Virial Corrections Research Articles

Two-capillary viscometer for temperatures and pressures relevant to CO2 capture, transport, and storage—operation and improved analysis at high pressure

High-pressure viscosity measurements are crucial for understanding CO2 transport and storage because CO2 is often transported as a supercritical fluid, at a high pressure and temperature above its critical point. In this study, we extended the operational range of our new two-capillary viscometer to handle pressures up to 20 MPa, focusing on the behaviour of CO2 at temperatures around 300 K. The analysis model is based on the low-pressure principle, which relied on virial descriptions of density and viscosity, proved inadequate under these conditions. Therefore, we introduced a modified hydrodynamic model as a function of density that is suitable for viscosity measurements at high pressure and liquid states. The modified model bypasses the need for a density virial correction. We conducted initial viscosity tests on pure CO2 at five isotherms: 280.01 K, 298.15 K, 300.01 K, 323.15 K, and 348.15 K to validate the performance of the new two capillary viscometer and the modified model at high pressures. The experimental viscosities agreed with the model predictions and comparable within the estimated uncertainty of the data. In addition, we thoroughly explained the calibrations and the analysis of uncertainty estimation. The uncertainty analysis showed a maximum extended combined uncertainty of 1.3% (k = 2) within all thermodynamic states—gas, liquid, and close to the critical region.

Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

Fluctuation aspects of isotope theory - III. Isotopic phase similarity in the set of deuterated methanes CHxD4-x

We have proposed the new principle of isotopic phase similarity (IPS) in the previous works I, II, of this series. The fundamental Born-Oppenheimer approximation maintains separately its applicability within each isotopic phase. The fluctuation-thermodynamic formalism is based on the developed earlier predictive model of CVL (congruent vapor-liquid) – diagram. It changes the mean-field concept of the macroscopic VLE (vapor-liquid equilibrium) – diagram to describe adequately the mesoscopic scale of volumes and time-intervals for a fluid state. The well-established by CVL-diagram fluctuation boundaries of the boil- Pb(T)- and dew-Pd(T)-pressures are important ones. They form the essential mesoscopic expansion of the single Pv(T)- vapor-pressure curve postulated by VLE- diagram. This mesoscopic peculiarity of a non-mean-field phase transition was revealed earlier for any one-component fluids. It provides the new insight into the classic theory of isotope effects. In the first instance the conventional interpretation of the vapor-pressure isotope effect (VPIE) and the molar-volume isotope effect needs an independent consideration by the comparison of CVL-diagrams for isotopes. In two previous works I, II we have introduced the undimensional fluctuation calibration complex Zoc=P0M/(RT0ρc) (P0=101.325kPa, T0=1K, M g/mol – molar mass of isotope, ρc - its critical density of mass) which provides the separation of VPIEs for the variety of isotopic families on two main types: (n) normal (Zocn<1) and (i) inverse (Zoci>1) at low temperatures. In this work III we have applied the same IPS-methodology to the set of partially deuterated methanes CHxD4-x of i-type. The set of exclusively n-type pairs {H2O/D2O/T2O; 36Ar/40Ar; 235U/238U} was considered in works I, II. The reasonable predictive capability of IPS-principle determines systematic shifts in the critical parameters of heavier isotopes if only those for the basic lighter isotope (CH4) are known. The most impressive confirmation of IPS-principle is the reasonable concordance of its dew-pressure isotope effect (DPIE)-predictions with the experimental absolute differences between small vapor pressures of isotopes ΔPv=Pv′−Pv. We have proposed and corroborated the concept of two coupled crossover Bancroft'sTbB and Clapeyron'sTlgC-points. They offer the study of the difference between the vaporization enthalpies of isotopes without virial correction for non-ideality of v-phase.

Coherence-decoherence transition in a spin-magnetoexcitonic ensemble in a quantum Hall system

The recent experimental studies of extremely long-lived macroscopic ensembles of spin-cyclotron excitons (magnetoexcitons) which have to obey the Bose-Einstein statistics signal the emergence of an excitonic coherent phase. In the present paper the theory of a weakly interacting Bose gas of spin-cyclotron excitations is developed in terms of a virial correction to the single-magnetoexciton energy. The condition for coherent-incoherent phase transition is discussed. It is expected to be strongly related to the studied long-distance interexcitonic correlations. The results obtained theoretically are discussed in terms of their agreement with specific experimental data.

Optical absorption by incoherent and coherent ensembles of spin excitations in an unpolarised quantum Hall system

In connection with recent studies of extremely long-living spin-cyclotron excitations that are actually magnetoexcitons in the quantum Hall electron gas, we discuss the contribution to light absorption related to the presence of a magnetoexcitonic ensemble in this purely electronic system. The distribution of magnetoexcitons in an ‘incoherent’ phase, as well as absorption of light, is determined by a smooth random potential inevitably present in a quantum well. Since weakly interacting excitations have to obey the Bose–Einstein statistics, one may expect the appearance of a coherent phase where all magnetoexcitons are in the same state. The absorption of light is still determined by disorder in the system, but it turns out to be about an order of magnitude higher. A comparative analysis is made of both incoherent and coherent cases. The condition for coherent–incoherent phase transition is discussed. It is expected to be strongly related to long-distance inter-excitonic correlations. The latter are accounted in terms of virial correction (i.e. depending on magnetoexciton concentration) for the single magnetoexciton energy found within the approximation of a slightly non-ideal gas.

The Virial Effect—Applications for SF6 and CH4 Thermal Plasmas

A tool based on the mass action law was developed to calculate plasma compositions and thermodynamic properties for pure gases and mixtures, assuming a local thermodynamic equilibrium for pressures of up to 300 bar. The collection of the data that was necessary for tool calculation was automated by another tool that was written using Python, and the formats for the model were adapted directly from the NIST and JANAF websites. In order to calculate the plasma compositions for high pressures, virial correction was introduced. The influences of the parameters that were chosen to calculate the Lennard–Jones (12-6) potential were studied. The results at high pressure show the importance of virial correction for low temperatures and the dependence of the dataset used. Experimental data are necessary to determine a good dataset, and to obtain interaction potential. However, the data available in the literature were not always provided, so they are not well-adapted to a large pressure range. Due to this lack, the formulation provided by L. I. Stiel and G. Thodos (Journal of Chemical and Engineering Data, vol. 7, 1962, p. 234–236) is a good alternative when the considered pressure is not close to the critical point. The results may depend strongly on the system studied: examples using SF6 and CH4 plasma compositions are given at high pressure.

Virial Approximation for Load and Loss in High-Speed Journal Bearings Using Pressurized Gases

We consider steady, laminar, compressible lubrication flows in a high-speed two-dimensional journal bearing governed by the appropriate Reynolds equation. The thermodynamic states correspond to pressurized gases and are in the single-phase regime. Simple explicit formulas for the load capacity, power loss, and attitude angle are derived by applying the virial (or small density) expansions of pressure and shear viscosity to results developed in previous studies. The present virial approximation was compared to the exact numerical solutions to the Reynolds equation. It was shown that the results based on our virial expansions are quite accurate at thermodynamic states corresponding to dense and supercritical gases. The first virial correction is seen to significantly improve predictions based on the ideal gas theory.

Characteristics of Interatomic and the Ion—Atom Interaction in Gases during the Dissociation Process

We consider the problem of the choice of “free” particle interaction potential and the calculation of virial corrections for interatomic and ion–atom interaction in chemical models with dissociation reactions. We perform a critical analysis of the potentials given in the available literature, propose simple formulas to calculate virial corrections with allowance for the limitations of the two-particle phase space, and present recommendations to apply these formulas.

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

The virial corrections to short-time self- and collective diffusion coefficients as well as the effective viscosity are calculated for suspensions of hard spheres with the same radii and constant (blocked within the particle) magnetization modelled by a point dipole. Analytic, integral formulae derived from basic principles of statistical mechanics are provided for both cases – in the absence and in the presence of an external magnetic field. In the former case the diffusion and viscosity coefficients are evaluated numerically as a function of the strength of magnetic interactions between the particles and it is reported that the translational collective diffusion coefficient is significantly greater than all the other coefficients. In the presence of an external magnetic field the coefficients become anisotropic and are evaluated in the asymptotic regime of weak interparticle magnetic interactions.

Connectivity percolation in suspensions of attractive square-well spherocylinders.

We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. In the 1980s the percolation threshold of slender fibers has been predicted to scale as the fibers' inverse aspect ratio [Phys. Rev. B 30, 3933 (1984)PRBMDO1098-012110.1103/PhysRevB.30.3933]. The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.

The consideration of virial corrections in the diffusion equations

The diffusion phenomenon is known to be a universal physical process and the basis of many industrial technologies for advanced materials. Abnormalities of diffusion have been observed which cannot be described by existing theory. The diffusion of atoms of the introduction (boron) possessing great energy of dissolution, results in significant deformation of the crystal lattice of iron in the radius of the first coordination spheres. Mayer's approach to the solution of the problem of getting diffusion equation with viral corrections, indicating the account of interparticle interaction in thise systems, has been offered in this work. In the ongoing project the model of diffusion of boron impurities, strongly interacting with the lattice has been described. Further directions in the solution of this problem have been suggested. To explain the anomalies observed in the diffusion mechanism of implementation a comparison of theoretical calculations has been attempted, in particular, in the system iron-boron.

An ion-molecular chemical model of dense aluminum vapor plasma

A chemical model of nonideal gas-plasma mixture is proposed to describe a dense plasma of aluminum vapors. The molecules and the molecular ions are taken into consideration in addition to the conventionaly utilized set of electrons, ions and atoms to advance to low temperatures; doubly and triply ionized ions are considered for the high-temperature region. The effects of density are taken into account in a virial approximation. The virial corrections for the charge-charge and the charge-atom interactions are critically analyzed and chosen. The caloric and thermal equation of state, as well as the plasma composition have been obtained. It has been shown that an important role play molecules and molecular ions of aluminum especially in the early stage of heating of metal vapors. A satisfactory agreement with experimental results is obtained in the range of applicability of the model.

Virial Excess Mixing Coefficient Corrections for the Adsorbed Solution Theory

The virial excess mixing coefficient (VEMC) model is proposed to describe multicomponent adsorption equilibria for nonideal systems. It expresses a nonideal adsorbed mixture by an ideal adsorbed solution with VEMC corrections. It reduces to the ideal adsorbed solution theory (IAST) when depicting an ideal adsorbed mixture. The model is thermodynamically sound and accurate in describing systems. Adsorbed-phase activity coefficients can be evaluated with the model. The VEMC model is used to investigate binary and ternary adsorption of hydrogen sulfide, carbon dioxide, and propane on H-mordenite and binary adsorption of n-hexane and water on BPL activated carbon.

Transferability of group energies and satisfaction of the virial theorem

The theory of atoms in molecules equates the energy of a group to the negative of its electronic kinetic energy, using the atomic statement of the virial theorem. In general, a correction must be applied because of the failure of the wave function to satisfy the virial theorem. This Letter examines the transferability of group energies using self-consistently scaled wave functions that satisfy the virial theorem at both single determinant and correlated levels of theory to demonstrate that apparent deviations in the transferability of the group energies found in certain homologous systems, is an artefact arising from the variation in the virial correction factor.

Transferability of energies of atoms in organic molecules

The variation of virial-corrected energies of atoms in organic molecules (AIMs) with the lengths of the attached alkyl chains and the nature of remote substituents is shown to be largely an artifact of the correction procedure itself. Thus, it is demonstrated that the virial correction for energies of AIMs should be avoided despite the fact that it produces values that sum up to the total molecular energies. Consequently, the assessment of transferability of AIMs should be carried out with either uncorrected total energies (i.e., negative kinetic energies) or atomic properties other than energy.

NONLOCAL KINETIC THEORY

The short time behavior of a disturbed system is influenced by off-shell motion and characterized by the reduced density matrix possessing high energetic tails. After this short time regime the time evolution is controlled by small gradients. This leads to a nonlocal Boltzmann equation for the quasiparticle distribution and a functional relating the latter one to the reduced density matrix. The nonlocalities are presented as time and space shifts arising from gradient expansion and are leading to virial corrections in the thermodynamical limit.

Nonlocal kinetic theory. II. Transport and virial corrections

After the short time regime the time evolution is controlled by small gradients. This leads to a nonlocal Boltzmann equation for the quasiparticle distribution and a functional relating the latter one to the reduced density matrix. The nonlocalities are presented as time and space shifts arising from gradient expansion and are leading to virial corrections in equilibrium.

Virial Corrections to Simulations of Heavy Ion Reactions

Within QMD simulations we demonstrate the effect of virial corrections on heavy ion reactions. Unlike in standard codes, the binary collisions are treated as non-local so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values. Complementary BUU simulations reveal that the non-locality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced pre-equilibrium emission of particles.

Transport theory with non-local corrections

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and non-instant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections and are proven to be consistent with the conservation laws.

A Quantum Kinetic Equation for Fermi Systems Including Three-Body Correlations

A single-time quantum transport equation, which includes effects beyond the quasiparticle approximation, is derived for Fermi systems in the framework of nonequilibrium real-time Green's functions theory. Ternary correlations are incorporated in the kinetic description via a cluster expansion for the self-energies (e.g., the transport vertex and the width) truncated at the level of three-body scattering amplitudes. A finite temperature/density formulation of the three-body problem is given. Corresponding three-body equations reduce to the well-known Faddeev equations in the vacuum limit. In equilibrium the equation of state contains virial corrections proportional to the third quantum virial coefficient.