Thermodynamics Of Fluids Research Articles

Thermodynamics of Fluids in Disordered Porous Materials

Abstract When a fluid is adsorbed in micro or meso-porous materials such as aerogels or porous glasses, its thermodynamic behavior is considerably altered. The changes result from the combined effect of geometric confinement, randomness of the matrix, and connectivity of the pore network, whose understanding requires a good theoretical description of the matrix microstructure and its interaction with the fluid particles. We present a liquid-state formalism in which the fluid-matrix system is modeled as a ‘quenched-annealed’ binary mixture formed by the matrix particles (quenched species) and the fluid particles (annealed species); the averaging over quenched disorder is handled via the replica method. Model calculations for the phase diagram of the confined fluid within the mean spherical approximation show that for sufficiently attractive matrix-fluid interaction, the liquid-gas transition has a higher critical density than that of the bulk fluid and is accompanied by an additional “pre-condensation” transition. In addition, the results obtained within various standard approximation schemes suggest that the behavior of the fluid at its liquid-gas critical point is the same as that of the random field Ising model (RFIM).

Wertheim cluster development of free energy functionals for general nearest-neighbor interactions in D=1

We develop a particle cluster technique for representing the equilibrium thermodynamics of an inhomogeneous multispecies classical fluid in one dimension with nearest-neighbor interactions. The corresponding free energy functionals take on the general Wertheim association form and make contact with the Widom insertion argument. Application is made to adhesive rod mixtures, for which first-order thermodynamic perturbation theory is seen to be exact, and to more general interactions, such as the square well, in which activity is no longer a local functional of the density and explicit relations must be generated by recursion. For a fluid on a loop, auxiliary two-point feedback functions appear, which correct the simply connected form.

The generalized engineering Bernoulli equation (GEBE) and the first and second laws of thermodynamics for viscoelastic fluids

In this work we thoroughly explore the meanings of dissipation (sometimes referred to as viscous dissipation) and stress power. To do this we utilize the Cauchy momentum equations and the first and second laws of thermodynamics. First, the generalized engineering Bernoulli equation (GEBE) is derived from the Cauchy momentum equations and it is clearly shown to have nothing to do with a balance of energy. Next, the first law of thermodynamics or energy balance is discussed and a combined equation by subtracting the two is derived which we refer to as the mechanoenergy balance (sometimes referred to as the ‘‘equation of thermal energy’’). The fact that a difference exists further reinforces that the GEBE is not related to a balance of energy. Finally, the second law of thermodynamics is presented and the concept of dissipation introduced. An example is presented to demonstrate the utility of these equations which will hopefully eliminate some confusion in the literature.

Thermodynamics of coal-derived fluids. 3. VLE and heat capacities of coal liquid fractions

Thermodynamics of coal-derived fluids. 3. VLE and heat capacities of coal liquid fractions

Thermodynamics of fluids obtained by mapping the collision properties.

Thermodynamics of fluids obtained by mapping the collision properties.

Thermodynamics of coal-derived fluids. 3. VLE and heat capacities of coal liquid fractions

A previously developed thermodynamic model for vapour-liquid equilibrium (VLE) properties of coal-derived liquids has been successfully revised and extended to compute calorimetric properties of these liquids. The revised model, which is based on the modified UNIFAC correlation, predicts accurately the phase coexistence and calorimetric properties of low-temperature fractions (b.p. <600 K). However, like the previous model, the revised model fails at higher temperatures, in part because of the limitation of the UNIFAC activity coefficient correlation, which uses binary interaction parameters regressed from low-temperature VLE and enthalpy data. To improve the applicability of the model at higher temperatures, high-temperature VLE and liquid enthalpy data for coal model compounds are necessary. In agreement with previous results, the revised model shows that for low-boiling fractions, two distributions (phenolic and non-phenolic) are sufficient to represent the coal liquid reasonably well. However, for accurate representation of higher-boiling coal liquids, in addition to average molecular weight distribution and functional group constitution, experimental data on actual molecular types are necessary, providing information on the functional groups that contain heteroatoms and distribution of molecular types that include these functional groups.

Thermodynamics of fluids in random microporous materials from scaled particle theory

The thermodynamic properties of fluids confined to disordered porous solids are studied using a scaled particle theory approach. For simple hard sphere fluids in matrices of hard spheres, this method is of comparable accuracy to those previously introduced. In past studies of such systems, a strong thermodynamic similarity between the partly quenched and fully annealed cases has been evident; an exception to this behavior occurs when the diameters are nonadditive. For adsorbed polymeric molecules, on the other hand, the scaled particle theory introduced in this paper is the only route to the thermodynamics yet presented. The partition coefficients for polymers at infinite dilution in matrices of various porosities agree well with simulation over many orders of magnitude. For bulk polymers, the scaled polymer predictions are in much closer agreement with simulation than those of the traditional pressure and compressibility equations.

Comment on ‘‘Thermodynamics of fluids in quenched disordered matrices’’ [J. Chem. Phys. 100, 5172 (1994)

A recent contention by Rosinberg et al. [J. Chem. Phys. 100, 5172 (1994)] that the Replica Ornstein–Zernicke equations are limited to host matrices arising from a thermal quench is disputed. A clarification of the meaning of the required direct correlation functions of the matrix is provided.

On the thermodynamics of simple non-isentropic perfect fluids in general relativity

We examine the consistency of the thermodynamics of irrotational and non-isentropic perfect fluids complying with matter conservation by looking at the integrability conditions of the Gibbs--Duhem relation. We show that the latter is always integrable for fluids of the following types: (i) static, (ii) isentropic (admits a barotropic equation of state) and (iii) the source of a spacetime for which , where r is the dimension of the orbit of the isometry group. This consistency scheme is also tested in two large classes of known exact solutions for which r< 2, in general: perfect fluid Szekeres solutions (classes I and II). In none of these cases is the Gibbs--Duhem relation integrable, in general, though specific particular cases of Szekeres class II (all complying with r<2) are identified for which the integrability of this relation can be achieved. We show that Szekeres class I solutions satisfy the integrability conditions only in two trivial cases, namely the spherically symmetric limiting case and the Friedman--Robertson--Walker (FRW) cosmology. Explicit forms of the state variables and equations of state linking them are given and discussed in relation to the FRW limits of the solutions. We show that fixing free parameters in these solutions by a formal identification with FRW parameters leads, in all cases examined, to unphysical temperature evolution laws, quite unrelated to those of their FRW limiting cosmologies.

On the thermodynamics of fluids adsorbed in porous media

We develop thermodynamics for partly quenched systems, i.e., systems in which some of the particles are quenched, or frozen in place, and some of which are annealed, or allowed to equilibrate. In particular, we focus on a class of models for fluids adsorbed in microporous media, in which the quenched particles constitute a microporous matrix, while the annealed particles constitute a fluid adsorbed in that matrix. The replica method is used to relate the matrix-averaged quantities describing such a model to the thermodynamic quantities of a corresponding fully equilibrated model, called the replicated model. For these models, we present averaging methods that give the matrix-averaged thermodynamic quantities of the fluid. We show that there are two natural definitions for the average pressure and three natural definitions for the chemical potential of these systems. We provide both operational definitions and Mayer expansions of these quantities. We establish the Gibbs–Duhem relations for these quantities. We also present new exact relations that express the thermodynamic quantities of partly quenched media in terms of the correlation functions in such media. These include a set of compressibility relations and a virial relation.

On the thermodynamics of tilted and collisionless gases in Friedmann-Robertson-Walker spacetimes

Some features of the thermodynamics of tilted fluids, as witnessed by observers comoving with the fluid, are analysed. The Gibbs equation, expressed in terms of quantities measured by preferred observers comoving with the metric, is obtained and the role played by the entropy production discussed. The results of Bedran and Calvão are analysed from the the point of view of kinetic theory. We focus our attention on a collisionless gases model proposed by Ellis et al and show that for the latter is a conformal Killing vector in accordance with Bedran and Calvão.

Local thermodynamics of inhomogeneous fluids at equilibrium.

Extensive thermodynamic parameters of inhomogeneous fluids in thermal equilibrium are expressed as integrals of corresponding locally defined quantities. In particular, the distinction between the grand canonical potential and the integrated mechanical pressure is discussed in terms of scale invariance, and a similar analysis is made of the Helmholtz free energy.

Structure and thermodynamics for some small polar interaction-site fluids

Thermodynamic properties of a number of small polar interaction-site models have been estimated using Reference Interaction Site Model (RISM), with hypernetted chain (HNC) closure for structure calculations. These models include the statistical process control (SPC) and TIPS models for water as well as a new model proposed in this work. The estimated properties are compared with experimental structure data as well as experimentally measured thermodynamic data for real fluids. For water, both SPC and TIPS predict values of residual energy that are significantly below the experimental values. The estimated structures for these models are also phase shifted with respect to recent neutron data. Pair-correlation functions for the new model are in better agreement with experimental neutron data, as well with energy data. Canonical molecular dynamics simulations of the SPC model and the new model indicate that the estimated structure from these simulations for the SPC model is in closer agreement with neutron data than the new model. Residual energies from the TIPS model for methanol are also underpredicted from RISM and HNC closure. Recalculation of the TIPS parameters to corresponding Lennard—Jones parameters and the adoption of the hydrogen core from the new water model brings the estimated energies closer to the experimental values. New models for H 2S and methylchloride needs further refinement and additional evaluations against results from molecular simulations. Comparisons of results for the new models of water and methanol indicate that a dielectric correction to the RISM equation induces minor changes to the residual energies for these components. Numerical solutions to the structure of a model system consisting of water and methanol in the dielectrically corrected RISM version is also presented.

A monofluid flow mathematical model of liquid helium II based on extended non-equilibrium thermodynamics

The present work is a generalization of a previous analysis which aims at a single-fluid description of the macroscopic behaviour of helium II. A single-fluid model of helium II, with a wider range of temperatures and pressures than the one previously described, is formulated here using the extended thermodynamics of a non-ideal fluid in the absence of dissipation. The model here formulated includes, according to experimental data, the propagation of the two sounds typical of superfluid helium, a relationship between the stress deviator and the square of heat flux and an explanation of the fountain effect.

Thermodynamics of diagenetic fluid and fluid/mineral reactions in the Eogene Xingouzui Formation, oil Field T, Jianghan Basin

This study focuses on the thermodynamics of diagenetic fluid from the Eogene Xingouzui Formation which represents the most important reservoir in Field Oil T in the Jianghan Basin. The measured homogenization temperatures (110–139 °C) of fluid inclusions in diagenetic minerals fell within the range of 67 –155 °C at the middle diagenetic stage. The pressure of diagenetic fluid is estimated at 10.2 –56 MPa. The activity of ions in the fluid shows a tendency of Ca2+ > Mg2+ > Na+ > K+ > Fe3+ > Fe2+ for cations, and HCO 3 − > SO 4 2− > F− > Cl− > CO 3 2− for anions. For the gaseous facies, there is a tendency of CO2> CO> H2S> CH4> H2. According to the thermodynamic calculations, the pH and Eh of the fluid are 5.86–6.47 and −0.73–−0.64V, respectively. As a result of the interaction between such a diagenetic fluid and minerals in the sediments, feldspars were dissolved or alterated by other minerals. The clay mineral kaolinite was instable and hence was replaced by illite and chloritoid.

Thermodynamics of coal-derived fluids: 2. Vapour-liquid equilibria of coal liquid fractions

A thermodynamic model for prediction of vapour-liquid equilibria (VLE) in coal-derived fluids has been developed. The model uses group contribution methods for property evaluations and a continuous thermodynamics approach for VLE computations. A coal fluid is defined by multiple molecular weight distributions, and each distribution is represented by an average molecule with fixed relative proportions of different functional groups. Besides the hydrocarbon group, phenolic, pyridinic and thiophenic groups are used to represent O, N and S heteroatoms. From the results it is concluded that for low-boiling coal liquid fractions the phenolic compounds need to be treated separately, as opposed to the use of a single average molecule to define the coal liquid. Comparison with published data shows that the model is successful in predicting boiling ranges for low-boiling fractions. Failure of the model at higher temperatures is attributed to the binary interaction parameters in the UNIFAC model which are regressed from low-temperature binary VLE data.

Structure and thermodynamics of heteronuclear two-centre Lennard-Jones fluids from Monte Carlo simulation and a reference hypernetted chain equation

We have performed extensive Monte Carlo (MC) simulations to evaluate structural and thermodynamic properties of heteronuclear two-centre Lennard-Jones fluids. Computations have been carried out for two uncharged molecular models which roughly describe liquid HCl and HBr. These simulations are used as test benchmarks for a reference hypernetted chain approximation (RHNC-VM), which is the natural extension to heteronuclear fluids of a previously developed approach fairly successful in the context of homonuclear diatomic fluids. The proposed theoretical approach leads to results in good agreement with MC simulation.

Thermodynamics of fluids in quenched disordered matrices

Using the replica method, we derive the thermodynamic relations for a fluid in equilibrium with a quenched porous matrix. In particular, the appropriate Gibbs–Duhem equation is obtained as well as the equivalence between grand canonical and canonical ensembles. The exact compressiblity and virial equations are derived. Whereas the compressibility equation remains a direct and practical way to obtain the adsorption isotherm, the virial equation involves terms which do not relate easily to the properties of the fluid/matrix system. This explains the inconsistency between previous theoretical predictions and computer simulation results.

Minimization of dimension for functional differential equations and the thermodynamics of the classical one-dimensional fluid

The method of minimization of dimension for systems of first-order partial differential equations (PDEs) is extended analogously to systems of functional differential equations (FDEs). This method is applied to an exact first-order system of FDEs for the grand partition function of a one-dimensional classical fluid giving an alternative derivation of the pair potentials found by Baxter, for which exact thermodynamics can be obtained. These potentials satisfy a constant-coefficient ordinary differential equation (ODE). The method also gives the eigenvalue problem for the thermodynamics in these cases which is illustrated by deriving it explicitly for the simplest case, which is the exponential potential. The connection is derived between the finite system with external field to which the method applies and the infinite system without external field. This clarifies some points in Baxter's work and sheds some light on possible extensions of it.

Extended irreversible thermodynamics of liquid helium II.

In this work a macroscopic monofluid theory of liquid helium II, which is based on the extended irreversible thermodynamics, is formulated both in the presence and in the absence of dissipative phenomena. The work is a generalization of previous papers, where the extended thermodynamics of an ideal monoatomic fluid was applied to liquid helium II. It is shown that the behavior of helium II can be described by means of an extended thermodynamic theory where four fields, namely density, temperature, velocity, and heat flux are involved as independent fields. In the presence of dissipative phenomena, constitutive relations for the trace and the deviator of the nonequilibrium stress tensor are determined. In these relations, in addition to the normal viscous terms (which take into account the mechanical dissipation), terms proportional to the gradient of heat flux (which take into account the thermal dissipation) are present. The proposed theory is able to explain the propagation of the two sounds that are typical of helium II, and the attenuation calculated for such sounds is in agreement with the experimental results. Finally, the proposed theory is compared with the two-fluid model making apparent the analogies and the differences.