Theory Of Irreversible Thermodynamics Research Articles

Strain-based anisotropic damage modelling and unilateral effects

A new continuum damage mechanics model is developed to describe the behaviour of quasi-brittle materials under general path loading. The induced damage is represented by a second rank symmetric tensor. The constitutive equations are based on irreversible thermodynamics theory. The strain-based model covers in an unified way the unsymmetrical behaviour in tension and in compression and the unilateral response due to crack closure effect. Uniaxial stress tests (in tension as in compression) show realistic non-linear responses in the stress–strain space. The different behaviour in both domains is covered by a single set of equations. A significant volume dilatation is noticed in compression. The model can be generalised to time-dependent phenomena.

Two-dimensional numerical simulation of thermo-gravitational convection in a vertical porous column filled with a binary fluid mixture

Convection has a very important effect on the thermal diffusion process in hydrocarbon porous media. We investigate the convection effect in a vertical cavity having an aspect ratio of 10 and subject to a lateral heating condition based on two-dimensional numerical simulation. Using the irreversible thermodynamics theory of Shukla and Firoozabadi [Ind. Engrg. Chem. Res. 37 (1998)], the space dependent thermal, molecular and pressure diffusion coefficients are calculated at each point of the grid as functions of the temperature, pressure and other properties of the mixture. The thermal diffusion process is simulated in a vertical porous media combined with natural convection flow over a range of permeability from 0.001 to 10 000 md. Numerical results reveal that the lighter fluid component migrates to the hot side of the cavity, and as the permeability increases, the component separation in the thermal diffusion, or Soret effect, process increases first, reaches its peak, and then decreases. This phenomenon is illustrated and discussed both numerically and physically.

Deformation Kinetics of Steady Creep in Sn/Pb Solder Alloys With Applications

AbstractIn this paper, a constitutive equation of steady creep rates:is derived based on a liaison of the theory of irreversible thermodynamics of continuous media with internal state variables (ISV); and the deformation kinetics. In steady creep, only one ISV is used, whose evolution equation is derived by the concepts of deformation kinetics, in which micromotions are generated by a group of atoms climbing over a tilted potential barrier of the highest height ε0.Applications of the constitutive equation in the cases of some Sn/Pb solder alloys-63Sn/37Pb, 60Sn/40Pb and 97.5Pb/2.5Sn under shear creep tests; and 98Pb/2Sn under tensile creep tests, show that the theoretical results can describe the experimental data quite well. These results pave the way for future research in the comparisons of creep resistance among solders with various Sn/Pb compositions and in the generalization of three-dimensional constitutive equation.

Cure kinetics, microheterogeneity, and mechanical properties of the high‐temperature cure of vinyl ester resins

AbstractA kinetic model has been developed that is based on the irreversible thermodynamic fluctuation theory, in which the conversion of comonomers is a function of the curing relaxation time, reaction time, and reaction temperature. This modified model permits a better prediction of the course of the high‐temperature cure reaction of vinyl ester (VE) resins under isothermal conditions. The microheterogeneity in cured resins was investigated through the measurement of the residual heat of isothermally cured samples with differential scanning calorimetry and through the observation of the fracture surfaces of samples under different cure conditions with scanning electron microscopy (SEM). The SEM photographs demonstrated the existence of clusters of microgels of about 20 μm in samples isothermally cured at 80°C for 3 h. The results of the dynamic mechanical thermal analysis of postcured samples verified the microheterogeneity in the cured samples and showed that the glass‐transition temperatures were not affected by the curing conditions. The effect of postcuring on the conversions of VE and styrene varied with the different cure schedules. The postcure for a sample isothermally cured at 80°C increased the tensile strength and flexural strength. On the contrary, the postcure for samples isothermally cured at 120°C reduced the tensile strength and flexural strength. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1124–1133, 2004

Analysis of Interfacial Damage and Debonding Life Estimation of Cold Forging Tool Coated with Hard Film

The behavior of the interface of a cold forging tool coated with a hard film is analyzed by the finite element method (FEM). The mechanical properties of the interface between a hard film and a tool material are modeled under the framework of the irreversible thermodynamic constitutive equation theory with continuum damage mechanics. The interface damage variable and its evolution law are introduced, which express the degradation of the interface. The hemispherical tool of SUJ2 in JIS coated with an electroplated coating of chromium indents into a cylindrical workpiece of S25C in JIS, which is performed to examine the validity of the proposed model. In FE analysis, the proposed constitutive equations are implemented by the nonlinear springs between opposite nodes of the interface. Calculated results show that the maximum interfacial normal displacement is observed close to the front of the lip of indentation, whereas maximum interfacial tangential displacement is observed close to the back of the lip of indentation. The region where debonding will first occur as indicated by the calculation results, is similar to the region of the behavior during an actual forging operation. Finally, a method of evaluating the interfacial debonding life of coated tools is proposed.

Diffusion of electrolytes in solution under gravitational forces

An equation was mathematically derived using the theory of irreversible thermodynamics for the diffusion of electrolytes in solution in the presence of an external gravitational force. It was demonstrated that diffusion coefficients of electrolyte species are dependent on the difference of radii and densities of anion and cation ionized from the electrolyte in solution. For a special case that radii and densities of the anion and cation are the same, the diffusion coefficient is independent of the external gravitational force. Entropy production was also estimated for the system under consideration. It was found that the rate of entropy production is proportional to the sum of the gravitational forces induced to all electrolyte species.

Relaxation phenomena in the Blume–Emery–Griffiths model near the critical and multicritical points

AbstractThe relaxation behaviour of the Blume–Emery–Griffiths (BEG) model Hamiltonian with bilinear and biquadratic nearest‐neighbour ferromagnetic exchange interaction and crystal field interactions is studied by using the molecular field approximation (MFA) and Onsager's theory of irreversible thermodynamics. First the equilibrium behaviour and the phase diagrams of the model in MFA are given briefly in order to understand the relaxation behaviour. Then, Onsager theory is applied to the model and the set of linear differential equations, which is also called the kinetic or rate equations, is obtained. By solving these equations a set of relaxation times is calculated and examined for temperatures near the critical and multicritical points. It is found that one of the relaxation times (τ1) is sharply cusped at the triple and critical points, whereas it approaches infinity near the critical‐end point. On the other hand, the other relaxation time (τ2) displays a jump‐discontinuity behaviour at the triple and critical points but it has a cusp at the critical‐end point. A maximum of τ2 has also been observed above the critical‐end point. Moreover, similar calculations are performed for non‐zero magnetic field (H) to investigate the effect of H on relaxation times. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermal diffusion of radon in porous media.

Based on the non-intersection model of cylindrical capillaries, the mean radius of the pores of some soils and building materials are estimated. In size, the above-mentioned radii are usually of the order of the free path of gas molecules at atmospheric pressure. A review of pore size distribution data also reveals that a large fraction of concrete pores belong to Knudsen's region. This fact indicates that the thermal gradient in these media must cause gas (radon) transport. The interpretation of the experimental data concerning the rate of emanation of 222Rn from a concrete-capped source subjected to a sudden increase in temperature is given, based on irreversible thermodynamics theory. The calculations given here for radon flux, caused by concentration and thermal gradients, are in satisfactory agreement with the experimental data. It is shown that thermodiffusion can significantly contribute to radon flux in concrete. The need to include the thermodiffusion radon flux in the radon entry model is discussed.

Weakly nonlocal irreversible thermodynamics

Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.

Weakly nonlocal irreversible thermodynamics

AbstractWeakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer‐Krumhansl, Ginzburg‐Landau and Cahn‐Hilliard type equations.

Critical behaviors of the sound attenuation in a spin-1 Ising model

Critical behaviors of the sound attenuation in a spin-1 Ising system with bilinear (J) and biquadratic (K) interactions are investigated within the framework of cluster variation method and Onsager theory of irreversible thermodynamics. The sound wave is assumed to couple mainly to the order parameter fluctuations which decay via order parameter relaxation processes. Two relaxation times are obtained and an expression is found for the sound attenuation coefficient (α) in terms of these relaxation times. The temperature behavior of the sound attenuation near the phase transition temperatures (Tc) is analyzed according to various values of Onsager coefficients (γij) and sound frequency (ω). For T<Tc it is found that the maxima of the attenuation shifted to lower temperatures with increasing ω and γij (i≠j) values. For T>Tc the data give evidence that there is no relaxational contribution to sound attenuation coming from order parameter fluctuations. On the other hand, a convergence is found in attenuation just below the critical and the tricritical points as (Tc−T), while a jump-discontinuity is observed for the first-order behavior. The frequency variation of the sound attenuation is also investigated and in addition to ω2-attenuation dependence observed in the hydrodynamic regime it is observed that in the high frequency region the attenuation is independent of ω and the ratio of two interaction parameters (J/K).

Entropy production and exergy loss in experimental distillation columns

Diabatic distillation, i.e. with heat exchangers on all trays, can increase the second law energy efficiency drastically compared to adiabatic distillation. The purpose of this research was to describe the entropy production rate in one adiabatic and one diabatic experimental water/ethanol rectifying column by applying the theory of irreversible thermodynamics. As a benchmark for the description, an exergy analysis of the two columns was used. This analysis showed that the diabatic column looses 39% less exergy than the adiabatic column. Heat and mass transfer on the trays and in the heat exchangers determined the entropy production rate, and neither pressure drop nor mixing effects played a large role in these columns. The significance of this work is the experimental confirmation of the theory on diabatic distillation.

Sound dispersion in a spin-1 Ising system near the second-order phase transition point

Sound dispersion relation is derived for a spin-1 Ising system and its behaviour near the second-order phase transition point or the critical point is analyzed. The method used is a combination of molecular field approximation and Onsager theory of irreversible thermodynamics. If we assume a linear coupling of sound wave with the order parameter fluctuations in the system, we find that the dispersion which is the relative sound velocity change with frequency behaves as ω 0 ε 0, where ω is the sound frequency and ε the temperature distance from the critical point. In the ordered region, one also observes a frequency-dependent velocity or dispersion minimum which is shifted from the corresponding attenuation maxima. These phenomena are in good agreement with the calculations of sound velocity in other magnetic systems such as magnetic metals, magnetic insulators, and magnetic semiconductors.

OSMOTIC DEHYDRATION OF FOODS: MASS TRANSFER AND MODELING ASPECTS

Biological materials contain a variety of individual soluble components. When cellular biological materials are immersed in osmotic solution, multicomponent mass transfer occurs, which ultimately leads to the loss of water from the food, or osmotic dehydration. Mass transfer of food constituents during osmotic dehydration may cause changes in food quality in terms of nutritional value, texture, color, and taste. The aspects that are important for mass transfer modeling are the driving force and the physical properties of cell units and tissue matrix of cellular material. The complex cell wall structure of cellular material acts as a semipermeable membrane, resulting in two simultaneous and countercurrent flows in the biological tissue: water transfer out of material tissue and transfer of the solute from the osmotic solution into the cellular tissue. When the cells remain intact, the chemical potential of water is the main local driving force for mass transfer towards the free intercellular spaces. At the same time, volume changes in the cellular tissue occur throughout the process after immersion in osmotic solution. Diffusion, osmotic processes, flux interactions, and tissue shrinkage should all be taken into account for accurate description of the mass transfer phenomena during osmotic dehydration. The mass transfer process has been modeled based on the theories of Fickian diffusion, irreversible thermodynamics, multicomponent diffusion, and hydrodynamic flow. The use of vacuum or pulsed vacuum has an effect on mass transfer, which reveals the effect of material structure property on mass transfer. Evaluation of the long-term equilibrium and the distribution of the phases in the tissue provide a better understanding of the phenomena that control the mass transfer processes in osmotic dehydration. It is important to link microstructural investigations with the processing parameters during osmotic dehydration, and the compositional and mechanical characteristics of the tissues. Knowledge of the structural characteristics of the materials and the relationship between all components in the mass transfer process needs to be further understood.

Measurement of electrokinetics in cake filtration

This paper addresses the role of the free surface charge in cake filtration with main emphasis on a new method to study electrokinetic effects in cake filtration by streaming current measurement. The method is based on the assumption that electrolyte- and cake resistance are purely ohmic, which allow a relationship between streaming current and measured current to be established. It is shown that streaming current can be found from the slope of the inverse measured current vs. the filtrate volume. The streaming current in combination with the theory of irreversible thermodynamics permits the effect of free surface charge on cake filtration to be quantified in terms of phenomenological filtration parameters, which allow electrokinetic filtration phenomena like electroviscous flow reduction to be distinguished from flow reduction cause by structural changes in the filter cake. In the present study the method is demonstrated on filtration of anatase titanium oxide particles.

Equilibrium properties and surface transfer coefficients from molecular dynamics simulations of two-component fluids

Abstract We report equilibrium and non-equilibrium molecular dynamics studies of an ideal and a non-ideal mixture of Lennard–Jones spline particles. Soave–Redlich–Kwong type equations of state for the vapor phases, and Clausius–Clapeyron type fits for the phase line were determined for the systems. The ideal mixture, that was made up by isotopes, had the same equilibrium properties as the pure component fluid. The isotope mixture was chosen for method development purposes, since its one-component system was known. The equilibrium properties were used to determine the position of the surface under non-equilibrium conditions, and thereafter the thermodynamic driving forces for transport of mass and heat. The temperatures and pressures were such that the systems on the average were closer to the critical line than to the triple line. It was shown that irreversible thermodynamic theory can be used to describe the transport phenomena. Non-zero coupling coefficients are essential in the description, since in the cases we studied, one component was transported against its main driving force. The surface transfer coefficients were next determined, using the composition and temperature variation in kinetic theory. The main coefficients of transfer that were derived, differed from the coefficients that were calculated from kinetic theory by a factor between 1.5 and 5, both systems considered, while the coupling coefficients differed much more. It was also found, in contrast to the results of kinetic theory, that the coupling coefficient(s) for heat and mass transfer were most of the time negative. This is unexpected, at least for the isotope mixture that behaves thermodynamically as a one-component system. On the average for the cases studied, the thermal resistivity of the non-ideal mixture was smaller, while the resistivities to mass transport were larger than those of the ideal mixture.

Weakly nonlocal irreversible thermodynamics—the Guyer–Krumhansl and the Cahn–Hilliard equations

Examples of irreversible thermodynamic theory of nonlocal phenomena are given, based on generalized entropy current. Thermodynamic currents and forces are identified to derive the Guyer-Krumhansl and Cahn-Hilliard equations. In the latter case Gurtin's rate dependent additional term is received through the thermodynamic approach.

Phenomenological modeling and numerical simulation of different modes of creep damage evolution

This paper deals with a numerical analysis of creep components until failure. We will take an interest in the macroscopic modeling of the creep curves with its three stages based on the irreversible thermodynamics theory with internal variables. A “unified” viscoplastic model is used to describe primary and secondary creep behaviors, and the tertiary creep description is based on the introduction of a scalar damage variable and the nonlinear effects of changes in geometry. Therefore, viscoplastic damage models in nonlinear geometry are defined in order to describe different modes of creep damage development. The numerical properties of the models allow us to obtain a different crack growth development, in order to know the post-critical behavior and the damage development until failure. The numerical treatment uses the finite element method and the large time increment method in a version adapted to solve nonlinear problems with geometrical nonlinearities, in order to obtain a rapid creep life assessment.

Maximum Specific Work for Power Optimized Endoreversible Gas Turbine Cycles

As a Carnot-like cycle the continuous Ericsson cycle represents the upper efficiency limit of multistage gas turbine operations using intercooling, reheating and regeneration. When considering linear external heat transfer modes, the theory of irreversible thermodynamics for continuous endoreversible Carnot-like cycles gives rise to an optimum efficiency at maximum power output of β= 1 — ( T L/ T H)0.5 in contrast to the upper limit of β = 1 — ( T L/ T H) obtained from classical thermodynamics for ideal Carnot-like cycles. It is shown here that, additionally, for continuous (gas turbine) endoreversible cycles like Carnot and Ericsson, the optimum specific work output at maximum power ( wopt), is exactly half of that obtained for externally reversible cycles (Carnot work, wrev ) operating between the same temperature limits (i.e. wopt = 1/2 wrev). Moreover, this optimum specific work output is the same expression for these and a family of other continuous cycles. The formulation used in the analysis makes use of the ideal gas model with constant specific heats, though the results are shown to be universal for cycles using linear heat transfer laws and using vapours and real gases having specific heats that vary only as a function of temperature. Also given for the first time for this general family of cycles are expressions for power optimized mass flow rates and the cycle operating temperatures which yield optimum power. These results quantify the absolute upper power limit for power optimized gas turbine operations where the external heat transfer is by linear modes.

Power optimized work limit for internally irreversible reciprocating engines

The theory of irreversible thermodynamics for reciprocating externally irreversible cycles gives rise to an optimum efficiency at maximum power output of η=1−( T L / T H ) 0.5 for internally reversible Carnot cycles, in contrast to the upper limit for Carnot cycles of η=1−( T L / T H ) obtained from classical thermodynamics. It is shown here in addition, for the internally irreversible reciprocating Carnot cycle using linear heat transfer modes, that the optimum work output at maximum power ( W opt ) is less than (and in the limit of no internal irreversibility is equal to) exactly one-half of the work potential of the externally reversible cycle operating at maximum thermal efficiency (Carnot work, W rev ) between the same temperature limits (i.e., W opt⩽ 1 2 W rev ). To accomplish this the analysis goes one step further than earlier works to make use of time symmetry to minimize overall cycle time and thus better optimize overall cycle power. Because this novel procedure implies the concurrent use of first and second laws of thermodynamics, it automatically ensures optimal allocation of thermal conductances at the hot and cold ends while simultaneously achieving both minimization of internal entropy generation and maximization of specific cycle work. Based on linear heat transfer laws, this expression for optimum work is shown to be independent of heat conductances.