Volume 24, Issue 2

Modeling of solute transport in non-saturated and non-isothermal porous media is dealt with by thermodynamics of irreversible processes. This rigorous approach enables us to consider the different kinds of transfer and the coupling. Every physical phenomenon as water phase transition and solute adsorption by the solid matrix can be taken into account. The final model may be applied to several fields such as civil engineering, agronomy, pollution and the assessment of radioactive waste repositories. A numerical modeling taking into account the effect of temperature gradient on solute transport (“Soret effect”) is in the process of implementation in the French software “CESAR-LCPC” of the “Laboratoire Central des Ponts et Chaussées”.

In this work we present an application of Linear Irreversible Thermodynamics to the problem of diffusion among miscible incompressible fluids. First, we suppose that the mixture density is a function of the volume fractions. This hypothesis allows us to reformulate the interface diffusion problem in terms of transport equations for the concentrations or the mass-volume fractions, the momentum balance equations for the diffusion flux and the energy balance equations for the relative internal energies, respectively. The transport equations so obtained are generalized equations of the classical diffusion equations obtained by means of fluctuating hydrodynamics and the H model of critical dynamics. Afterwards we apply linear irreversible thermodynamics in order to get the entropy production and then assume a linear relation between fluxes and forces, obtaining the constitutive equations for the diffusion flux, the heat flux, the stress tensor for each component. Finally, from this choice we compare our results with those originated from fluctuating hydrodynamics and continuum theory. We also show that the constitutive equation for diffusion flux is a Maxwell-Cattaneo's type relaxation equation and therefore a generalization of Fick's law. Also the stress tensor constitutive equation generalizes the Korteweg de Vries stress tensor equations and we present how to arrive at a telegrapher type hyperbolic equation for the concentrations or the mass-volume fractions.

In this work it is rigorously shown that, even in the presence of highly nonlinear phenomena, provided that they belong to the thermodynamic branch, there is mathematical equivalence between the formulation of an extended thermodynamic theory with several fields where a relaxation time is successively set equal to zero and the direct formulation of a theory with a reduced number of independent fields where a constitutive relation is postulated for the eliminated field. This result is obtained as a consequence of the fact that for vanishing relaxation times of these fields the corresponding intrinsic Lagrange multipliers in the Liu procedure of Extended Thermodynamics also vanish, and of the fact that these multipliers can be chosen, together with the velocity, as global variables in Extended Thermodynamics.

The minimum free energy for a rigid dielectric with linear memory is found under isothermal conditions. The resulting expression is given in the frequency domain, i.e., in terms of the Fourier transform of the variables. By means of such a thermodynamic potential and of the Clausius-Duhem inequality an explicit formula of the dissipation is obtained. Thus the minimum free energy restores the customary relation between the dissipativity and the Clausius-Duhem inequality, that had been proved to fail when memory effects occur. Finally, by virtue of some of its properties, the minimum free energy is viewed as the square of a norm in a suitable space of the variables.

We use an irreversible thermodynamics approach to derive hydrodynamic equations which govern the flow-induced concentration changes produced by inhomogeneous stresses in a viscoelastic binary mixture. The most relevant effects arising from these inhomogeneous flows are manifested in the migration of the dispersed phase and as flow-induced concentration fluctuations. Coupled constitutive equations for the mass flux and the stress tensor are derived self-consistently from our formalism. We show that our approach is consistent with different existing isothermal formalisms which predict the growth of concentration fluctuations and shear-induced diffusion of mass. Finally, we also comment on the possibility of extending our approach to incorporate nonisothermal effects and on the limitations and advantages of our description.

Simple upper bound formulae for the efficiency of converting the energy of thermal radiation into mechanical work are derived. They are upper bounds as they refer to a large class of systems. They are simple as they are functions of two parameters only, namely the temperatures of the energy sources. The original contributions are as follow: (1) Two sorts of “cold” thermal reservoirs are considered. (2) An endoreversible thermal engine is used here to convert radiation energy into work. A number of existing theories are particular cases of the present approach.