Classical Thermodynamic Approach Research Articles

A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite

Coupling between initial and damage-induced anisotropies in 3D elastic damaged materials has been so far addressed by homogenization techniques only for particular microcracks configurations. The main difficulty in developing a general 3D micromechanical model lies in the lack of closed-form solutions of the Eshelby tensor corresponding to cracks arbitrarily oriented in an elastic anisotropic medium. In this study, we begin to present analytical expressions of the Eshelby tensor S (equivalently the Hill tensor P) that we derived for a cylindrical crack embedded in an orthotropic material. The obtained expressions reduce to existing results in the 2D case or in particular 3D cracks configurations. The effective compliance of the orthotropic medium containing arbitrarily oriented cracks is then derived by using the newly derived expressions of the Eshelby tensor. Finally, a damage model is formulated by combining the above results with classical thermodynamics approach. The ability of the model to capture coupling between initial orthotropy and damage induced anisotropy is demonstrated through a comparison with experimental data available for a ceramic matrix composite (unidirectional SiC–SiC).

Nonlinear Thermoelastic Materials with Viscosity, and Subject to Internal Constraints: A Classical Continuum Thermodynamics Approach

A general approach to continuum thermodynamics that was advocated by R.S. Rivlin is carried out for thermoelastic materials which can also depend on strain rate. An entropy function is constructed (rather than assumed to exist). A method for treating thermomechanical internal constraints for such materials is also presented. In this method, the properties of a constrained material are inherited from those of a related equivalence class of unconstrained materials.

Comparison of exergy found by a classical thermodynamic approach and by the use of the information stored in the genome

It is possible to calculate the exergy for organisms based on classic thermodynamics as already demonstrated by Mejer and Jorgensen [Mejer, H., Jorgensen, S.E., 1979. Exergy and ecological buffer capacity. State-of-the-art in Ecol. Model. 7, 829–846]. The calculation of exergy as eco-exergy, which is based on the information stored in the genome, has lately been proposed by Jørgensen and co-workers. Recently, Ludovisi [Ludovisi, A., 2009. Exergy vs information in ecological successions: interpreting community changes by a classical thermodynamic approach. Ecol. Model. 220, 1566–1577] has put forward a method based on classical thermodynamics, which leads to the calculation of “virtual” values of concentration at equilibrium for a number of organic compounds ( VEC) and freshwater organisms ( VECE). This paper compares the two approaches by analysing the correlation existing between the VECE- and the β-values derived by Jørgensen et al. [Jørgensen, S.E., Ladegaard, N., Debeljak, M., Marques, J.C., 2005. Calculations of exergy for organisms. Ecol. Model. 185, 165–175]. It was found that there was a good correlation, which can be useful for estimating β-values for organisms whose genome is not known in a sufficient detail. The relationship between VECE- and β-values suggests that two proposed thermodynamic orientors based on these quantities – the eco-exergy index and the structural information – should lead to coherent results when applied to the evaluation of the development state of ecosystems. A numerical simulation shows that this expectation is verified in a major case, but also that different, even opposite, responses can arise, depending on the biological composition of the biocoenosis investigated.

Exergy vs information in ecological successions: Interpreting community changes by a classical thermodynamic approach

This work proposes a methodology based on classical thermodynamics, which allows the variation in ecosystem composition to be interpreted within the framework of the exergy concept. The basic equation of exergy [Mejer, H., Jorgensen, S.E., 1979. Exergy and ecological buffer capacity. State-of-the-art in Ecological Modelling 7, 829–846] was decomposed into three terms – size ( C), structural information ( I) and concentration ( X) – and their significance as indicators of ecosystem state was evaluated by simulating different scenarios of development in a simplified freshwater ecosystem. In order to calculate the exergy terms, the most critical issue in using exergy in an ecological context, i.e. the estimate of reference equilibrium values for organic matter and organisms, had to be faced. With this aim, the equations of classical thermodynamics in solution were applied, and “virtual” values of concentration at equilibrium were calculated for a number of organic compounds ( VEC) and freshwater organisms ( VECE). The results of the simulation showed that, whereas exergy and the exergy terms inherently connected with the a-biotic component varied consistently with the incorporation of biomass into the ecosystem, the structural information of the biotic component followed different, even opposite, pathways of variation, which were dependent only on the change in the size spectrum of the community. Due to the strict dependence of the VECE values on organism size, the increase of structural information with increasing abundance of large and complex species is also consistent with the general pattern of succession delineated by the classical r– K model. S tructural information is therefore proposed as an indicator of the development state, as well as an ecological orientor, whose maximisation is expected during ecosystem development. However, since an increase in structural information is not necessarily accompanied by an increase in exergy, a sort of “antagonism” between these two related orientors emerges, whose resolution may contribute to shed light on the fundamental forces which drive ecosystem development.

The Third Principle of thermodynamics and the zero-point entropy of glasses: History and new developments

A survey is given on the historical development of ideas, concerning the Third Principle of thermodynamics and the thermodynamic nature of glasses. The classical thermodynamic approach of Nernst, Einstein and Planck is given in its development together with the way thermodynamics of irreversible processes is treating the kinetics of glass-transition. It is shown that both these classical ideas and the generic application of non-equilibrium thermodynamics determine the non-zero value of the zero-point entropy of glasses and the value of the other frozen-in thermodynamic functions of glass, their dependence on cooling rate and on glass structure. For many years glass science was governed by ideas, formulated 80 years ago by F. Simon: glasses as non-equilibrium, non-thermodynamic systems do not obey the classical requirements of the Third Principle. It is shown here that in fact glasses and most probably any other frozen-in systems, every non-equilibrium body, follow the Third Principle, although in a particular way. In glasses a considerable amount of configurational entropy is frozen-in and this statement is confirmed by experiment. The frozen-in value of the configurational entropy, determining substantially the properties of a glass, does not prevent vitrified systems to follow the requirements of a sufficiently generally formulated version of the Third Principle (different from the formulation commonly assigned to Planck), in the same way as matter in non-equilibrium states follows the requirements (again in a specific way) of both the Second and the First Principles of thermodynamics. It is shown, that calorimetric determinations, vapor pressure measurements, dissolution kinetics, the analysis of volume properties and the viscosity course upon vitrification directly demonstrate the existence of a frozen-in configurational entropy of glasses and its dependence on the vitrification kinetics.

Derivation of Azizian–Volkov (AV)-isotherm based on statistical thermodynamics

The Azizian–Volkov (AV)-isotherm is a general isotherm for gas adsorption with two different states of an adsorbate. It has been derived previously by a classical thermodynamic approach. The new AV-isotherm gives the possibility to analyze multi and single centered adsorption and the interfacial structure in a general case. The AV-isotherm takes into account the interaction between adsorbed molecules and adsorbent and provides information about the orientation of adsorbates. Traditional isotherms (Henry, Langmuir, and Frumkin) for homogeneous adsorption can be derived from the AV-isotherm. In the present work the AV-isotherm is derived using statistical thermodynamics. This derivation provides a stronger basis for this isotherm. A new concept of the important parameter ( η) of AV-isotherm is obtained. Finally, the AV-isotherm was simplified and its application was justified by analysis of the equilibrium data of a numerically generated and experimental systems.

On the Gibbs conditions of stable equilibrium, convexity and the second-order variations of thermodynamic potentials in nonlinear thermoelasticity

The Gibbs conditions of stable thermodynamic equilibrium are formulated for nonlinear thermoelastic materials, based on the constrained minimization of four fundamental thermodynamic potentials. Sufficient conditions for incremental stability are stated in each case. The previously unexplored connections between the second-order variations of thermodynamic potentials are used to establish the convexity or concavity properties of all thermodynamic potentials in relation to each other, and to derive the relationships between the specific heats at constant stress and deformation, and between the isentropic and isothermal elastic moduli and compliances. The comparison with the derivation based on the classical thermodynamic approach is also given.

Classical thermodynamic approach to void nucleation in irradiated materials

One of the major problems in building a future fusion power station is the development of suitable structural materials. These materials will be exposed to high energy neutron bombardment, with consequent changes in their mechanical properties – embrittlement, hardening and swelling, for example. A missing link in modelling these effects is an effective treatment of the nucleation of voids under irradiation. These voids are initially stabilised by transmutation helium but, once formed, grow by vacancy accumulation. In this paper, a quasi-chemical model is developed to calculate the entropy of a steel/helium system. Although a substantial contribution from quasi-chemical effects might be expected, the steady state concentrations of dissolved helium are found to be too low for such effects to manifest. The steady state concentration of dissolved helium is low in absolute terms, but the resulting supersaturation is very high, making it reasonable to assume that all available nucleation sites are instantaneously activated.

Modeling gas hydrate equilibria in electrolyte solutions

Virtually all gas hydrate models use a statistical thermodynamic approach to describe solid phase gas hydrates. An alternative to this model is a “solid solution” model based on classical thermodynamics. Various models are used to describe associated gas phase and aqueous electrolyte properties. None of the electrolyte models, however, are state-of-the-art with respect to gas/electrolyte interactions. The objectives of this work were to (1) develop a classical thermodynamic approach for gas hydrate equilibria, (2) incorporate these hydrate chemistries into a state-of-the-art electrolyte model, and (3) validate the gas hydrate/electrolyte model. The model used the Pitzer approach to estimate as functions of temperature and pressure: (1) activity coefficients for cations, anions, and soluble gases, and (2) the activity of water. This model explicitly considers interactions between soluble gases and electrolytes. The Duan model was used to characterize the gas phase. Solubility products were calculated for CH 4⋅6H 2O ( T = 180 – 298 K ) and CO 2⋅6H 2O ( T = 180 – 283 K ) . A “solid solution” model was used to define mixed CH 4–CO 2 gas hydrates. Model fits to electrolyte/gas hydrate experimental data were an improvement over previously published models. For example, average errors for four salt–CO 2⋅6H 2O systems were reduced from 7.2 ( ± 4.1 ) % to 3.0 ( ± 1.8 ) % . Similarly, average errors for 13 salt–CH 4⋅6H 2O systems were reduced from 4.3 ( ± 1.1 ) % to 3.0 ( ± 0.6 ) % . The results of this work demonstrate the critical importance of the electrolyte component in gas hydrate models.

Studying thermodynamics of metastable states

Simple classical thermodynamic approach to the general description of metastable states is presented. It makes it possible to calculate the explicit dependence of the Gibbs free energy on temperature, to calculate the heat capacity, the thermodynamic barrier, dividing metastable and more stable states, and the thermal expansion coefficient. Thermodynamic stability under mechanical loading is considered. The influence of the heating (cooling) rate on the measured dynamic heat capacity is investigated. A phase shift of the temperature oscillations of an ac heated sample is shown to be determined by the relaxation time of the relaxation of the metastable nonequilibrium state back to the metastable equilibrium one. This dependence allows one to calculate the relaxation time. A general description of the metastable phase equilibrium is proposed. Metastable states in AB3 alloys are considered. Reasons for the change from the diffusional mechanism of the supercritical nucleus growth to the martensitic one as the heating rate increases are discussed. The Ostwald stage rule is derived.

Thermodynamic analysis of liquid desiccants

Liquid desiccants are widely used in many solar applications. In order to analyze the performance of the system using desiccant technology, the thermophysical properties of desiccants are essential. In particular, the vapor pressure of the liquid desiccant is one of the important properties in air dehumidification. In this paper, an attempt is made to predict this property based on a classical thermodynamics approach and it is found that the predicted values for lithium chloride agree very well with the experimental results. The desired sorption properties can also be obtained by mixing the desiccants, which is another method of developing a new cost-effective liquid desiccant. In this paper, simple mixing rules are used to predict the vapor pressure, density, and viscosity of the desiccant mixture, namely calcium chloride and lithium chloride. It is found that the interaction parameter need not be included in calculating the density and vapor pressure of the above mixture but must be included in predicting the viscosity.

Structure of Gaseous Detonation Waves and Chemical Kinetics

The tridimensional unsteady character of the flow field for detonations has been established about thirty years ago. The shock pattern is rather complex and the complete description of the phenomenon remains beyond the power of fast computer even today. However the classical thermodynamic approach allows to grasp what are the dominating factors of the whole process: leading shock inducing an exothermic reaction governed by the chemical kinetic mechanism of the heat release. The dynamics of gaseous detonation is coupled therefore closely to the rate of the heat release which in turn influences the time-dependent shock structure of the front. Measurements of the detonation velocity (D) are close to the values of the Chapman-Jouguet model of a detonation which is based on full thermodynamic equilibrium. But, the structure as evidenced from the soot records is more sensitive to the initial conditions :pressure, equivalence ratio, diluent nature and percentage, as well as the type of fuels, promoters and inhibitors of combustion processes. From systematic measurements of the length (L) of the detonation cell imprinted on soot for several mixtures, it has been possible to demonstrate the promoting role of hydrogen, and the inhibiting role of halocarbons on the detonation of CO/O2/Ar mixtures. Some detailed studies of OH emission, shock velocity of the unsteady leading shock, pressure inside a cell have shown the self-similar character of the flow field inside one cell. It demonstrates that the detonation phenomenon can be viewed as a periodic reinitiation of reactive shocks at a frequency identical to the reciprocal of the characteristic time as defined by the ratio: L/D. Irregular cell structure can occur in more complex mixtures such as CH4/O2. In that case the higher values of the activation energy of the conversion process induce a much higher sensitivity to the elaborate temperature fluctuations of the flow field. More recently, numerical simulations have allowed to model the unsteady bidimensional model of a detonation. The following papers could be referred to for more details about this approach of the gaseous detonations: -J.C.LIBOUTON, M.DORMAL, and P.J.VAN TIGGELEN, Progress in Astronautics and Aeronautics, Vol. 75 pp 358-369 (1981) -P.J.VAN TIGGELEN et J.C.LIBOUTON, Annales de Physique, Vol. 14 pp 649-660 (1989) -M.H.LEFEBVRE, E.S.ORAN, K.KAILASANATH, and P.J.VAN TIGGELEN, Progress in Astronautics and Aeronautics, Vol. 153 pp 64-76 (1992) -M.H.LEFEBVRE, E.S.ORAN, K.KAILASANATH,and P.J.VAN TIGGELEN, Combustion and Flame Vol. 95 pp 206-218 (1993).

Imaging through inhomogeneous media using time reversal mirrors

In this work, we present a new method for the design of heat flux manipulating devices, with emphasis on their manufacturability. The design is obtained as solution of a nonlinear optimization problem where the objective function represents the given heat flux manipulation task, and the design variables define the material distribution in the device. In order to facilitate the fabrication of the device, the material at a given point is chosen between two materials with highly different conductivity. By this way, the whole device can be seen, in the large scale, as a metamaterial having a specific anisotropic effective conductivity. As an application example, we designed a heat flux inverter which was so simple that it could be hand-made. The performance of this device for heat flux inversion was experimentally tested, proving that it was more efficient than a more complex device designed using the classical transformation thermodynamics approach.

A thermodynamic interpretation of the behavior of higher fatty alcohols and acids upon the chromatographic paper

An idea was presented of treating the chromatographed substance as a “solute,” and the chromatographic system, composed of the stationary and the mobile phase as a “solvent.” Moreover the concept of “local equilibrium” was introduced, allowing to regard a given chromatographic spot as a “binary solution.” Thus a possibility arose to apply the classical thermodynamic approach, normally used for binary solutions, and namely: μ i = μ i ⊕ + RT ln x iƒ i , where μ i—chemical potential of the “ i”-th compound in the solution, μ i ⊕—chemical potential of the pure “ i”-th compound, x i -molar fraction of the “ i”-th compound, ƒ i —its activity coefficient, in a modified form, suitable for the chromatographic purpose.

Variational thermodynamics of viscous compressible heat-conducting fluids

A new variational principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to compressible heat-conducting fluids with Newtonian and non-Newtonian viscosity. The principle is applied in the context of Eulerian formalism where the flow is described with reference to a fixed coordinate system. New concepts of entropy displacement and mass displacement are used as well as a new definition of the chemical potential which avoids the usual ambiguities of the classical thermodynamic approach. The variational principle is used to derive a novel form of field differential equations for the coupled fluid dynamics and convective heat transfer.

Liquid State Physics—A Statistical Mechanical Introduction

First published in 1974, Dr Croxton's book takes the reader from a consideration of the early ways in which the kinetic theory of gases was modified and applied to the liquid state, through a classical thermodynamic approach, to the modern cluster-diagrammatic quantum and statistical mechanical techniques. He includes chapters on the development and numerical solution of the integral equations relating the atomic structure to the pair potential, on the nature of the liquid surface, on the computer simulation schemes and on transport processes and irreversibility in the liquid phase.