Showing papers on "Non-equilibrium thermodynamics published in 1986"

Assessment of a two-temperature kinetic model for dissociating and weakly ionizing nitrogen

Abstract: The validity of the author's two-temperature, chemical/kinetic model which the author has recently improved is assessed by comparing the calculated results with the existing experimental data for nitrogen in the dissociating and weakly ionizing regime produced behind a normal shock wave. The computer program Shock Tube Radiation Program (STRAP) based on the two-temperature model is used in calculating the flow properties behind the shock wave and the Nonequilibrium Air Radiation (NEQAIR) program, in determining the radiative characteristics of the flow. Both programs were developed earlier. Comparison is made between the calculated and the existing shock tube data on (1) spectra in the equilibrium region, (2) rotational temperature of the N2(+) B state, (3) vibrational temperature of the N2(+) B state, (4) electronic excitation temperature of the N2 B state, (5) the shape of time-variation of radiation intensities, (6) the times to reach the peak in radiation intensity and equilibrium, and (7) the ratio of nonequilibrium to equilibrium radiative heat fluxes. Good agreement is seen between the experimental data and the present calculation except for the vibrational temperature. A possible reason for the discrepancy is given.

Principles and Models of Biological Transport.

Abstract: Equilibrium Thermodynamics.- Free Diffusion.- The Cell.- Facilitated Diffusion: Channels and Carriers.- Active Transport.- Nonequilibrium Thermodynamics.- Models of Transport Across Cell Membranes.- Regulation and Feedback.- Excitable Cells.- Epithelial Transport.- Gas Transport.

Nonequilibrium statistical mechanics of concentrated colloidal dispersions: Hard spheres in weak flows

Abstract: We formulate a theory for the nonequilibrium structure and stresses in a sheared suspension with a fluid rest state. Many body interactions are handled exactly in the thermodynamics but truncated at the pair level for the hydrodynamics. Evaluation for hard spheres in weak flows demonstrates the importance of stresses arising from the nonequilibrium structure and explains the shear rate dependence observed at volume fractions greater than 0.25–0.30.

Heat and matter transport in binary liquid mixtures

Abstract: Following some preliminary clarification of microscopic heat current definitions for mixtures, we describe nonequilibrium molecular dynamics algorithms for the evaluation of heat and matter transport coefficients in binary liquid mixtures. Simulations have been carried out for a dense fluid of Lennard-Jones atoms, approximating an equimolar argon-krypton mixture, at a thermodynamic state which has been studied in several previous equilibrium simulations. Our results suggest that the estimates of the mutual diffusion coefficient from these equilibrium simulations are \ensuremath{\sim}15% too high. Most importantly, we determine the cross-coupling coefficients which characterize the Soret and Dufour effects. These are obtained from two entirely independent sets of simulations and are found to be equal, in accordance with an Onsager reciprocal relation. When we run our algorithms with high external fields, we incidentally find evidence of demixing which is of interest in the general context of nonequilibrium phase transitions.

Brownian motion and nonequilibrium statistical mechanics.

Abstract: This article is a personal reflection of the branch of nonequilibrium statistical mechanics called the linear response theory that has as its heart the fluctuation-dissipation thereom, which states that irreversible processes ip nonequilibrium are necessarily related to thermal fluctuations in equilibrium. Its origi lies in the Einstein relation for the diffusion constant and the mobility of a Brownian particle. The short history of the fluctuation-dissipation theorem is described. Then the linear response theory is brifly summarized and the meaning of stochastization is considered. The Langevin equation approach and its extensions are reviewed.

Nonequilibrium thermodynamics and statistical physics of surfaces

Abstract: Description phenomenologique des processus irreversibles qui ont lieu au niveau d'une surface de discontinuite entre des phases volumiques

Effect of radial flow on deviations from local equilibrium during sorbing solute transport through homogeneous soils

Abstract: Several laboratory and theoretical studies of sorbing solute transport through one-dimensional homogeneous soil columns have recently addressed the validity of the local chemical equilibrium assumption (LEA)This paper extends previous theoretical results to the case of ideal radial flow in homogeneous aquifers Sorption kinetics are assumed to follow a first-order reversible rate law Two sample problems are considered: one involves injection of a contaminant pulse into a diverging radial flow field; the other, extraction of polluted groundwater by a purge well in a converging radial flow field An analytical time moment analysis is performed to derive formulas for solute breakthrough curve time moments Comparison of time moment formulas for the kinetic and equilibrium models leads to the definition of criteria for LEA validity These criteria explicitly show the effect of basic system parameters (eg, pumping rate, dispersion coefficient, distribution coefficient, reaction rate coefficient) upon deviations from equilibrium behavior For the case of converging radial flow, formulas are derived to calculate the impact of desorption kinetics upon the time required for aquifer decontamination The results also show that significant nonequilibrium effects are confined to the vicinity close to the injection-extraction wells

Stochastic thermodynamics of nonequilibrium steady states in chemical reaction systems

Abstract: We present a stochastic theory of entropy production for steady states in chemical reaction systems. Small scale internal fluctuations around steady states are considered in the Gaussian regime. It is shown that in addition to the usual Gibbsian form of entropy production, there is an entropy production due to fluctuation which is of order O(V0). This comes from the non‐Poisson character of the probability distribution in a nonequilibrium system. Two approaches are considered: in the first, we use an entropy balance equation based on the master equation; in the second, we use a stochastic potential related to the probability distribution and built from the generalized Einstein relation. We show that both approaches give the same result for the entropy production of fluctuation (diS/dt) f . Next we consider a simple one‐component nonequilibrium system under the perturbation of a macroscopically large external fluctuation as a power generator. We interpret (diS/dt) f in terms of net power gain factor under...

Model for nonequilibrium computer simulation methods

Abstract: Several methods for nonequilibrium computer simulation of plane Couette flow are analyzed by kinetic theory The boundary-value problem for the nonlinear Boltzmann equation is related to the stochastic, Lees-Edwards, and ``non-Newtonian'' dynamics methods It is found that the kinetic-theory and computer simulation methods can be put into close correspondence, except for one form of the non-Newtonian equations of motion The effects of homogeneous, nonconservative forces used to maintain constant temperature are also studied For a special interatomic force law exact scaling relations are obtained to relate isothermal and nonisothermal solutions to the Boltzmann equation For other force laws this scaling relationship is only approximate

Nonequilibrium structure of the homogeneous phase of block copolymers under steady flow

Abstract: A theory is developed to describe the scattering function of a diblock copolymer in the presence of a steady homogeneous flow field. The nonequilibrium steady state under flow conditions is analyzed within a mean field approximation that is expected to accurately describe the disordered phase of block copolymer melts. In the absence of flow the theory reduces to the equilibrium theory of Leibler. Simple shear and extensional flows are seen to render the scattering function highly anisotropic and to attenuate the peak intensity. The instability at the spinodal is predicted to disappear for very strong flows, such as a uniaxial extensional flow. The theory provides an expression for the structure factor that will allow for quantitative interpretation of neutron and x‐ray scattering experiments on diblock melts under steady macroscopic flow.

Prandtl Number Effect on Bénard Convection in Porous Media

Abstract: A numerical study of buoyance-driven two-dimensional convection in a fluid-saturated horizontal porous layer is reported emphasizing the nonlinear inerital effect on heat transport. The Forchheimer-Brinkman-Darcy-Boussinesq formulation and a single energy equation for the volume-average temperature are used. Closure to the wavenumber selection problem is sought through a criterion based on the Glansdorff and Prigogine theory of nonequilibrium thermodynamics. Good agreement with laboratory data and the analogy with th Rayleigh-Benard problem are corroborative facts which justify smililar non-Darcian formulations and demonstrate the role of the quadratic inertial terms in decreasing the mean convective heat transfer across the layer.

Fundamentals of engineering thermodynamics

Abstract: Energy and energy transfer properties of common substances first law of thermodynamics entropy and the second law of thermodynamics thermodynamic cycle analysis and applications to gas cycles vapor cycle analysis analysis using the second law of thermodynamics general property relations and equations of state multicomponent systems without chemical reaction chemical reactions and combustion phase and chemical equilibrium introduction to microscopic thermodyanmics.

Three-Dimensional AOTV Flowfields in Chemical Nonequilibrium

Abstract: A technique for upwind differencing of the three-dimensional species continuity equations is presented which permits computation of steady flows in chemical equilibrium and nonequilibrium. The capabilities and shortcomings of the present approach for equilibrium and nonequilibrium flows is discussed. Modifications now being investigated to improve computational time are outlined.

Nonequilibrium phase transitions in stochastic lattice systems: Influence of the hopping rates

Abstract: Two-dimensional lattice-gas models with attractive interactions and particle-conserving hopping dynamics under the influence of a very large external electric field ⇀E along a principal axis are studied in the case of different ratiosγ between the jump rates in the field direction and perpendicular to it using different transition probabilities. We investigate the dependence of the non-equilibrium steady-state properties on the transition mechanism. We find self-similarity with respect to (T, γ) and a coexistence curve critical exponent which, for smallγ, seems independent ofγ. There is some evidence that this exponent might be halfway between the equilibrium mean field and Onsager's values. A crossover toward mean-field behavior for largeγ seems also identified.

The fast rate limit of driven diffusive systems

Abstract: We study the stationary nonequilibrium states of the van Beijeren/Schulman model of a driven lattice gas in two dimensions. In this model, jumps are much faster in the direction of the driving force than orthogonal to it. Van Kampen's Ω-expansion provides a suitable description of the model in the high-temperature region and specifies the critical temperature and the spinodal curve. We find the rate dependence ofT c and show that independently of the jump rates the critical exponents of the transition are classical, except for anomalous energy fluctuations. We then study the stationary solution of the deterministic equations (zeroth-orderΩ-expansion). They can be obtained as trajectories of a dissipative dynamical system with a three-dimensional phase space. Within a certain temperature range belowT c, these equations have a kink solution whose asymptotic densities we identify with those of phase coexistence. They appear to coincide with the results of the “Maxwell construction.” This provides a dynamical justification for the use of this construction in this nonequilibrium model. The relation of the Freidlin-Wentzell theory of small random perturbations of dynamical systems to the steady-state distribution belowT c is discussed.

Nonequilibrium fluctuations studied by a rarefied-gas simulation

Abstract: A dilute gas under a constant heat flux is studied with use of a Monte Carlo simulation based on the Boltzmann equation. Results for several spatial correlation functions of equal-time fluctuations are reported and compared qualitatively with previous fluctuating hydrodynamics calculations for liquids.

A theorem on Lyapunov stability for dynamical systems and a conjecture on a property of entropy

Abstract: For a general dynamical system, it is proved that an equilibrium state belonging to a continuous family of conditionally stable equilibrium states is stable. The result is applied to quantum thermodynamics to clarify in what restricted sense the entropy functional s( ρ)=−k Tr ρ ln ρ can provide a Lyapunov criterion for the stability of thermodynamic equilibrium. A conjecture on a special positive‐definiteness property of −k Tr ρ ln ρ remains to be proved.

The temperature paradox in the kinetic theory of evaporation

Abstract: It is shown that the inverted temperature profile between an evaporating and a condensing surface, which is a controversial result of kinetic theory, cannot be excluded by nonequilibrium thermodynamics.

Statistical mechanics of a two-temperature, classical plasma.

Abstract: Weakly coupled, nonequilibrium plasmas have often been described by assigning separate temperatures to the electron and ion velocity distributions. In this paper we present a model for the complete phase-space probability function which describes a two-temperature ensemble for arbitrary coupling. We discuss the ''thermodynamics'' predicted by the model, and in the limit of weak electron-ion coupling, we obtain explicit expressions for both the static and dynamic structure factors, which remain valid even for strong ion-ion coupling. When the ions become weakly coupled, our results for the static structure factors reduce to those of Salpeter. However, even in this limit there remains a small difference from Salpeter's dynamic structure factor due to the nonergodicity of the ensemble.

Virtual power and thermodynamics for electromagnetic continua with interfaces

Abstract: This paper presents a systematic and rational formulation of the electromagnetic theory of deformable and fluent bodies swept out by singular surfaces that may carry their own thermodynamics (interfaces). The treatment is based on the principle of virtual power for finite velocity fields, which is so formulated that, when combined, for real velocity fields, with the first principle of thermodynamics in global form, it yields directly the so‐called energy theorem both in the bulk and at the singular surface. Then the corresponding rates of entropy production are deduced after introduction of the second principle of thermodynamics. The various alternate expressions of the ponderomotive force, couple, and electromagnetic energy, obtained in the bulk from the Lorentz theory of electrons are developed across the singular surface by means of the generalized transport and Green–Gauss theorems. Finally, an extension of the constitutive theory (well established in the bulk) is given to account for surface phenomena in the case of an electromagnetic fluid. Thermodynamical restrictions are discussed, and comparisons are made with previous works.

Extended thermodynamics of a non-Newtonian fluid

Abstract: Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.

Formal Theory of Nonlinear Response

Abstract: A new method is presented of calculating nonlinear responses to external perturbations, which is based on the theory of explicitly time-dependent dynamical invariant. In terms of dynamical invariants, a general form of nonequilibrium density matrix is given. This general formalism is examined in detail. A generalization of Onsager reciprocity relations and an evolution criterion of macroscopic systems are presented. The arguments are illustrated by applying the new method to derive generalized Langevin equations. The present theory is thus appropriate for the microscopic description of nonlinear nonequilibrium thermodynamics.

Thermodynamical derivation of equations of motion for multicomponent fluids

Abstract: In this work the thermodynamics of multicomponent fluids is treated, based on the mechanics of superposed continua. Balances of diffusion’s momentum and energy are derived, and possible definitions and balances of internal energy are discussed. An entropy function is given, where the diffusion currents are the dynamic variables, thus the balances of the latter come from mechanical considerations. Constitutive equations of the components’ pressure tensor and friction, and of heat conduction are derived, applying the local form of the Gyarmati Principle. The equivalence of Newton’s Third Law and Onsager’s Reciprocity Relations is shown for diffusion. The equations of motion lead to a system of telegraphist’s equations, if viscosities are neglected. The results are compared with those of the “Wave Approach of Thermodynamics”, and with the Theory of Dynamic Variables.

An approximate variational method for improved thermodynamics of molecular fluids

Abstract: For a certain class of thermodynamic perturbation theories, a generalization of the Gibbs–Bogoliubov inequality holds through second order of perturbation theory and for a subset of terms the inequality is true to infinite order. Using this approximate variational principle, a perturbation theory is chosen for which the Helmholtz free energy of the reference system is minimized under the constraint that the first order term is identically zero. We apply these ideas to the determination of effective spherical potentials that accurately reproduce the thermodynamics of nonspherical molecular potentials. For a diatomic‐Lennard‐Jones (DLJ) potential with l/σ=0.793, the resulting spherical reference potential is identical to the median average over angles for the repulsive part of the potential, but differs in the attractive well. The variational effective spherical potential leads to more accurate thermodynamics than the median, however, particularly in the triple point region.

Saha decrements and collisional-radiative recombination and ionization coefficients for a nonequilibrium nitrogen plasma

Abstract: Using a time-dependent approach, a collisional-radiative model is developed for a nitrogen plasma Effective recombination and ionization coefficients are calculated for optically thin and optically thick cases in bound-bound uv radiation The steady-state population densities for neutral and ionic states are presented in terms of their deviations from Saha equilibrium predictions These results show the approach of the plasma to local thermodynamic equilibrium (LTE) as a function of electron temperature and density The computations focus on temperatures between 10 and 30 eV and electron densities between 1016 and 1019 cm−3

Linear viscoelasticity and irreversible thermodynamics

Abstract: The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.