from nucleon–nucleon collisions at the boundary (corona) of the overlapping region of the two colliding nuclei. This model nicely accounts for the enhancement of ϕ meson and strange particle production as a function of centrality observed in relativistic heavy ion collisions at that energy. The enhancement is mainly a geometrical effect, that is the increasing weight of the core with respect to corona for higher centrality, while strangeness canonical suppression in the core seems to play a role only in very peripheral collisions. This model, if confirmed at lower energy, would settle the long-standing problem of strangeness under-saturation in relativistic heavy ion collisions, parametrized by γS. Furthermore, it would give a unique tool to locate the onset of deconfinement in nuclear collisions both as a function of energy and centrality if this is to be associated to the onset of the formation of a fully equilibrated core.

Simulating Equilibrium Surface Forces in Polymer Solutions Using a Canonical Grid Method

A new simulation method for nonuniform polymer solutions between planar surfaces at full chemical equilibrium is described. The technique uses a grid of points in a two-dimensional thermodynamic space, labeled by surface area and surface separations. Free energy differences between these points are determined via Bennett's optimized rates method in the canonical ensemble. Subsequently, loci of constant chemical potential are determined within the grid via simple numerical interpolation. In this way, a series of free energy versus separation curves are determined for a number of different chemical potentials. The method is applied to the case of hard sphere polymers between attractive surfaces, and its veracity is confirmed via comparisons with established alternative simulation techniques, namely, the grand canonical ensemble and isotension ensemble methods. The former method is shown to fail when the degree of polymerization is too large. An interesting interplay between repulsive steric interactions and attractive bridging forces occurs as the surface attraction and bulk monomer density are varied. This behavior is further explored using polymer density functional theory, which is shown to be in good agreement with the simulations. Our results are also discussed in light of recent self-consistent field calculations which correct the original deGennes results for infinitely long polymers. In particular, we look at the role of chain ends by investigating the behavior of ring polymers.

A new approach to construct dynamic models for NOx control in a FGR furnace

This paper presents a new approach to construct dynamic models for NOx control of an industrial furnace with flue gas recirculation (FGR). In this paper, the full‐scale computational fluid dynamics (CFD) simulations are carried out for the FGR furnace and the CFD results are used to construct the transfer functions to represent the linearized dynamic models of the furnace. The controllers are then designed based on these models. Finally, the results obtained from full‐scale CFD simulation are used to validate the dynamic models. It is indicated that the dynamic models obtained by the new approach are capable of capturing the dynamic characteristics of the combustion system. The numerical simulation of the turbulent non‐premixed combustion process in the furnace is conducted using a moment closure method with the assumed – probability density function (PDF) for the mixture fraction. The combustion model is derived based on the assumption of instantaneous full chemical equilibrium. The discrete transfer radiation model is chosen as the radiation heat transfer model, and the weighted‐sum‐of‐gray‐gases model is used to calculate the absorption coefficient.

Persistencia de errores conceptuales en el estudio del equilibrio químico

This paper exposes the existence of certain conceptual errors in the study of chemical equilibrium, lack of differentiation between full chemical reaction and equilibrium compartimentation of equilibrium,.., and, in particular, the strong persistance of the error of mass -concentration oí substances. For it, examples were taken from two different groups: Pre -University course students and teachers students.

Abundance of cosmological relics in low-temperature scenarios

We investigate the relic density ${n}_{\ensuremath{\chi}}$ of nonrelativistic long-lived or stable particles $\ensuremath{\chi}$ in cosmological scenarios in which the temperature $T$ is too low for $\ensuremath{\chi}$ to achieve full chemical equilibrium. The case with a heavier particle decaying into $\ensuremath{\chi}$ is also investigated. We derive approximate solutions for ${n}_{\ensuremath{\chi}}(T)$ which accurately reproduce numerical results when full thermal equilibrium is not achieved. If full equilibrium is reached, our ansatz no longer reproduces the correct temperature dependence of the $\ensuremath{\chi}$ number density. However, it does give the correct final relic density, to an accuracy of about 3% or better, for all cross sections and initial temperatures.

Sensitivity Analysis of a FGR Industrial Furnace for NOx Emission Using Frequency Domain Method

Preliminary study has shown that the flue gas recirculation (FGR) is one of the effective ways to reduce the nitric oxides (NOx) emission in industrial furnaces. The sensitivity of the NOx emission from a FGR industrial furnace to the change in three major furnace input variables—inlet combustion air mass flow rate, inlet combustion air temperature, and pressure head of the FGR fan—is investigated numerically in this study. The investigation is carried out in frequency domain by superimposing sinusoidal signals of different frequencies on to the furnace control inputs around the design operating condition, and observing the frequency responses. The results obtained in this study can be used in the design of active combustion control systems to reduce NOx emission. The numerical simulation of the turbulent non-premixed combustion process in the furnace is conducted using a moment closure method with the assumed β probability density function for the mixture fraction. The combustion model is derived based on the assumption of instantaneous full chemical equilibrium. The discrete transfer radiation model is chosen as the radiation heat transfer model, and the weighted-sum-of-gray-gases model is used to calculate the absorption coefficient.

SHARE: Statistical hadronization with resonances

SHARE: Statistical hadronization with resonances

Reduction of NOx in a Regenerative Industrial Furnace With the Addition of Methanol in the Fuel

The analysis of the combustion process and NOx emission in a gas-fired regenerative industrial furnace has been carried out numerically. The effect of the additive, methanol CH3OH, to the fuel on the NOx emission is studied. A moment closure method with the assumed β Probability Density Function (PDF) for the mixture fraction is used to model the turbulent non-premixed combustion process in the furnace. The combustion model is based on the assumption of instantaneous full chemical equilibrium. The P-1 model is chosen as the radiation model, and the Weighted-Sum-of-Gray-Gases Model is used to calculate the absorption coefficient. The numerical results showed that the use of CH3OH is effective in the reduction of NOx in a regenerative industrial furnace. The mechanism of NOx reduction by the use of CH3OH is also discussed.

Source conditions and degradation processes of light hydrocarbons in volcanic gases: an example from El Chichón volcano (Chiapas State, Mexico)

Since the 1982 plinian eruption, El Chichón volcano (Chiapas State, Mexico) has exhibited intense hydrothermal activity. Fumaroles, bubbling gases, hot springs, and acid water pools discharge at both the crater floor and the volcano flanks. Sixteen different hydrocarbon species were identified in fumaroles and bubbling gases , including alkanes, alkenes, and aromatic hydrocarbons. Among the possible reactions, dehydrogenation involving light alkenes and alkanes pairs (C 2 up to linear C 4) approaches metastable equilibria when redox state is controlled by the rock mineral assemblage. Reequilibration conditions of the C 3 and n-C 4 alkanes with their unsaturated counterparts appear to be established at temperature and redox conditions, similar to those of CH 4/CO 2 pair. Conversely, C 2 and branched C 4 alkene/alkane ratios, although controlled by a similar rock redox buffer system, appear to reflect equilibrium at different temperature and/or redox conditions, probably due to the slow kinetics of the reactions involved. Therefore, a full chemical equilibrium simultaneously involving CH 4 and heavier hydrocarbons is not attained. Thermodynamic evaluation indicates that cracking reactions involving the CC bond breakage do not achieve a thermodynamic equilibrium. However, their relative distribution appears to be consistent with a thermal—rather than a biological—origin. Catalytic processes are also invoked in the production of benzene, whose distribution appears to be related to the measured H 2 concentration, other than to possible nonoxidative and oxidative conversion of methane.

Chemical equilibrium study in nucleus-nucleus collisions at relativistic energies

We present a detailed study of chemical freeze-out in nucleus-nucleus collisions at beam energies of $11.6A$, $30A$, $40A$, $80A$, and $158A\phantom{\rule{0.3em}{0ex}}\text{GeV}$. By analyzing hadronic multiplicities within the statistical hadronization approach, we have studied the strangeness production as a function of center-of-mass energy and of the parameters of the source. We have tested and compared different versions of the statistical model, with special emphasis on possible explanations of the observed strangeness hadronic phase space undersaturation. We show that, in this energy range, the use of hadron yields at midrapidity instead of in full phase space artificially enhances strangeness production and could lead to incorrect conclusions as far as the occurrence of full chemical equilibrium is concerned. In addition to the basic model with an extra strange quark nonequilibrium parameter, we have tested three more schemes: a two-component model superimposing hadrons coming out of single nucleon-nucleon interactions to those emerging from large fireballs at equilibrium, a model with local strangeness neutrality and a model with strange and light quark nonequilibrium parameters. The behavior of the source parameters as a function of colliding system and collision energy is studied. The description of strangeness production entails a nonmonotonic energy dependence of strangeness saturation parameter ${\ensuremath{\gamma}}_{S}$ with a maximum around $30A\phantom{\rule{0.3em}{0ex}}\text{GeV}$. We also present predictions of the production rates of still unmeasured hadrons including the newly discovered ${\ensuremath{\Theta}}^{+}(1540)$ pentaquark baryon.