Showing papers on "Non-equilibrium thermodynamics published in 1985"

Validity of the local equilibrium assumption for modeling sorbing solute transport through homogeneous soils

Abstract: Sorption processes that occur during reactive solute movement through porous media can be modeled using either an equilibrium or kinetic approach. Because of the resulting conceptual and mathematical simplification, many transport models assume local chemical equilibrium is valid for describing sorption reactions. This paper presents quantitative criteria to assess the validity of the local equilibrium assumption for one-dimensional, steady flow through homogeneous soils. A method is described whereby formulas for solute breakthrough curve time moments can be determined without knowledge of the nalytical solution to the mass transport model. This method is applied to several commonly used nonequilibrium formulations as well as the standard linear equilibrium model. The formulations considered include both the physical nonequilibrium models where the sorption rate is controlled by diffusive solute transfer between mobile and stagnant fluid zones and the chemical nonequilibrium models where the overall sorption rate is governed by the rate of reaction at the soil-solution interfaces. Criteria for local equilibrium to be valid are derived by comparing the time moment formulas for the nonequilibrium and equilibrium models. These criteria explicitly show that basic system parameters (e.g., seepage velocity, dispersion coefficient, distribution coefficient, sorption rate, boundary conditions) have a significant influence on the attainment of local equilibrium.

Stoichiometry and Thermodynamics of Metallurgical Processes

Abstract: Preface 1. Introduction 2. Stoichiometry: material balances in metallurgical processes 3. First law of thermodynamics 4. Fuels and combustion 5. Energy balances 6. Second law of thermodynamics 7. Auxiliary functions 8. Theory of solutions I 9. The Gibbs free-energy changes and the equilibrium constant 10. Phase equilibria 1. Equilibria in complex systems 12. Theory of solutions II Appendices Answers to problems Nomenclature Index.

Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems

Abstract: The weak-noise limit of Fokker-Planck models is studied for the case where the steady-state probability density in that limit cannot be represented by a continuously differentiable nonequilibrium potential. In a previous paper [J. Stat. Phys. 35, 729 (1984)], we have shown that this corresponds to the general case in systems outside thermodynamic equilibrium. By using an extremum principle, the nondifferentiable potential is constructed, which generalizes the differentiable case. The relation of approximate differentiable potentials to the exact nondifferentiable potential is considered and discussed for two examples with attracting limit cycles, a periodically forced nonlinear oscillator, and two phase-coupled nonlinear oscillators. The relevance of nondifferentiable potentials for non- equilibrium thermodynamics is pointed out.

Nonequilibrium statistical thermodynamics

Abstract: Preface Nonequilibrium Thermodynamics Brownian Motion Theory Stochastic Foundations of Nonequilibrium Thermodynamics Onsager-Machlup Theory The Kinetic Analog of Boltzmann's Principle Stochastic H Theorem The Thermodynamic Limit Index

The theory of thermodynamics

Abstract: Preface 1. Introduction: thermodynamic systems seen from outside 2. The statistical foundations 3. Temperature 4. Entropy 5. Elementary theory of the ideal monatomic gas 6. The basic principles of classical thermodynamics 7. Energies in classical thermodynamics 8. Thermodynamic relations 9. Statistical calculation of thermodynamic quantities 10. Waves in a box 11. Systems with variable contents 12. Indistinguishable particles 13. Classical statistical mechanics 14. The problem of the equation of state 15. Electric and magnetic systems 16. Fluctuations and the approach to equilibrium 17. Transport properties 18. Phase transitions 19. The fundamental assumptions reviewed Answers to problems Appendices.

Flow-force relationships for a six-state proton pump model: intrinsic uncoupling, kinetic equivalence of input and output forces, and domain of approximate linearity.

Abstract: General flow-force relations have been determined, by the Hill diagram method, for a six-state proton pump model with and without intrinsic uncoupling (molecular slipping). A computer-aided analysis of the resulting sigmoidal flow-force curves has been performed by using a set of physically meaningful rate constants. It is shown that gating effects and apparent irreversibility can arise from sigmoidicity. The regions of approximate linearity in the vicinity of inflection points, which may be far from equilibrium, have been examined with a view to characterization in terms of linear phenomenological equations, with due regard to the problems of kinetic equivalence of the forces and symmetry. The determination of thermodynamic parameters such as the degree of coupling, the phenomenological stoichiometry, and the efficiency in these regions is discussed, and their meaning is analyzed in relation to the parameters characterizing the Onsager domain close to equilibrium. The application of the phenomenological equations of near-equilibrium nonequilibrium thermodynamics to such regions is at best a simplification to be treated with great caution. A knowledge of the distance from equilibrium of the flow-controlling ranges of the forces (i.e., the ranges of approximate linearity) turns out to be crucial for the interpretation of thermodynamic parameters determined by manipulating one of the forces while the other remains constant, as well as for the interpretation of measurements of force ratios at static head. The latter approaches can give good estimates of the magnitude of the mechanistic stoichiometry and of the constant force if the pumps are highly coupled and are operating not far from equilibrium. The force-flow relationships are shown to be modified by intrinsic uncoupling, reflecting the regulatory influence of the forces on the extent and nature of the slip. Thus reaction slip increases, for example, as the force against which the proton pump operates increases. The possible physiological significance of regulated intrinsic uncoupling is discussed.

Nonequilibrium thermodynamics of pressure solution

Abstract: This paper is concerned with the thermodynamic theory of solution and precipitation processes in wet crustal rocks and with the mechanism of steady pressure-solution slip in ‘contact zones,’ such as grain-to-grain contacts, fracture surfaces, and permeable gouge layers, that are infiltrated by a mobile aqueous solution phase. A local dissipation jump condition at the phase boundary is fundamental to identifying the thermodynamic force driving the solution and precipitation process and is used here in setting up linear phenomenological relations to model near-equilibrium phase transformation kinetics. The local thermodynamic equilibrium of a stressed pure solid in contact with its melt or solution phase is governed by Gibbs's relation, which is rederived here, in a manner emphasizing its independence of constitutive assumptions for the solid while neglecting surface tension and diffusion in the solid. Fluid-infiltrated contact zones, such as those formed by rough surfaces, cannot generally be in thermodynamic equilibrium, especially during an ongoing process of pressure-solution slip, and the existing equilibrium formulations are incorrect in overlooking dissipative processes tending to eliminate fluctuations in superficial free energies due to stress concentrations near asperities, defects, or impurities. Steady pressure-solution slip is likely to exhibit a nonlinear dependence of slip rate on shear stress and effective normal stress, due to a dependence of the contact-zone state on the latter. Given that this dependence is negligible within some range, linear relations for pressure-solution slip can be derived for the limiting cases of diffusion-controlled and interface-reaction-controlled rates. A criterion for rate control by one of these mechanisms is set by the magnitude of the dimensionless quantitykδ/2C pD, wherek is the interfacial transfer coefficient, δ is the mean diffusion path length,C p is the solubility at pressurep, andD is the mass diffusivity.

Mutual diffusion and self-diffusion in the frictional formalism of non-equilibrium thermodynamics

Abstract: Conceptual differences between mutual diffusion and self-diffusion are analysed using the frictional formalism of non-equilibrium thermodynamics. Expressions for the two diffusion coefficients are derived and it is shown that the friction coefficient operative in self-diffusion is different from the corresponding friction coefficient in mutual diffusion. A common error in the recent literature concerning the expression for the mutual-diffusion coefficient is corrected.

Origins of thixotropy.

Abstract: Soft-sphere scaling laws and nonequilibrium particle-dynamics simulations show that timedependent shear-thinning behavior involving structural ordering (thixotropy), typically seen in complex colloidal dispersions, derives from a first-order thermodynamic phase transition between a normal shearing fluid and a partially ordered smectic phase. The transition stems from a perturbation of the equilibrium fluid freezing point by the applied strain rate.

Generalized hydrodynamics and extended irreversible thermodynamics

Abstract: The thermodynamic implications of the first deviations with respect to the classical hydrodynamic behavior in high-frequency, short-wavelength phenomena are examined. The constitutive equations arising from an extended irreversible-thermodynamic formalism taking into account spatial inhomogeneities in the space of state variables are compared with those used in generalized hydrodynamics. The so-called exponential model for the memory function of the transverse-velocity correlation function is derived under the assumptions of extended irreversible thermodynamics only. Furthermore, it is also shown how more complicated memory functions can be derived. The results are carefully analyzed and compared with some microscopic derivations.

Heat, work, and the thermodynamic temperature at nonequilibrium steady states

Abstract: We continue our investigation of the properties of matter at nonequilibrium steady states using a thermodynamic formalism derived from molecular fluctuations. Based on the generalized Clausius inequality, we extend the definition of ‘‘reversible’’ process to include transformations between steady states and relate reversible work and heat to changes in state functions. The variable which is thermodynamically conjugate to the internal energy, that is, the inverse of the generalized thermodynamic temperature, is an integrating factor for the reversible heat. We discuss the relationship of the generalized temperature to the Kelvin temperature, how the generalized intensive variables can be measured, define generalized heat capacities, and obtain the Gibbs–Duhem relationship satisfied by the intensive variables. These ideas are illustrated for two simple steady state systems, a fluid under homogeneous shear and a two level gas which is pumped by radiation. Finally we analyze under appropriate conditions the electromotive force of a chemical reaction system held at a nonequilibrium state. We predict corrections to the Nernst equation which depend on how far the chemical reactions are removed from equilibrium.

Morphological Stability in the Course of Solid State Reactions: The System Fe3O4 ‐ Mn3O4 ‐ Cr2O3

Abstract: We have investigated experimentally and theoretically the problem of morphological stability of interfaces in a nonequilibrium two-phase ternary system while it equilibrates. The system chosen for this study was Fe3O4 - Mn3O4 - Cr2O3 at T = 1400 °C. Depending on the spinel reactant and the sesquioxide reactant, the initially planar interface is either unchanged, or develops nonplanar morphologies of different kind. The theoretical analysis starts with the independent flux equations and the appropriate boundary conditions and investigates whether or not small perturbations of the planar interface will grow or decay in the course of time. A critical parameter can be defined which is negative for stable and positive for unstable interfaces. This parameter is a complicated function of all the transport coefficients, the starting compositions and the chemical potentials of the components in both phases and can in principle be calculated, as long as local equilibrium prevails during the reaction.

Corresponding states for thermal conductivities via nonequilibrium molecular dynamics

Abstract: We follow Rosenfeld in comparing fluid‐phase thermal conductivities for several simple pair potentials. Within about ten percent these (nonelectronic) conductivities satisfy a corresponding states relation involving the equilibrium entropy. This corresponding states relation, deduced directly from the results of computer simulations, is also suggested by hard‐sphere perturbation theory and by the quasiharmonic cell‐model approach. The conductivity‐entropy relation should be useful for estimating transport coefficients from the equation of state of monatomic fluids with arbitrary pair potentials.

Stochastic free energy transduction

Abstract: Theoretical free-energy coupling systems in which the free energy coupling intermediate (e.g., the proton) occurs only in small numbers of molecules per coupling unit are shown to exhibit a number of peculiar properties: (i) the reactions involving the intermediates do not follow conventional kinetic (or nonequilibrium thermodynamic) rate laws in terms of the average concentration or chemical potential of the intermediate, (ii) the variation of the output reaction rate with the average intermediate concentration (or apparent chemical potential) is not unequivocal but depends on whether the input reaction or the leak is varied to alter that concentration, and (iii) when the apparent free energy contained in the average concentration of the intermediate is compared with the average free energy recovered in the output reaction, apparent violations of the second law of thermodynamics can occur. These phenomena are reminiscent of experimental observations in proton-linked free-energy transducing systems that suggest a more direct coupling between electron transfer chains and H+-ATPases than only through a bulk proton gradient, delta muH. Consequently, the chemiosmotic coupling theory can account for those observations if it limits the number of free energy coupling protons per chemiosmotic coupling unit to small values.

Fluctuation–dissipation theorem for QCD plasma

Abstract: We explore a quantum‐chromodynamic (QCD) plasma in stationary nonequilibrium states assuming that the process of thermalization is governed by Fokker–Planck dynamics. The generalized thermodynamic potential appropriate to the state is obtained. A relationship is developed between the response function and the fluctuations in the stationary state.

A self-consistent theory of nonequilibrium excitation transport in energetically disordered systems

Abstract: The migration of incoherent excitations in energetically disordered systems is studied theoretically using a self‐consistent diagrammatic approximation. Spatial diffusion and energy relaxation observables are related to the solutions of a nonlinear integral equation. Extensive numerical illustrations are given for two‐component and multicomponent systems. In the latter, spatial transport is found to be highly dispersive (nondiffusive) over an extremely wide range of timescales, in accordance with results from simulations and experiments. The dependence of spatial and spectral transport properties upon the spatial range and the energy dependence of the intermolecular hopping rates is examined. Several measures of energy relaxation, including detailed probability distributions in energy space, relaxation‐time spectra, and the nonequilibrium entropy are calculated and compared. The intimate relationship between spatial transport and energy relaxation is discussed in detail.

Nonequilibrium air radiation (Nequair) program: User's manual

Abstract: A supplement to the data relating to the calculation of nonequilibrium radiation in flight regimes of aeroassisted orbital transfer vehicles contains the listings of the computer code NEQAIR (Nonequilibrium Air Radiation), its primary input data, and explanation of the user-supplied input variables. The user-supplied input variables are the thermodynamic variables of air at a given point, i.e., number densities of various chemical species, translational temperatures of heavy particles and electrons, and vibrational temperature. These thermodynamic variables do not necessarily have to be in thermodynamic equilibrium. The code calculates emission and absorption characteristics of air under these given conditions.

A network thermodynamic approach to Hill and King–Altman reaction–diffusion kinetics

Abstract: The major graphical approaches to kinetics—Hill diagrams and the King–Altman rules—can be considerably simplified using network techniques. An algorithmic procedure is developed and applied to several concrete examples which permits systems described in terms of first order transitions to be represented as connected networks. The utility of this representation is: (1) it permits powerful results from network thermodynamics and network theory to be applied to complex kinetic networks such as those representing biological dynamic systems. (2) The intrinsic role played by the thermodynamic principle of microscopic reversibility in networks containing cycles is emphasized: microscopic reversibility implies Onsager reciprocity for perturbed equilibrium systems. It now becomes clear that Onsager reciprocity is a topological property of systems to which thermodynamics is applicable. Reciprocity, or its lack can be rigorously established for macroscopic systems far outside the domain of Onsager’s original demonst...

Multi-level non-LTE line formation calculations using approximate Lambda-operators

Abstract: Nouvelle methode de calcul utilisant l'operateur lambda presente par Scharmer (1981) pour la description du probleme de transfert radiatif dans une atmosphere stellaire

Irreversible thermodynamics of rarefied gases

Abstract: For transport phenomena in gases the Onsager scheme can be extended so as to include the quantities occurring in a complete set of linearized Burnett equations. To show this, the linearized Boltzmann equation is solved in the Chapman-Enskog manner, allowing for ∇∇T and ∇∇ν terms among the thermodynamic forces. Microscopic and macroscopic Burnett fluxes are introduced, and the phenomenological equations and formal expressions for the transport coefficients derived. The matrix of these coefficients is symmetric in the Onsager way, in agreement with an expression one can derive for the entropy density source. The scheme simplifies for the bulk part of plane flows between parallel plates, with their separation assumed to be greater than a few mean free paths. Boundary layers must be treated separately. The corresponding expression for the entropy source suggests another set of phenomenological equations, involving slip coefficients. The symmetry relations among the coefficients that were earlier obtained indirectly are thereby explained in Onsager's sense.

A computer simulation for model fluid hydrogen chloride

Abstract: We report results of computer simulation studies of a model for fluid hydrogen chloride. The intermolecular potential consists of a central Lennard-Jones part, to which are added point dipoles, quadrupoles and also polarizability. The latter introduces effective many-body intermolecular interactions. The model parameters were obtained from dilute gas properties. The simulations were carried out using both molecular dynamics (equilibrium and nonequilibrium) and Monte-Carlo methods. Properties calculated include the dimer, liquid and solid structure, mean squared force and torque, self-diffusion coefficient, shear viscosity, dielectric constant, and thermodynamic properties. The simulation results have been compared with experimental data to demonstrate the adequacy of this comparatively simple model for a very wide range of both static and dynamic properties over a range of state conditions.

Response theory as a free-energy extremum.

Abstract: We show that the formal results of many-body, isothermal response theory can be generated from thermodynamic extremum principles. It is shown that this method yields the correct time-dependent response to a perturbing external field.

Nonequilibrium phenomena in dense polyatomic fluids. I. Transport coefficients for axially symmetric (polar) molecules

Abstract: Formulas are derived for the viscosity coefficients and thermal conductivity of a dense fluid of rigid, axially symmetric molecules. The only quantities appearing in these formulas which have not been evaluated explicitly are integrals over the orientational coordinates of two interacting molecules. The theory is based on a kinetic equation which incorporates a Vlasov term, an Enskog operator specific to the short‐ranged noncentral impulsive forces, and Fokker–Planck operators associated with the longer ranged interactions. The method of moments is used to construct an approximate solution of this kinetic equation. The theory and the transport coefficients it produces are compared with those of earlier investigations.

Stationary nonequilibrium solutions of model Boltzmann equation

Abstract: We give an explicit solution of a model Boltzmann kinetic equation describing a gas between two walls maintained at different temperatures. In the model, which is essentially one-dimensional, there is a probability for collisions to reverse the velocities of particles traveling in opposite directions. Particle number and speeds (but not momentum) are collision invariants. The solution, which depends on the stochastic collision kernels at the walls, has a linear density profile and the energy flux satisfies Fourier's law.