Equations Of Nonequilibrium Thermodynamics Research Articles

Solidification Modeling of Continuous Casting Process

The aim of the present work was to utilize a new systematic mathematical-informational approach based on informational macrodynamics (IMD) to model and optimize the casting process, taking as an example horizontal continuous casting (HCC). The IMD model takes into account the interrelated thermal, diffusion, kinetic, hydrodynamic, and mechanical effects that are essential for the given casting process. The optimum technological process parameters are determined by the simultaneous solution of problems of identification and optimal control. The control functions of the synthesized optimal model are found from the extremum of the entropy functional having a particular sense of an integrated assessment of the continuous cast bar physicochemical properties. For the physical system considered, the IMD structures of the optimal model are connected with controllable equations of nonequilibrium thermodynamics. This approach was applied to the HCC of ductile iron, and the results were compared with experimental data and numerical simulation. Good agreement was confirmed between the predicted and practical data, as well as between new and traditional methods.

On the causality requirement for diffusive-hyperbolic systems in non-equilibrium thermodynamics

The consequences of the Causality Principle for the constitutive equations of non-equilibrium thermodynamics are investigated. It is proved that such a principle, once interpreted in the light of the experimental results, is compatible with both the hyperbolic and parabolic thermodynamic theories. As an example, a diffusive-hyperbolic model of heat conduction is presented.

A simulation study of the pore size dependence of transport selectivity in cylindrical pores

The equilibrium adsorption and transport properties of mixtures of methane and carbon dioxide, modelled as spherical molecules, have been studied in cylindrical model pores with graphitic properties over a range of cylinder radii. The equilibrium isotherms exhibit packing transitions similar to those observed for single adsorbates; as a consequence, optimum separation factors are found at particular radii, depending on the fugacity (or pressure) in the system. The equations of non-equilibrium thermodynamics have been developed so as to represent the flux of each component in a Fickian form, as a coefficient multiplying the gradient of the total density. Diffusion coefficients were calculated from streaming velocity correlations and NEMD was used to obtain the ‘apparent’ viscous component. The results show that diffusion coefficients from equilibrium molecular dynamics and viscous diffusion coefficients from non-equilibrium calculations are identical within the errors of the calculation. It follows that equilibrium and dynamic separation factors have the same values over a range of pore sizes.

Kinetic Phenomena in the Diffusion of Gases in Capillaries and Porous Bodies

The flow of gases and gaseous mixtures in capillaries and porous bodies were considered. Phenomenological transfer equations were derived using methods of non-equilibrium thermodynamics. Integral and local equations of non-equilibrium thermodynamics were constructed and phenomenological relations of two types were obtained. Different approaches to the calculation of kinetic coefficients were indicated. Methods of kinetic theory based on Boltzmann's equation and the dusty gas model were analyzed separately. Results of the calculations of kinetic coefficients for small and large Knudsen numbers were reported with allowance for incomplete accommodation of molecules on the surface of channel walls. A number of kinetic effects exhibiting during the flow of gases and gaseous mixtures through the capillaries and porous bodies was discussed.

Bracket formulation as a source for the development of dynamic equations in continuum mechanics

The bracket formulation of the dynamic equations in nonequilibrium thermodynamics is examined here. After a short review of the early historical development of the subject, we present an introduction to the theoretical foundations of the one-generator bracket formalism, where the one generator is the Hamiltonian. The Hamiltonian represents the system’s total (extended) internal energy but, through a Legendre transform similar to that used in equilibrium thermodynamics, its derivatives can also be calculated from the available expression for the system’s extended free energy. First, the conservative component of the bracket is recognized as the Poisson bracket of Hamiltonian mechanics. Its properties are briefly reviewed and justified based on its connection to Hamiltonian mechanics. The Poisson structure of the conservative bracket is also manifested in a variety of other formalisms of the dynamic equations of nonequilibrium thermodynamics, thus providing a unilying connection. Next, the nonconservative, dissipative component is presented in the one-generator formalism, a more extensive treatment of which can be found in the research monograph by Beris and Edwards [A.N. Beris, B.J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure, Oxford University Press, New York, 1994]. We further address here some of the more recent developments that have taken place since the publication of the above-mentioned work. Hence, the two-generator form of the bracket equations that corresponds to the GENERIC framework of description is considered next. The two generators are the Hamiltonian (or total energy), which drives the conservative part of the dynamics, and the entropy, which drives the dissipative part. Differences and similarities between the two- and the one-generator formalisms are pointed out. Finally, the advantage of the use of the bracket formulation is illustrated, as a number of recent applications are reviewed.

Modeling Self-diffusion in Multicomponent Aqueous Electrolyte Systems in Wide Concentration Ranges

A comprehensive model has been developed for calculating self-diffusion coefficients in multicomponent aqueous electrolyte systems. The model combines contributions of long-range (Coulombic) and short-range interactions. The long-range interaction contribution, which manifests itself in the relaxation effect, is obtained from the dielectric continuum-based mean-spherical approximation (MSA) theory for the unrestricted primitive model. The short-range interactions are represented using the hard-sphere model. In the combined model, aqueous species are characterized by effective radii, which depend on the ionic environment. For multicomponent systems, a mixing rule has been developed on the basis of phenomenological equations of nonequilibrium thermodynamics. The effects of complexation are taken into account by combining the diffusivity model with thermodynamic speciation calculations. The model accurately reproduces self-diffusivities of ions and neutral species in aqueous solutions ranging from infinitely...

Atomic transport in solids: models and their parameterization

This paper reviews the structure of the modern theory of atomic transport in solids. It starts with the macroscopic equations of non-equilibrium thermodynamics and then proceeds to the methods offered by statistical mechanics for the evaluation of transport coefficients, etc. The application of these methods to stochastic models is then considered in both general terms and for particular models suggested by the theory of lattice imperfections. These particular examples include isothermal diffusion in dilute and concentrated solid solutions and also transport in temperature gradients. The value of solid state theory in the parameterization of these models is emphasised.

Mechanodiffusion in a slightly rarefied gas mixture

The flow of a rarefied gas mixture in a plane channel with mobile plate is considered. The plates of channel are assumed to be of different nature. Entropy production in the system is calculated and phenomenological equations of non-equilibrium thermodynamics are obtained. The validity of the Onsager relation for kinetic coefficients is shown. A phenomenon called mechanodiffusion is predicted, and an experimental investigation of the phenomenon is carried out. The experimental results confirm the theoretical predictions. The effect can be used for gas mixtures and isotopes separation.

Deficiency of red cell sodium-potassium pump activity in bipolar affective disorder

The rat proximal tubule epithelium is represented as well-stirred, compliant cellular and paracellular compartments bounded by mucosal and serosal bathing solutions. With a uniform pCO2 throughout the epithelium, the model variables include the concentrations of Na, K, Cl, HCO3, H2PO4, HPO4, and H, as well as hydrostatic pressure and electrical potential. Except for a metabolically driven Na-K exchanger at the basolateral cell membrane, all membrane transport within the epithelium is passive and is represented by the linear equations of nonequilibrium thermodynamics. In particular, this includes the cotransport of Na-Cl and Na-H2PO4 and countertransport of Na-H at the apical cell membrane. Experimental constraints on the choice of ionic conductivities are satisfied by allowing K-Cl cotransport at the basolateral membrane. The model equations include those for mass balance of the nonreacting species, as well as chemical equilibrium for the acidification reactions. Time-dependent terms are retained to permit the study of transient phenomena. In the steady state the energy dissipation is computed and verified equal to the sum of input from the Na-K exchanger plus the Gibbs free energy of mass addition to the system. The parameter dependence of coupled water transport is studied and shown to be consistent with the predictions of previous analytical models of the lateral intercellular space. Water transport in the presence of an end-proximal (HCO3-depleted) luminal solution is investigated. Here the lower permeability and higher reflection coefficient of HCO3 enhance net sodium and water transport. Due to enhanced flux across the tight junction, this process may permit proximal tubule Na transport to proceed with diminished energy dissipation.

The moment method and rarefied gas flow in channels. General relations

The relation between mass and heat fluxes and the distribution function moments at the channel walls have been established by an example of pure gas flow in a plane channel. The bulk and the Knudsen contributions to the fluxes have been separated. Phenomenological equations of non-equilibrium thermodynamics for boundary fluxes valid for arbitrary Knudsen numbers have been obtained. The validity of the Onsager relations for coefficients both in classical and in boundary phenomenological equations of non-equilibrium thermodynamics has been shown.

The existence of thermodynamic constants characterizing the properties of substances and materials in spontaneous processes

The equations of nonequilibrium thermodynamics show that one of the higher time derivatives of the maximum thermodynamic work remains constant along the trajectory of a spontaneous process. The theoretical prediction is confirmed by experimental data on mechanical motion with friction. The constant characterizing the friction process is called the coefficient of thermodynamic friction losses (KTL). In contrast to the friction coefficient in mechanics, the KTL does not depend on the velocity and acceleration of relative motion of parts of the frictional pair on the trajectory of spontaneous slowing down. The KTL may be regarded as a nonequilibrium thermodynamic parameter specifying at a given temperature the properties of materials involved in the friction process. The usefulness and advantages of utilizing the KTL in engineering computations are noted.

Description of dynamic lung fluid transport phenomena by linear non-equilibrium thermodynamic equations

We propose a mathematical model of dynamic lung transvascular fluid flow based on linear non-equilibrium thermodynamic equations. The model makes use of experimental results concerning lung fluid balance during hydrodynamic and hypooncotic loading. An ‘inexact problem’ solution method was employed to solve the mathematical problem and to obtain coefficients of mass transfer. Transport features dependent on the system's condition and on boundary phase surface phenomena were also considered. A complex analysis of such a multi-unit system as the lung is useful for the evaluation of fluid balance mechanisms and their application to the development of artificial mass exchange devices.

Non-equilibrium thermodynamics in thermal engineering

We describe energy-transfer processes in thermal engineering by the equations of non-equilibrium thermodynamics. Deviations from equilibrium are assumed to be small in order to conserve the ordinary meaning of the term temperature. An important special case involves strictly stationary flow.

Algebraic symmetry in chemical reaction systems at stationary states arbitrarily far from thermodynamic equilibrium

For systems of chemical reactions the phenomenological equations of nonequilibrium thermodynamics display the differential symmetry of Onsager reciprocity in general only for stationary states in the vicinity of thermodynamic equilibrium, as is well known. It will be shown here, however, that systems of chemical reactions, on the macroscopic, phenomenological level of chemical kinetics, do show a less stringent symmetry at all stationary states arbitrarily far from equilibrium. The key is a reformulation of the kinetic equations for single chemical reactions as resistive laws relating the force driving a reaction to the rate of the reaction through a (nonlinear) generalized chemical resistance; these laws are analogous to the ‘‘voltage=current times resistance’’ laws for resistive elements in electrical networks. The resistive laws for single reactions then lead naturally to stationary state relations for systems of coupled chemical reactions of the form of the phenomenological equations of nonequilibrium thermodynamics, and these relations display algebraic symmetry at stationary states arbitrarily far from equilibrium, although the differential symmetry of Onsager reciprocity is in general not valid. An example illustrates the relation of the symmetry property for chemical reactions to that displayed by RC electrical networks and how the chemical symmetry follows from analogs of Kirchhoff’s laws obeyed by systems of chemical reactions.

Irreversibility for active structures

We compare the field equations for homogeneous dissipative systems, namely the equations of nonequilibrium thermodynamics which are notoriously irreversible with the recently developed analogous equations for homogeneous active systems. That these last equations are also irreversible is not obvious at first sight and we show it with a brief critical discussion on the concept of irreversibility.

Effect of space charge and nonuniform temperature on a solid state galvanic cell

The complete set of differential equations of nonequilibrium thermodynamics has been solved for a solid state galvanic cell consisting of single electrolyte sandwiched between electrodes. Electroneutrality is not assumed anywhere, and it is therefore possible to assess the effects of nonzero space charge in the electrolyte near the electrodes. A special transformation of concentration variables into a neutral part and a charge part facilitates both the analytical and the numerical solution of the mathematical problem. Formulas are obtained for the electric field, the ionic concentration, the space charge, the cell potential, and the efficiency of the cell at steady state. Inclusion of appropriate temperature gradient terms in all equations permits evaluation of the effects of nonuniform temperature on all cell properties including efficiency. For specificity, numerical results are obtained for the particular galvanic cell consisting of cerium oxide doped with calcium oxide as the electrolyte contained between oxygen electodes. Efficiency is enhanced — more current is produced with less ohmic loss — if the product Q ∗(ΔT) is negative, with Q ∗ the heat of transport of the electrolyte and ΔT the temperature difference between the cathode and the anode.

Nonequilibrium thermodynamic model of the rat proximal tubule epithelium

The rat proximal tubule epithelium is represented as well-stirred, compliant cellular and paracellular compartments bounded by mucosal and serosal bathing solutions. With a uniform pCO2 throughout the epithelium, the model variables include the concentrations of Na, K, Cl, HCO3, H2PO4, HPO4, and H, as well as hydrostatic pressure and electrical potential. Except for a metabolically driven Na-K exchanger at the basolateral cell membrane, all membrane transport within the epithelium is passive and is represented by the linear equations of nonequilibrium thermodynamics. In particular, this includes the cotransport of Na-Cl and Na-H2PO4 and countertransport of Na-H at the apical cell membrane. Experimental constraints on the choice of ionic conductivities are satisfied by allowing K-Cl cotransport at the basolateral membrane. The model equations include those for mass balance of the nonreacting species, as well as chemical equilibrium for the acidification reactions. Time-dependent terms are retained to permit the study of transient phenomena. In the steady state the energy dissipation is computed and verified equal to the sum of input from the Na-K exchanger plus the Gibbs free energy of mass addition to the system. The parameter dependence of coupled water transport is studied and shown to be consistent with the predictions of previous analytical models of the lateral intercellular space. Water transport in the presence of an end-proximal (HCO3-depleted) luminal solution is investigated. Here the lower permeability and higher reflection coefficient of HCO3 enhance net sodium and water transport. Due to enhanced flux across the tight junction, this process may permit proximal tubule Na transport to proceed with diminished energy dissipation.

Computer simulation of transport phenomena during dialysis deglycerolization of red blood cells

A computer simulation model has been developed to aid in the understanding, parameter prediction, and performance optimization of a unique dialysis process where glycerol is removed from cryopreserved red blood cells using a semipermeable membrane pouch fixed in a mildly agitated transport cell. The dynamic system considered here consists of flow channels and the membrane blood pouch which contains the red blood cells, extracellular fluid, and cryopreservatives. Dialysate flows over the membrane surfaces while salt enters the pouch preventing osmotic hemolysis. The glycerol diffuses rapidly from the red cells and plasma across the membrane into the dialysate which carries it out of the transport cell. The system is discretized into completely mixed subdomains. Constituent transport and solvent flux are modeled with the transient convection-diffusion equation and linear equations of nonequilibrium thermodynamics, respectively. The integrated compartment method was used to solve for the principal variables, that is, salt and glycerol concentrations, water flow rates, and pressure in space and time. The computer simulation model, calibrated and verified with in-house data sets, is a reliable, cost-effective and flexible tool for dialysis system investigations, prediction, and optimal design.

Temperature Gradient Enhancement of Solid State Battery Performance

ABSTRACTThe equations of nonequilibrium thermodynamics are used to investigate how temperature gradients may be utilized to enhance performance of solid state batteries. One result is that the efficiency of a battery with doped cerium oxide as the electrolyte may be increased by imposition of a temperature gradient. This may lead to greater use of electrolytes of appreciable electronic conductivity. Moreover, temperature gradients may be used to increase mobile ion diffusivity in intercalation electrodes during battery discharge and recharge.

Theory of electrokinetic phenomena

A complete hydrodynamic theory of electrokinetic phenomena in porous media and gels is presented. The treatment is based on the frictional formalism and is compared with the more familiar thermodynamic approach. The phenomenological coefficients in the flow equations of non-equilibrium thermodynamics are expressed in terms of the molar friction coefficients, and the Onsager reciprocal relations are deduced from Newton's third law. A proof of the Saxén relations is also given.