Irreversible Thermodynamics Research Articles

A thermodynamics-consistent spatiotemporally-nonlocal model for microstructure-dependent heat conduction

The spatiotemporally-nonlocal phenomena in heat conduction become significant but challenging for metamaterials with artificial microstructures. However, the microstructure-dependent heat conduction phenomena are captured under the hypothesis of spatiotemporally local equilibrium. To capture the microstructure-dependent heat conduction phenomena, a generalized nonlocal irreversible thermodynamics is proposed by removing both the temporally-local and spatially-local equilibrium hypotheses from the classical irreversible thermodynamics. The generalized nonlocal irreversible thermodynamics has intrinsic length and time parameters and thus can provide a thermodynamics basis for the spatiotemporally-nonlocal law of heat conduction. To remove the temporally-local equilibrium hypothesis, the generalized entropy is assumed to depend not only on the internal energy but also on its first-order and high-order time derivatives. To remove the spatially local equilibrium hypothesis, the thermodynamics flux field in the dissipation function is assumed to relate not only to the thermodynamics force at the reference point but also to the thermodynamics force of the neighboring points. With the developed theoretical framework, the thermodynamics-consistent spatiotemporally-nonlocal models can then be developed for heat transfer problems. Two examples are provided to illustrate the applications of steady-state and transient heat conduction problems.

A novel treatment of solute drag and solute trapping at a solid–liquid interface during rapid solidification of multicomponent alloys

AbstractIn response to the renewed interest in solute drag and solute trapping models fueled by their applications to additive manufacturing, a novel treatment is proposed to describe the diffusional behaviors of solute at a migrating solid–liquid interface during rapid solidification of multicomponent alloys. While the treatment is still built on irreversible thermodynamics and linear kinetic law, its novelty lies in breaking up the classical trans‐interface diffusional flux into two separate fluxes one is the transferred‐back flux with its ending point at the interface and the other is the bumping‐back flux with its starting point at the interface. This novel treatment entails three significant improvements in reference to the existing models. Firstly, it reveals that the degree of solute drag is dependent on the ratio of liquid diffusive speed over interface diffusive speed. Secondly, a novel relation between the distribution coefficient and interface velocity is derived. It amends the confusing behavior seen in Aziz’s without‐drag continuous growth model. Thirdly, the proposed treatment eliminates the need of prescribing the degree of solute drag parameter for the kinetic phase diagram calculation. The numerical solution to the proposed model is presented, and it is ready to be used for the kinetic phase diagram calculation.

Irreversible thermodynamics and the ZT figure of merit for thermophotovoltaics

Irreversible thermodynamics and the <i>ZT</i> figure of merit for thermophotovoltaics

Constitutive modeling of functional fatigue with tension–compression asymmetry for superelastic NiTi shape memory alloy

Under cyclic loads, superelastic shape memory alloys (SMAs) exhibit stress–strain responses featured by functional fatigue, i.e., degradation of superelasticity and accumulation of irrecoverable deformation as cycling number increases, together with an asymmetry between tensile and compressive responses. Comprehensive understanding and modeling of these material complexities are crucial for the design and analysis of various superelastic SMA structures in practical applications. This work has developed a novel constitutive model based on irreversible thermodynamics to account for functional fatigue with tension–compression asymmetry. A potential function, defined as a weighted sum of two potentials that are calibrated against the tensile and compressive responses respectively, is employed to generate the asymmetric responses, and functional fatigue is represented by degradation of superelastic properties and growth of plastic strain as martensitic transformation accumulates. The model is adopted in numerical simulations for superelastic SMA tubes under cyclic lateral compression, which is experimentally investigated as a model problem. The agreement between simulations and experiments shows the validity and effectiveness of this constitutive modeling. Through additional finite element simulations incorporating this model, the effects of tension–compression asymmetry under cycling and diameter-to-thickness ratio of the tubular geometry upon mechanical responses of laterally compressed SMA tubes are also unveiled.

Dynamic density functional theory of polymers with salt in electric fields.

We present a dynamic density functional theory for modeling the effects of applied electric fields on the local structure of polymers with added salt (polymer electrolytes). Time-dependent equations for the local electrostatic potential and volume fractions of polymer, cation, and anion of added salt are developed using the principles of linear irreversible thermodynamics. For such a development, a field theoretic description of the free energy of polymer melts doped with salts is used, which captures the effects of local variations in the dielectric function. Connections of the dynamic density functional theory with experiments are established by relating the three phenomenological Onsager's transport coefficients of the theory to the mutual diffusion of electrolyte, ionic conductivity, and transference number of one of the ions. The theory is connected with a statistical mechanical model developed by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1958)] after relating the three transport coefficients to friction coefficients. The steady-state limit of the dynamic density functional theory is used to understand the effects of dielectric inhomogeneity on the phase separation in polymer electrolytes. The theory developed here provides not only a way to connect with experiments but also to develop multi-scale models for studying connections between local structure and ion transport in polymer electrolytes.

Effect of Coherent Nanoprecipitate on Strain Hardening of Al Alloys: Breaking through the Strength-Ductility Trade-Off.

So-called strength-ductility trade-off is usually an inevitable scenario in precipitation-strengthened alloys. To address this challenge, high-density coherent nanoprecipitates (CNPs) as a microstructure effectively promote ductility though multiple interactions between CNPs and dislocations (i.e., coherency, order, or Orowan mechanism). Although some strain hardening theories have been reported for individual strengthening, how to increase, artificially and quantitatively, the ductility arising from cooperative strengthening due to the multiple interactions has not been realized. Accordingly, a dislocation-based theoretical framework for strain hardening is constructed in terms of irreversible thermodynamics, where nucleation, gliding, and annihilation arising from dislocations have been integrated, so that the cooperative strengthening can be treated through thermodynamic driving force ∆G and the kinetic energy barrier. Further combined with synchrotron high-energy X-ray diffraction, the current model is verified. Following the modeling, the yield stress σy is proved to be correlated with the modified strengthening mechanism, whereas the necking strain εn is shown to depend on the evolving dislocation density and, essentially, the enhanced activation volume. A criterion of high ∆G-high generalized stability is proposed to guarantee the volume fraction of CNPs improving σy and the radius of CNPs accelerating εn. This strategy of breaking the strength-ductility trade-off phenomena by controlling the cooperative strengthening can be generalized to designing metallic structured materials.

Energy-Momentum Squared Gravity: A Brief Overview

In this work, we present a review of Energy-Momentum Squared Gravity (EMSG)—more specifically, f(R,TμνTμν) gravity, where R represents the Ricci scalar and Tμν denotes the energy-momentum tensor. The inclusion of quadratic contributions from the energy-momentum components has intriguing cosmological implications, particularly during the Universe’s early epochs. These effects dominate under high-energy conditions, enabling EMSG to potentially address unresolved issues in General Relativity (GR), such as the initial singularity and aspects of big-bang nucleosynthesis in certain models. The theory’s explicit non-minimal coupling between matter and geometry leads to the non-conservation of the energy-momentum tensor, which prompts the investigation of cosmological scenarios through the framework of irreversible thermodynamics of open systems. By employing this formalism, we interpret the energy-balance equations within EMSG from a thermodynamic perspective, viewing them as descriptions of irreversible matter creation processes. Since EMSG converges to GR in a vacuum and differences emerge only in the presence of an energy-momentum distribution, these distinctions become significant in high-curvature regions. Therefore, deviations from GR are expected to be pronounced in the dense cores of compact objects. This review delves into these facets of EMSG, highlighting its potential to shed light on some of the fundamental questions in modern cosmology and gravitational theory.

Investigation of the energy dissipation mechanism for centrifugal air compressor used for fuel cell based on CFD coupling with CIT

Effective evaluation indicator is the focus of air compressor structural optimization and development of control strategies, leaving to be further investigated from physical occurrence mechanism. Considering air expansion and compression, on the basis of coupling computational fluid dynamics (CFD) with classical irreversible thermodynamics (CIT), an extended entropy generation rate was established. Accordingly, various entropy generation rates for air compressor under wide operating conditions was investigated, aiming to what, where and how much the energy was dissipated. Results show that entropy generation rate related to air expansion and compression is always the largest contributor to the total entropy generation of the system under all operating conditions. A new dimensionless number R is defined to distinguish the fluid-related entropy generation rate and mechanical-related entropy generation rate. Furthermore, physical-based empirical models concerning the relationship of entropy generation rates, motor speeds and loads are proposed in this study, whose usage for guiding structural design was discussed. The work done in this paper can not only provide a new method for guiding the structural design of air compressors, but also providing a new idea for air compressor-fuel cell system’s optimal control.

Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model

In the literature, one can find numerous modifications of Fourier’s law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme’s stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics.

Dissipative fracton superfluids

We present a comprehensive study of hydrodynamic theories for superfluids with dipole symmetry. Taking diffusion as an example, we systematically construct a hydrodynamic framework that incorporates an intrinsic dipole degree of freedom in analogy to spin density in micropolar (spinful) fluids. Subsequently, we study a dipole condensed phase and propose a model that captures the spontaneous breaking of the U(1) charge. The theory explains the role of the inverse Higgs constraint for this class of theories, and naturally generates the gapless field. Next, we introduce finite temperature theory using the Hamiltonian formalism and study the hydrodynamics of ideal fracton superfluids. Finally, we postulate a derivative counting scheme and incorporate dissipative effects using the method of irreversible thermodynamics. We verify the consistency of the dispersion relations and argue that our counting is systematic.

Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time

Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time

Active interfacial degradation/deposition of an elastic matrix by a fluid inclusion: Theory and pattern formation

During collective invasion in 3D, cohesive cellular tissues migrate within a fibrous extracellular matrix (ECM). This process requires significant remodeling of the ECM by cells, notably proteolysis at the cell–ECM interface by specialized molecules. Motivated by this problem, we develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition. To account for the active nature of this process, we develop a continuum theory based on irreversible thermodynamics, leading to a kinetic relation for the degradation front that locally resembles the force–velocity relation of a molecular motor. We further study the effect of mechanotransduction on the stability of the cell–ECM interface, finding a variety of self-organized dynamical patterns of collective invasion. Our work identifies ECM proteolysis as an active process possibly driving the self-organization of cellular tissues.

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.

Dissipation in hydrodynamics from micro- to macroscale: wisdom from Boltzmann and stochastic thermodynamics

We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production, in particular, is a measure of the loss of many-particle correlations in the same way in which it measures the loss of system-reservoirs correlations in stochastic thermodynamics (ST). More specifically, we first show that boundary conditions at the macroscopic level define a natural decomposition of the entropy production rate (EPR) in terms of thermodynamic forces multiplying their conjugate currents, as well as a change in suitable nonequilibrium potential that acts as a Lyapunov function in the absence of forces. Moving to the microscale, we identify the exact identities at the origin of these dissipative contributions for isolated Hamiltonian systems. We then show that the molecular chaos hypothesis, which gives rise to the Boltzmann equation at the mesoscale, leads to a positive rate of loss of many-particle correlations, which we identify with the Boltzmann EPR. By generalizing the Boltzmann equation to account for boundaries with nonuniform temperature and nonzero velocity, and resorting to the Chapman–Enskog expansion, we recover the macroscopic theory we started from. Finally, using a linearized Boltzmann equation we derive ST for dilute particles in a weakly out-of-equilibrium fluid and its corresponding macroscopic thermodynamics. Our work unambiguously demonstrates the information-theoretical origin of thermodynamic notions of entropy and dissipation in macroscale irreversible thermodynamics.

Systems and Methods for Transformation and Degradation Analysis.

Modern concepts in irreversible thermodynamics are applied to system transformation and degradation analyses. Phenomenological entropy generation (PEG) theorem is combined with the Degradation-Entropy Generation (DEG) theorem for instantaneous multi-disciplinary, multi-scale, multi-component system characterization. A transformation-PEG theorem and space materialize with system and process defining elements and dimensions. The near-100% accurate, consistent results and features in recent publications demonstrating and applying the new TPEG methods to frictional wear, grease aging, electrochemical power system cycling-including lithium-ion battery thermal runaway-metal fatigue loading and pump flow are collated herein, demonstrating the practicality of the new and universal PEG theorem and the predictive power of models that combine and utilize both theorems. The methodology is useful for design, analysis, prognostics, diagnostics, maintenance and optimization.

Thermodynamics of Irreversible Processes: Fundamental Constraints, Representations, and Formulation of Boundary Conditions

Starting from the analysis of the lack of positivity of the Cattaneo heat equation, this work addresses the thermodynamic relevance of the positivity constraint in irreversible thermodynamics, that is at least as significant as the entropic constraints. The fulfillment of this condition in hyperbolic models leads to the parametrization of the concentration fields with respect to internal variables associated with the microscopic dynamics. Using Brownian motion theory as a landmark example for deriving macroscopic transport equations from the equations of motion at the particle/molecular level, we discuss two typical problems involving hydrodynamic interactions at the microscale: surface chemical reactions at a solid interface of a diffusing reactant, and mass-balance equations in a complex viscoelastic fluid, in which the physics of the interaction leads either to overcoming the parabolic diffusion model or to considering the parametrization of the concentration with respect to the degrees of freedom associated with the relaxation dynamics of the solvent fluid.

Modeling for time-dependent mechanical responses of rock based on irreversible thermodynamics

Modeling for time-dependent mechanical responses of rock based on irreversible thermodynamics

Mathematical Model for a Lithium-Ion Battery with a SiO/Graphite Blended Electrode Based on a Reduced Order Model Derived Using Perturbation Theory

Silicon oxide (SiO) is a promising anode material for high-energy lithium-ion batteries, as it is made from low-cost precursors, has a potential close to that of Li, and has high theoretical specific capacity. However, the applications of SiO are limited by the intrinsic low electrical conductivity, large volume change, and low coulombic efficiency, which often lead to poor cycling performance. A common strategy to address these shortcomings is to blend SiO with graphite active materials to form a composite anode for better capacity retention. In this work, we derive a reduced order model (ROM1) using perturbation theory. We employ the multi-site, multi-reaction (MSMR) framework of a composite porous electrode blend consisting of two lithium-host materials, SiO and graphite. The ROM1 model employs a single-particle model (SPM) approach as the leading-order solution and involves the numerical analysis of a single, nonlinear partial differential equation for each host material that describes diffusion by means of irreversible thermodynamics, wherein chemical-potential gradients are the driving forces for the diffusion. The first-order correction treats losses other than that of the SPM.

Finite element methods for multicomponent convection-diffusion

Abstract We develop finite element methods for coupling the steady-state Onsager–Stefan–Maxwell (OSM) equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Developing a variational formulation for discretizing these equations is challenging: the formulation must balance physical relevance of the variables and boundary data, regularity assumptions, tractability of the analysis, enforcement of thermodynamic constraints, ease of discretization and extensibility to the transient, anisothermal and nonideal settings. To resolve these competing goals, we employ two augmentations: the first enforces the definition of mass-average velocity in the OSM equations, while its dual modifies the Stokes momentum equation to enforce symmetry. Remarkably, with these augmentations we achieve a Picard linearization of symmetric saddle point type, despite the equations not possessing a Lagrangian structure. Exploiting structure mandated by linear irreversible thermodynamics, we prove the inf-sup condition for this linearization, and identify finite element function spaces that automatically inherit well-posedness. We verify our error estimates with a numerical example, and illustrate the application of the method to nonideal fluids with a simulation of the microfluidic mixing of hydrocarbons.

Numerical Analysis of Non-Fourier Model-Based Bio-Heat Transfer in the Laser-irradiated Axisymmetric Living Tissue.

The current work is related to the numerical investigation of non-Fourier heat transfer inside the short-pulsed laser-irradiated axisymmetric soft tissue phantom. It utilizes the modified discrete ordinate method to solve the transient radiative transfer equation (TRTE) for determining the intensity field. The laser energy absorbed by the soft tissue phantom behaves like a source in the Fourier/non-Fourier heat conduction model based-bio-heat transfer equation (BHTE), which is solved by employing the finite volume method (FVM) to determine the temperature distribution. Despite the prevalent use of non-Fourier BHTE for this purpose, a second law analysis is considered crucial to detect any potential anomalies. Equilibrium entropy production rates (EPR) are initially computed based on classical irreversible thermodynamics (CIT), which may yield negative values, possibly contravening the second law. Consequently, the EPR based on CIT is adjusted using the extended irreversible thermodynamics (EIT) hypothesis to ensure positivity. After that, the current research findings are compared with the results from the literature, and found good agreement between them. Then, the independent study is performed to select the optimum grid size, control angle size, and time step. A comparative analysis of results between the traditional Fourier and non-Fourier models has been performed. The impact of different parameters on the temperature fields and EPRs, is discussed. The effect of the optical properties of the inhomogeneity on the temperature distribution has been investigated. This study may help to enhance the effectiveness of the laser-based photo-thermal therapy.