Basis Of Irreversible Thermodynamics Research Articles

An Anisotropic Continuum Damage Mechanics Model for the Simulation of Yield Surface Evolution and Ratcheting

A new anisotropic continuum damage model was presented on the basis of irreversible thermodynamics. Second rank symmetric damage tensor, kinematic hardening tensor, and damage potential surface were introduced. The yield surface in this study has been modeled to distort in the stress space by the evolution of the damage tensor. The new model was applied in yield surface characterization and led to a well description of the subsequent yield surfaces. This model is then applied to predict experimental results of the cyclic nonproportional loading paths obtained by Kang et al. [2004], Hassan et al. [2002] and Taleb and Cailletaud [2011]. It is demonstrated that the new model can predict the yield surface distortion and the ratcheting strains of multiaxial nonproportional cyclic loading with acceptable accuracy and by using less material constants with respect to the previous models.

Onsager's reciprocal relations for electroacoustic and sedimentation: Application to (concentrated) colloidal suspensions.

In this article, the relations for electroacoustic phenomena, such as sedimentation potential, sedimentation intensity, colloid vibration potential, colloid vibration intensity/current, or electric sonic amplitude, are given, on the basis of irreversible thermodynamics. This formalism allows in particular to discuss the different expressions for concentrated suspensions found by various authors, which are of great practical interest. It was found that some existing expressions have to be corrected. Relations between the electrophoretic mobilities assessed by the different experiments are derived.

A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes

Thermal–electrical–chemical–mechanical coupling controls the behavior of many transport and electrochemical reactions processes in physical, chemical and biological systems. Hence, advanced understanding of the coupled behavior is crucial and attracting a large research interest. However, most of the existing coupling theories are limited to the partial coupling or particular process. In this paper, on the basis of irreversible thermodynamics, a variational principle for the thermal electrical chemical mechanical fully coupling problems is proposed. The complete fully coupling governing equations, including the heat conduction, mass diffusion, electrochemical reactions and electrostatic potential, are derived from the variational principle. Here, the piezoelectricity, conductivity, and electrochemical reactions are taken into account. Both the constitutive relations and evolving equations are fully coupled. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, piezoelectric and nonpiezoelectric dielectrics. As an application of this work, a developed boundary value problem is solved numerically in a mixed ion-electronic conductor (MIEC). Numerical results show that the coupling between electric field, diffusion, and chemical reactions influence the defect distribution, electrostatic potential and mechanical stress.

Synthesis, characterization and properties of polystyrene incorporated calcium tungstate membrane and studies of its physicochemical and transport behavior

This article reports the synthesis of an inorganic nanocomposite material blended with an organic binder by sol–gel method which has been applied as a potential membrane system. The prepared hybrid compound has been extensively characterized by TG–DTA, SEM and FTIR. The XRD study reveals that the polycrystalline nanocomposite is composed of small crystals with an average granular size of 15.8nm. Ion-exchange capacity, water content and volume void porosity of the composite were determined in order to study the physicochemical properties of the membrane. The values of potentials measured across the polystyrene blended calcium tungstate membrane, using various uni-univalent electrolytes (aqueous KCl, NaCl, LiCl and NH4Cl solutions), were used to evaluate the fixed charge density using different approaches on the basis of irreversible thermodynamics. The counter-ion transport number, mobility ratio and permselectivity of the tungstate membrane were figured out and were found to follow the order Li+>NH4+>K+>Na+ i.e. the inorganic–organic hybrid membrane is more cation selective towards Li+ ions for the same electrolytic concentration.

Free Energies of the Ion Equilibrium Partition of KCl into Nanofiltration Membranes Based on Transmembrane Electrical Potential and Rejection

The free energies of ion equilibrium partition between an aqueous KCl solution and nanofiltration (NF) membranes were investigated on the basis of the relationship of the transmembrane electrical potential (TMEP) and rejection. The measurements of TMEP and rejection were performed for Filmtec NF membranes in KCl solutions over a wide range of salt concentrations (1-60 mol·m(-3)) and pH values (3-10) at the feed side, with pressure differences in the range 0.1-0.6 MPa. The reflection coefficient and transport number, which were used to obtain the distribution coefficients on basis of irreversible thermodynamics, were fitted by the two-layer model with consideration of the activity coefficient. Evidence for dielectric exclusion under the experimental conditions was obtained by analyzing the rejection of KCl at the isoelectric point. The free energies were calculated, and the contribution of the electrostatic effect, dielectric exclusion, steric hindrance, and activity coefficient on the ion partitioning is elucidated. It is clearly demonstrated that the dielectric exclusion plays a central role.

Structural and Thermodynamic Explanations of Ostwald's Rule

Ostwald proposed that the solid first formed on crystallisation of a melt or a solution would be the least stable polymorph. It is shown that this can be rationalized on the basis of irreversible thermodynamics, structural relationships, or a combined consideration of statistical thermodynamics and structural variation with temperature. It is concluded that the rule cannot be a universal law but is only in the nature of a possible preferred tendency.

Diffusion in binary mixtures and osmotic pressure gradient

The relation between mutual diffusion in binary mixtures and collective diffusion in colloidal suspensions is studied on the basis of irreversible thermodynamics. Emphasis is placed on the relation between the gradient of the chemical potential driving mutual diffusion and the osmotic pressure gradient and its dependence on relative particle size. The analysis is illustrated by a study of ideal solvent mixtures, isotopic mixtures, and hard-sphere mixtures. It is shown that the two Onsager transport coefficients characterizing mutual diffusion of both components are related by a symmetry relation.

Comment on “Transport equations for concentrated electrolyte solutions: Reference frame, mutual diffusion” [J. Chem. Phys. 116, 2085 (2002)

The definition of the mutual diffusion coefficient of a binary electrolyte solution is discussed on the basis of irreversible thermodynamics. An expression for the mutual diffusion coefficient in terms of Onsager transport coefficients and thermodynamic derivatives is derived. It is shown how the mutual diffusion coefficient is related to another coefficient defined recently [J.-F. Dufrêche, O. Bernard, and P. Turq J. Chem. Phys. 116, 2085 (2002)].

Constitutive Modeling of Creep and Damage Behaviors of the Non-Mises Type for a Class of Polycrystalline Metals

Phenomenological constitutive models to describe the creep and damage behaviors that deviate from the von Mises type for a class of polycrystalline materials are developed. Theoretical and empirical approaches are taken to the formulation. The effective stresses that govern the rates of creep and damage are scaled to describe any deviation from the response of the von Mises type. A general form of scaling parameter is proposed which can consider the hydrostatic stress and/or the third invariant of the stress deviator. A kinematic hardening model is first formulated on the basis of irreversible thermodynamics using the scaling parameters for creep and damage. Then, two kinds of empirical basis models are presented for cases of kinematic hardening and isotropic hardening, respectively. The proposed models can describe the primary, secondary and tertiary creep behaviors and distinguish between the creep and damage behaviors under different modes of loading. To illustrate the features of the proposed models, numerical simulations of the unequal creep behaviors under tension, compression, and torsion are carried out and compared with experimental results.

About Complex Heat Capacities and Temperature-Modulated Calorimetry

With increasing use of temperature-modulated calorimetry, TMC, it is has been proposed to use a complex heat capacity for the description of the response of samples to periodic temperature changes. In this article the ramifications of this approach are discussed on the basis of irreversible thermodynamics. Experimental results are summarized which describe heat capacities of liquids and solids, as well as TMC during transitions. It is concluded that the complex heat capacity is of limited value. Solids and liquids have no dissipative (imaginary) contributions. In the glass transition, the thermal response is nonlinear, so that a detailed kinetic model (in real notation) is more advantageous to describe the heat capacity. The crystallization is often so far from equilibrium that it is not modulated. During melting and chemical reactions the heat flow is frequently so large, that steady state is lost and complex heat capacity is of questionable value, even if modulation is accomplished.

Analysis of an electrodialysis unit on the basis of irreversible thermodynamics

The performance of an ED basic unit is analyzed on the basis of irreversible thermodynamics. The influence of the thickness of polarization layers, the distance between membranes, the concentration of diluate, and the current density as well as the transport coefficients of membranes on the current efficiency, CE, and the efficiency of energy conversion, η, is shown.

Transport properties of cation-exchange membranes in aqueous and methanolic solutions. Diffusion and osmosis

The swelling and transport behaviour of cation-exchange membranes (Nafion 417, Nafion 423 and KESD) in aqueous and methanolic solutions were investigated. Sodium chloride and sulfuric acid were used as electrolytes. The results are interpreted on the basis of irreversible thermodynamics.

Characteristics of Ion-Exchange Membranes for Electrodialysis on the Basis of Irreversible Thermodynamics

Characteristics of Ion-Exchange Membranes for Electrodialysis on the Basis of Irreversible Thermodynamics

Elastic damage and energy dissipation in anisotropic solid material

On the basis of irreversible thermodynamics with internal state variables, a concept of damage energy dissipation rate which can characterize the mechanical response of elastic material with anisotropic damage is presented in this paper. The damage energy dissipation rate has been formulated in tensorial form from the generalized elastic damage theory proposed by the present author. In illustration of application, a set of values in tensorial components (such as the damage factor, the damage energy dissipation rate and the damage energy release rate as well) of the given element of composite plate in loading process have been estimated from experimental data. Then the principal values and the principal direction of these tensors have been determined to explain the damage process of material. Furthermore, based on the experimental results of two kinds of notched laminate under uniaxial tension, the failure criterion of the damage energy release rate describing the capability against damage evolution of laminate have been established.

Development of a new pore model: II. Electrokinetic transport properties, surface conductance, and convective charge transport

The semisinusoidal pore model describes the electrokinetic transport correctly when electrical conductance is predominantly bulk conductance. On the basis of irreversible thermodynamics and the semisinusoidal pore model a stability diagram can be constructed showing the conditions under which stationary transport is possible. In describing surface conductance and convective charge transport, differences between model predictions and experimental data exist. It is shown that these differences are related to assumptions concerning the electrical charge distribution rather than to the pore model itself.

Steady flow through asymmetric membranes

Abstract For the two special cases that the permeability of the membrane is (1) an exponential and (2) a power function of location and pressure, the pressure dependence of the current, the average permeability, and the asymmetry of permeability Δ = / — 1 were calculated on the basis of irreversible thermodynamics. The asymmetry is small in both cases. It increases rather fast for small pressure but reaches soon a slightly inclined plateau in the former case and a maximum with a small subsequent drop in the latter case. The maximum value is close to 0.5 in case 1 and about 0.2 in case 2. It is also shown that Fick's law cannot be applied to inhomogeneous or nonideal membranes.

Purity Determination of Organic Compounds by a Newly Designed DTA Apparatus

Abstract An apparatus of differential thermal analysis has been designed and constructed for the purpose of determining the purity of organic compounds with as small an amount of sample as possible, within a short time and yet with an accuracy of better than ±0.001 mol%. Degussa platinum thermometers were used. They were calibrated with a precision of better than ±0.004° against a standard platinum resistance thermometer. Methods for determining the impurities in samples on the basis of irreversible thermodynamics have been developed. The results were compared with those obtained by using an adiabatic calorimeter of our laboratory and by the National Bureau of Standards. The apparatus proved to be useful in determining the purity of about 1 ml of samples, whose melting points lie in the temperature range −200°C–+200°C within an accuracy of ±0.004 mol% in about 1.5 hr.

Rheological Equation of Anisotropic Viscoelastic Material and its Application to Problems Pertinent to Rock Mechanics

It has been suggested that the rheological equation of anisotropic viscoelastic material should be expressed in the form of differential equation, and its differential operators can be determined by consideration of Biot's equation derived on the basis of irreversible thermodynamics. The differential equation is given in two different forms, one of which is applicable to the analysis of relaxation phenomenon, and the other is to the creep analysis. There exist some relations among the differential operators in the two different forms of the equation.The correspondence principle proposed by Lee can be extended to the anisotropic case by introducing into it the suggested rheological equation. The extended correspondence principle has been adopted to making the analysis of the creep strain of orthotropic viscoelastic material under the plane strain condition, and its results may be applied to determining the viscoelastic constants of the material through experimental data. Discussion has also been made on the analysis of a circular tunnel subjected to uniformly distributed internal pressure in an orthotropic viscoelastic medium.

On the Thermo-Rheology of 2-Phase Systems

This paper is concerned with the formulation of a thermodynamic strain-time function for a 2-phase material when subjected to a constant stress in an isothermal temperature field.It is shown on basis of irreversible thermodynamics that the stress-deformation relation of such systems is of the same mathematical form as the relation obtained from a simple rheological model described in an earlier publication. A correspondence is established between the phenomenological coefficients contained in the thermodynamic function and the structural parameters employed in the mechanical model.