Relativistic Theory of Irreversible Thermodynamics for Multi-Component Fluids and Its Post-Newtonian Limit in Relation to Classical Extended Thermodynamics

2020 ◽  
Vol 45 (2) ◽  
pp. 133-153
Author(s):  
Thoralf Chrobok ◽  
Horst-Heino von Borzeszkowski
Keyword(s):  
Relativistic Theory ◽  
Particle Number ◽  
Thermodynamic Description ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamics ◽  
Newtonian Limit ◽  
Irreversible Processes ◽  
Total System ◽  
Gibbs Equation ◽  
Physical Consequences

AbstractFirst, the special-relativistic Theory of Irreversible Processes for a multi-component fluid is formulated. It is based on (i) the balance equations of the particle number and the energy-momentum for the total system (i. e., the mixture of the components) as well as the sub-systems (i. e., the components) and (ii) the dissipation inequality and the Gibbs equation for the mixture. In order to allow for reactions between the single components, in contrast to the total system, the sub-systems are assumed to be open, which means that their particle number and energy-momentum are not constrained by conservation laws. Without making any assumptions on the thermodynamic behavior of the interacting components, one arrives at a thermodynamic description of the mixture showing now heat conduction and viscosity. In particular, this makes it possible to calculate the entropy production and, thus, to identify thermodynamic currents and forces. In a second part, the post-Newtonian limit of this theory is calculated to show that for the mixture there result relations known from classical Extended Thermodynamics that partly are corrected by entrainment terms. The mathematical origin and physical consequences of these terms are discussed.

An overview of entropy principle

2021 ◽  
pp. 1-6
Author(s):  
I-Shih Liu
Keyword(s):  
Mathematical Formulation ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamics ◽  
Basic Assumptions ◽  
Entropy Principle ◽  
Linear Irreversible Thermodynamics

A brief overview of the development from classical linear irreversible thermodynamics to the modern rational thermodynamics with Coleman–Noll and Müller–Liu procedures is presented, emphasizing the basic assumptions and formulation details. The major arguments concerned are the improvement of physical assumptions and mathematical formulation differences. Extended thermodynamics is also briefly commented.

Shock-Induced Chemical Reactions in Multi-Functional Structural Energetic Intermetallic Nanocomposite Mixtures

Aerospace ◽  
2005 ◽  
Author(s):  
V. Narayanan ◽  
X. Lu ◽  
S. Hanagud
Keyword(s):  
Metal Oxides ◽  
Chemical Reactions ◽  
Energetic Materials ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Irreversible Thermodynamics ◽  
Irreversible Processes ◽  
Finite Difference Schemes ◽  
Dual Functional ◽  
Metal Metal

Shock induced chemical reactions of intermetallics or mixtures of metal and metal-oxides are also used to synthesize new materials with unique phases and microstructures. These materials are also of significant interest to the energetics community because of the significant amount of heat energy released during chemical reactions when subjected to shock and/or thermal loading. Binary energetic materials are classified into two categories— metal/metal oxides and intermetallics. When these materials are synthesized at a nano level with binders and other structural reinforcements, the strength of the resulting mixture increases. Thus, these materials can be used as dual-functional binary energetic structural materials. In this paper, we study the shock-induced chemical reactions of intermetallic mixtures of nickel and aluminum of varying volume fractions of the constituents. The chemical reaction between nickel and aluminum produces different products based on the volume fraction of the starting nickel and aluminum. These chemical reactions along with the transition state are modeled at the continuum level. In this paper, the intermetallic mixture is impact loaded and the subsequent shock process and associated irreversible processes such as void collapse and chemical reactions are modeled in the framework of non-equilibrium thermodynamics. Extended irreversible thermodynamics (EIT) is used to describe the fluxes in this system and account for the associated irreversible processes. Numerical simulations of the intermetallic mixture are carried out using finite difference schemes.

scholarly journals QUADRATIC REHEATING

1999 ◽  
Vol 08 (03) ◽  
pp. 307-323 ◽  
Author(s):  
LUIS P. CHIMENTO ◽  
ALEJANDRO S. JAKUBI
Keyword(s):  
Entropy Production ◽  
Linear Model ◽  
Particle Number ◽  
Equilibrium Mixture ◽  
Irreversible Thermodynamics ◽  
Decay Rates ◽  
Inflaton Field ◽  
Inflationary Scenario ◽  
Self Consistent ◽  
Reheating Process

The reheating process for the inflationary scenario is investigated phenomenologically. The decay of the oscillating massive inflaton field into light bosons is modeled after an out of equilibrium mixture of interacting fluids within the framework of irreversible thermodynamics. Self-consistent, analytic results for the evolution of the main macroscopic magnitudes like temperature and particle number densities are obtained. The models for linear and quadratic decay rates are investigated in the quasiperfect regime. The linear model is shown to reheat very slowly while the quadratic one is shown to yield explosive particle and entropy production. The maximum reheating temperature is reached much faster and its magnitude is comparable with the inflaton mass.

scholarly journals Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 46
Author(s):  
Dick Bedeaux ◽  
Signe Kjelstrup
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Control Volume ◽  
Thermodynamic Description ◽  
Flow In Porous Media ◽  
Gibbs Equation ◽  
Shape Dependence ◽  
Fluctuation Dissipation ◽  
Weakly Coupled ◽  
Multi Phase

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed.

scholarly journals A Unified Extended Thermodynamic Description of Diffusion, Thermo-Diffusion, Suspensions, and Porous Media

2005 ◽  
Vol 73 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Georgy Lebon ◽  
Thomas Desaive ◽  
Pierre Dauby
Keyword(s):  
Porous Media ◽  
Evolution Equations ◽  
Diffusion Flux ◽  
Thermodynamic Description ◽  
Fluid Flows ◽  
Irreversible Thermodynamics ◽  
Heat Fluxes ◽  
Flows In Porous Media ◽  
Extended Thermodynamic ◽  
Higher Order Terms

It is shown that extended irreversible thermodynamics (EIT) provides a unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier, Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.

Irreversible Thermodynamic Description of Domain Occurrences in Ferroics

2012 ◽  
Vol 560-561 ◽  
pp. 140-144
Author(s):  
Yuan Zhen Cai
Keyword(s):  
Phase Transitions ◽  
Entropy Production ◽  
Stationary State ◽  
Thermodynamic Description ◽  
Irreversible Thermodynamic ◽  
Irreversible Thermodynamics ◽  
Minimum Entropy ◽  
Spatial Symmetry ◽  
Domain Structures ◽  
Minimum Entropy Production

Based on the irreversible thermodynamics, a irreversible thermodynamic description of domain occurrences in ferroics such as ferroelectrics, ferromagnetics and ferroelastics was given. The ferroic domain structures occur at the ferroic phase transitions from the prototype phases to the ferroic phases. The processes of transition are stationary state processes so that the principle of minimum entropy production is satisfied. The domain occurrences are a consequence of this principle. The time-spatial symmetry related to the domains and their occurrences was also expounded.

scholarly journals Erroneous or Arrhenius: A Degradation Rate-Based Model for EPDM during Homogeneous Ageing

Polymers ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2152
Author(s):  
Maha Zaghdoudi ◽  
Anja Kömmling ◽  
Matthias Jaunich ◽  
Dietmar Wolff
Keyword(s):  
Activation Energy ◽  
Stress Relaxation ◽  
Degradation Rate ◽  
Irreversible Processes ◽  
Total System ◽  
Chemical Relaxation ◽  
Additive Contribution ◽  
Superposition Technique ◽  
Physical And Chemical

To improve the predictive capability of long-term stress relaxation of elastomers during thermo-oxidative ageing, a method to separate reversible and irreversible processes was adopted. The separation is performed through the analysis of compression set after tempering. On the basis of this separation, a numerical model for long-term stress relaxation during homogeneous ageing is proposed. The model consists of an additive contribution of physical and chemical relaxation. Computer simulations of compression stress relaxation were performed for long ageing times and the results were validated with the Arrhenius treatment, the kinetic study and the time-temperature superposition technique based on experimental data. For chemical relaxation, two decay functions are introduced each with an activation energy and a degradative process. The first process with the lower activation energy dominates at lower ageing times, while the second one with the higher activation energy at longer ageing times. A degradation-rate based model for the evolution of each process and its contribution to the total system during homogeneous ageing is proposed. The main advantage of the model is the possibility to quickly validate the interpolation at lower temperatures within the range of slower chemical processes without forcing a straight-line extrapolation.

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