Principles Of Nonequilibrium Thermodynamics Research Articles

Kinetic and thermodynamic approach to precisely solve the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas under external force influence

Abstract An extension and further development of our previous article [J. Non-equilibrium Thermodyne. 37 (2012), 119–141] is presented. We study the irreversible non-equilibrium thermodynamics (INT) properties of the exact solution to the dilute homogeneously charged gas problem with unsteady Rayleigh flow. In contrast to previous research, the charged gas flows under the influence of an external force, the flat plate oscillates, and the displacement current term is considered, leading to significant advancements in understanding natural plasma dynamics. We are solving the Boltzmann kinetic equation (BKE) Krook model supplemented by Maxwell’s equations. We used a travelling wave and moments method with an electron velocity distribution function (EVDF). To the best of our knowledge, as three new scientific achievements, we introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and fluxes variables, Equations (28–40) and (50–54). Second, we determined, with reasonable accuracy, the thermodynamic equilibrium time of electrons, t equ = 26.7955, under an external force. We clarify the difference between equilibrium EVDF and perturbed EVDF and take advantage of BKE to account for non-equilibrium thermodynamic principles. For diamagnetic and paramagnetic plasmas, the extended Gibbs equation predicts ratios between various contributions to the internal energy change (IEC) is presented. A standard laboratory argon plasma model is used to apply the results.

Nonlinear constitutive model of CFRP composites under constant direct current: Combined effects of thermal damage and dielectric degradation

Prolonged exposure to low-density direct current (DC) can lead to mechanical degradation of carbon fiber-reinforced polymer (CFRP) composites, posing significant risks to material safety and reliability. This paper presents a nonlinear constitutive model to elucidate the mechanical degradation of CFRP composites when subjected to DC influences. Grounded in the principles of non-equilibrium thermodynamics, this model introduces two internal variables to account for the impact of thermal damage and dielectric degradation on the Helmholtz free energy. Furthermore, specialized dissipation functions are employed to derive the evolution equations governing these internal variables. Utilizing the model, we analyze the damage progression in carbon fiber–epoxy laminates subjected to constant DC loading. The theoretically projected resistivity and elastic modulus align closely with available experimental data in literature, thus confirming the rationality and accuracy of the proposed model. This model holds the potential to forecast the long-term evolution of mechanical properties in unidirectionally reinforced composite materials with varying carbon fiber contents under the influence of DC, thereby furnishing a theoretical foundation for enhancing the reliability design of CFRP composites in electrically-charged environments.

Non-classical theory of electro-thermo-elasticity incorporating local mass displacement and nonlocal heat conduction

A non-classical local gradient theory of nonferromagnetic thermoelastic dielectrics is presented, incorporating both the local mass-displacement process and the heat-flux gradient effect. The process of local mass displacement is related to the changes in material microstructure. The nonlocal heat conduction law is also addressed in the model. Thus, the generalized relationship between the higher-grade heat and entropy fluxes is adopted. The gradient-type constitutive relations and governing equations are derived using the fundamental principles of continuum mechanics, non-equilibrium thermodynamics, and electrodynamics. Due to the contribution of higher-grade flux, the nonlocal law of heat conduction is obtained. The constitutive relations for isotropic materials with the corresponding additional material constants are derived. To illustrate the local gradient theory and to show the electro-thermo-mechanical coupling effect in isotropic materials, a straightforward problem is analytically solved for a layered non-piezoelectric structure under non-uniform temperature distribution. The analytical results reveal that the thermal polarization effect can also be pronounced in isotropic materials. To illustrate the model considering the effect of nonlocal heat conduction, the propagation of spherical thermoelastic harmonic waves in a homogeneous and isotropic elastic medium with non-classical heat conduction law is studied.

Local gradient theory of dielectrics incorporating polarization inertia and flexodynamic effect

A higher-grade theory of non-ferromagnetic thermo-elastic dielectrics which incorporates the local mass displacement, the heat flux gradient, polarization inertia, and flexodynamic effects is developed. The process of local mass displacement is associated with changes in material microstructure. Using the fundamental principles of continuum mechanics, electrodynamics, and non-equilibrium thermodynamics, the gradient-type constitutive equations are derived. Due to accounting for the polarization inertia, the rheological constitutive equation for the polarization vector is obtained. In the balance equation of linear momentum, an additional term with the second time derivative of the polarization vector appears in comparison with the classical theory. This term controls the influence of the dynamic flexoelectric effect on the mechanical motion of dielectric solids. The propagation of a plane harmonic wave is analyzed within the context of the developed theory. It is shown that the theory allows for capturing the experimentally observed phenomenon of high-frequency dispersion of a longitudinal elastic wave. The theory may be useful for modeling coupled processes in nanodielectrics and heterogeneous polarized systems.

Gear Shifting in Biological Energy Transduction.

Confronted with thermodynamically adverse output processes, free-energy transducers may shift to lower gears, thereby reducing output per unit input. This option is well known for inanimate machines such as automobiles, but unappreciated in biology. The present study extends existing non-equilibrium thermodynamic principles to underpin biological gear shifting and identify possible mechanisms. It shows that gear shifting differs from altering the degree of coupling and that living systems may use it to optimize their performance: microbial growth is ultimately powered by the Gibbs energy of catabolism, which is partially transformed into Gibbs energy ('output force') in the ATP that is produced. If this output force is high, the cell may turn to a catabolic pathway with a lower ATP stoichiometry. Notwithstanding the reduced stoichiometry, the ATP synthesis flux may then actually increase as compared to that in a system without gear shift, in which growth might come to a halt. A 'variomatic' gear switching strategy should be optimal, explaining why organisms avail themselves of multiple catabolic pathways, as these enable them to shift gears when the growing gets tough.

On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review

A brief review of the development of ideas on extremal principles in the theory of heat and mass transfer processes (including those in reacting media) is given. The extremal principles of non-equilibrium thermodynamics are critically examined. Examples are shown in which the mechanical use of entropy production-based principles turns out to be inefficient and even contradictory. The main problem of extremal principles in the theory of irreversible processes is the impossibility of their generalization, often even within the framework of a class of problems. Alternative extremal formulations are considered: variational principles for heat and mass transfer equations and other dissipative systems. Several extremal principles are singled out, which make it possible to simplify the numerical solution of the initial equations. Criteria are proposed that allow one to classify extremal principles according to their areas of applicability. Possible directions for further research in the search for extremal principles in the theory of irreversible processes are given.

ESD Ideas: planetary antifragility: a new dimension in the definition of the safe operating space for humanity

Abstract. Combining well-established non-equilibrium thermodynamic principles and a system dynamics approach, we define, for the first time, the concept of planetary antifragility as changes of Fisher information of Earth's entropy production. As a first approximation for entropy production, we propose using shortwave global albedo anomalies and provide a first quantitative example with data for the July months in the Northern Hemisphere from 1982 to 2010. These preliminary results show a net reduction of 47.63 % in albedo's Fisher information. This loss of antifragility implies a compounding problem because human perturbations such as climate or land-use changes are increasing, but at the same time, the planet is losing its capacity to respond to them. We discuss the concept of antifragility in the context of safe operating space for humanity and planetary boundaries. We conclude that not only does interaction among state variables of the boundaries matter, but more importantly the perturbation response capacity dimension is also missing. In conclusion we speculate on improving the operational definition for ecosystems.

Generalized Poisson-Nernst-Planck-Based Physical Model of the O2∣LSM∣YSZ Electrode

The paper presents a generalized Poisson-Nernst-Planck model of an yttria-stabilized zirconia electrolyte developed from first principles of nonequilibrium thermodynamics which allows for spatial resolution of the space charge layer. It takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a reaction kinetic model describing the triple phase boundary with electron conducting lanthanum strontium manganite and gaseous phase oxygen. By comparing the outcome of numerical simulations based on different formulations of the kinetic Eqs. with the results of EIS and CV measurements we attempt to discern the existence of separate surface lattice sites for oxygen adatoms and surface oxides from the assumption of shared ones. Moreover, we show that the mass-action kinetics model is sensitive to oxygen partial pressure unlike exponential kinetics models. The resulting model is fitted to a dataset of EIS and CVs spanning multiple temperatures and pressures, using various relative weights of EIS and CV data in the fitness function. The model successfully describes the physics of the interface around the OCV.

Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach

Abstract A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

Systematic derivation of hydrodynamic equations for viscoelastic phase separation

We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the second law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics. The derivation proceeds in two steps: firstly, we derive an extended model comprising two scalar and four vector fields, such that inertial dynamics of the macromolecules and of the relative motion of the two fluids is taken into account. In the second step, we eliminate these inertial contributions and, as a replacement, introduce phenomenological dissipative terms, which can be modeled easily by taking into account the principles of non-equilibrium thermodynamics. The final simplified model comprises the momentum conservation equation, which includes both interfacial and elastic stresses, a convection–diffusion equation where interfacial and elastic contributions occur as well, and a suitably convected relaxation equation for the end-to-end vector field. In contrast to the traditional two-scale description that is used to derive rheological equations of motion, we here treat the hydrodynamic and the macromolecular degrees of freedom on the same basis. Nevertheless, the resulting model is fairly similar, though not fully identical, to models that have been discussed previously. Notably, we find a rheological constitutive equation that differs from the standard Oldroyd-B model. Within the framework of kinetic theory, this difference may be traced back to a different underlying statistical-mechanical ensemble that is used for averaging the stress. To what extent the model is able to reproduce the full phenomenology of viscoelastic phase separation is presently an open question, which shall be investigated in the future.

Unified Extended Irreversible Thermodynamics and the Stability of Relativistic Theories for Dissipation

In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. In particular, the theory aims at modeling any diffusion-type process (like heat as diffusion of energy, viscosity as diffusion of momentum, charge-conductivity as diffusion of particles) directly from thermodynamic laws. Although in Newtonian physics this task can be achieved with a first-order approach to dissipation (i.e. Navier–Stokes–Fourier like equations), in a relativistic framework the relativity of simultaneity poses serious challenges to the first-order methodology, originating instabilities which are, instead, naturally eliminated within EIT. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. We call this approach Unified Extended Irreversible Thermodynamics (UEIT), because it contains, as particular cases, EIT itself, in particular the Israel-Stewart theory and the divergence-type theories, plus Carter’s approach and most branches of non-equilibrium thermodynamics, such as relativistic chemistry and radiation hydrodynamics. We use this formalism to explain why all these theories are stable by construction (provided that the microscopic input is correct), showing that their (Lyapunov) stability is a direct consequence of the second law of thermodynamics.

Mathematical modeling of the cardiac tissue

An improved mathematical model of soft heart tissue has been developed here. Nonlinear material equations were derived from the fundamental principles of nonequilibrium thermodynamics. The passive and active phases of cardiac tissue deformation are considered using the nonlinear theory of hyperelasticity. Elastic potentials for both phases are presented in a simple form convenient for numerical calculations. To take into account muscle contraction in the active phase of deformation, coupled equations of mechanochemical kinetics are obtained. The proposed model can be used for computer modeling of the heart and circulatory system.

Dynamic Stationary Form of Crystal

The limiting free form of a crystal growing in an open system in kinetic and diffusion modes of stationary process has been geometrically described based on the limiting principle of nonequilibrium thermodynamics (entropy-production minimum). An analog for an equilibrium closed thermodynamic system is the Wulff theorem. However, the equilibrium form of a mineral crystal can barely be found in nature, whereas the stationary form is abundant and (taking into account the natural variations in the growth rates of faces) is presented by a class of full-face morphological types of polyhedral crystals of simple habit crystallographic form.

The crucial role of catalysts in the reaction of low temperature decomposition of hydrogen sulfide: Non-equilibrium thermodynamics of the irreversible process in an open system

The reaction mechanisms of low-temperature H2S decomposition on sulfide and metal catalysts are considered in the framework of thermodynamics of non-equilibrium irreversible biological processes for open systems, since these reactions occur at room temperature without supplying thermal energy from the outside owing to the internal energy of substrate molecules – hydrogen sulfide. On sulfide catalysts the irreversible process of H2S decomposition proceeds through the stage of formation of hydrogen disulfide (disulfane), H2S2, as a key intermediate, and the reaction products are hydrogen and solid sulfur. The reaction occurs through a sequence of consecutive exothermic stages of dissociation of H2S molecules, in which the entropy of the system is reduced due to its dissipation into environment as the bound (waste) energy TΔS. The remaining part of the free energy ΔG is accumulated on the catalyst surface and is used for the implementation of the energy-intensive step of decomposition of the adsorbed intermediate. Similarly, the metal catalyst provides capture and accumulation of energy from the exothermic processes of adsorption and dissociation of the initial H2S molecules in the atomic adsorbed species of hydrogen and sulfur. The stored energy is used for chemical conversion of adsorbed intermediates into the final reaction products – molecular hydrogen and diatomic triplet sulfur, followed by it does desorption into the gas phase. When H2S is decomposed on metal catalysts at room temperature, along with hydrogen, previously unknown diatomic gaseous sulfur in the ground triplet state is obtained, the existence of which is predicted by quantum chemistry. Some properties of the triplet sulfur and the white globular hexagonal sulfur obtained from its saturated aqueous solutions (which is also a previously unknown allotrope of solid sulfur) are considered. Similarity of the morphology of hydrophilic white sulfur globules and bacterial colorless sulfur S0 obtained by sulfur bacteria in the processes of chemosynthesis of organic matter from CO2 and H2S, allowed to develop an alternative hypothesis about the nature of bacterial sulfur S0 and possible mechanism of chemosynthesis of carbohydrates with the participation of sulfur bacteria. Apparently, the low-temperature catalytic decomposition of hydrogen sulfide is the first example in heterogeneous catalysis, when the principles of non-equilibrium biological thermodynamics in open systems are used to justify the possibility implementing a heterogeneous catalytic reaction.

Thermodynamic Uncertainty Relation for Arbitrary Initial States.

The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs presuppose either specific initial states or an infinite-time average, which severely limits the range of applicability. Here we derive a finite-time TUR valid for arbitrary initial states from the Cramér-Rao inequality. We find that the variance of an accumulated current is bounded from below by the instantaneous current at the final time, which suggests that "the boundary is constrained by the bulk". We apply our results to feedback-controlled processes and successfully explain a recent experiment which reports a violation of a modified TUR with feedback control. We also derive a TUR that is linear in the total entropy production and valid for discrete-time Markov chains with nonsteady initial states. The obtained bound exponentially improves the existing bounds in a discrete-time regime.

Effect of operating parameters on gas-solid exergy transfer performance in sinter annular cooler

The exergy transfer process of sinter granular bed in an annular cooler is numerically studied. According to the principle of non-equilibrium thermodynamics, the exergy transfer coefficient and Nu expressions of the horizontal moving bed were derived by applying the second law of thermodynamics. A steady-state calculation model was established and verified by experimental data, and the influence of thermal parameters on the exergy transfer performance of the annular cooler was analyzed. The results show that increasing the cooling gas inlet velocity, cooling gas inlet temperature, sintered ore layer height or trolley moving velocity, the exergy transfer performance within the sinter granular bed would be enhanced. The cooling gas inlet speed and cooling gas inlet temperature have a significant effect on the average synthetic exergy transfer coefficient in the bed. Compared with the two factors mentioned earlier, the impact of the sinter height and the speed of the trolley on the exergy transfer process is small, but it should still attract the attention of the designer. This is of great significance for strengthening the cooling process of sintered ore, and provides a novel theoretical idea for designing similar cooling equipment.

CREATION OF AFTERBURNING TURBOFAN ENGINE – HISTORY AND PRESENT

The main problems of the creation of afterburning turbofan engines, among which the irremovable surge of the compressor, is disclosed by historical analysis. According to the published models, such surge is a hydrodynamic instability in the form of rotating stall mutual transitions to surge with the primary cause of instability in the form of stall or vibration combustion in the afterburner. The Pratt & Whitney F100 serial engine, which based on TF30 is one of the first in which the irremovable surge was detected. As a result, several planes F-15 crashed, so far as the compressor could not be restored to a stable state without stopping and restarting the engine. Dissection of the problem with this phenomenon led to the conclusion that this irremovable surge problem was generated by the engine design. To eliminate it, the company had to refine several systems, such as an electronic engine control system, fuel supply of the afterburner along with the nozzle locations, firing belt, combustion stabilization, an extension of flow separation along the contours, etc. According to the analysis of publications, particular difficulties arose with the recoverable unsurge operation of such engines. It is noteworthy that today, the F-135-PW100 engines have been installed on the F-35 aircraft, the predecessors of which are the F-100 engines with the same problems. The results of experimental studies of a fan are presented in the article to deepen in the stall flow mechanism and the occurrence of rotating stall of the fan blades. The perturbations from vibrational combustion in the afterburner combustion chamber to the fan stall boundary in the afterburning turbofan engine system at bench conditions were simulated by independent throttling of the duct over a wide range of the bypass ratio. Numerous monographs and publications according to vibrational combustion, in particular in afterburner combustion chambers TRDF AL-21F and TRDDF AL-31F, of A. M. Lulka, confirm the possibility of the propagation of perturbations against the flow in the bypass duct and the impossibility of their propagation through the turbines. The propagation of surge perturbations in the afterburning turbofan engine to the compressor of the internal duct behind the fan occurs through the interaction of the duct. The more reliable way to prevent emergencies is to provide stability margin area of compressors. Estimation of the pre-stall state of the flow traditionally is carried out by the diffusivity factor of Lieblein FD, which is applicable in 2D calculations. The integral variational principle of nonequilibrium thermodynamics of the “maximum flow of mechanical energy” of V. N. Yershov was applied.

Dynamic modeling of dielectric elastomer actuator with conical shape.

With desirable physical performances of impressive actuation strain, high energy density, high degree of electromechanical coupling and high mechanical compliance, dielectric elastomer actuators (DEAs) are widely employed to actuate the soft robots. However, there are many challenges to establish the dynamic models for DEAs, such as their inherent nonlinearity, complex electromechanical coupling, and time-dependent viscoelastic behavior. Moreover, most previous studies concentrated on the planar DEAs, but the studies on DEAs with some other functional shapes are insufficient. In this paper, by investigating a conical DEA with the material of polydimethylsiloxane and considering the influence of inertia, we propose a dynamic model based on the principles of nonequilibrium thermodynamics. This dynamic model can describe the complex motion characteristics of the conical DEA. Based on the experimental data, the differential evolution algorithm is employed to identify the undetermined parameters of the developed dynamic model. The result of the model validation demonstrates the effectiveness of the model.

Calculation of the Thermodynamic Equilibrium of a Multicomponent Two-Phase System Based on Minimization of the Gibbs Potential

The authors have proposed a method to model the thermodynamic equilibrium of the two-phase multicomponent system “solution–vapor” by solving a system of ordinary differential equations following from the principles of nonequilibrium thermodynamics and statistical physics. Calculation of the thermodynamics of liquid and vapor phases was based on the equation of state. During the solution of the system of ordinary differential equations, the authors determined the molar volumes of the solution and the vapor, the molar composition of the phases, and the pressures of the onset of boiling of the solution and condensation of the vapor. The proposed method is fundamentally different from the popular empirical Rachford–Rice method. Results of calculating with this method have been presented.

Phase-field modelling of the effect of density change on solidification revisited: model development and analytical solutions for single component materials

In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of statistical physics, while the constitutive relations are developed in the framework of the standard phase-field theory, by following the variational formalism and the principles of non-equilibrium thermodynamics. To enhance the numerical practicality of the model, quasi-incompressible hydrodynamic equations are derived, where sound waves are absent (but density change is still possible), and therefore the time scale of solidification is accessible in numerical simulations. The model development is followed by a comprehensive mathematical analysis of the equilibrium and propagating one-dimensional solid–liquid interfaces for different density-phase couplings. It is shown, that the fluid flow decelerates/accelerates the solidification front in case of shrinkage/expansion of the solid compared to the case when no density contrast is present between the phases. Furthermore, such a free energy construction is proposed, in which the shape of the equilibrium planar phase-field interface is independent from the density-phase coupling, and the equilibrium interface represents an exact propagating planar interface solution of the quasi-incompressible hydrodynamic equations. Our results are in agreement with previous theoretical predictions.