Volume 34, Issue 2

In this paper thermodiffusion models developed to estimate the thermal diffusion factor in nonideal liquid mixtures are reviewed; the merits and shortcomings of each model are discussed in detail. Most of these models are multicomponent in principle; however our focus here is on binary mixtures. Two rather different groups of models are identified: models needing a matching parameter to be obtained usually from the outside of thermodynamics, and the self-contained or independent models. Derivation of the matching parameter models using linear non-equilibrium thermodynamics and the details of how to find the matching parameters are investigated. The physical meaning of parameters such as the net heat of transport and the activation energy of viscous flow is elucidated, as the literature is overwhelmed with confusing and misleading information. The so-called dynamic and static models and their relations to the matching and non-matching parameter models are also discussed. We conclude that modeling the net heat of transport by the activation energy of self-diffusion may provide better results than approximating it by the activation energy of viscous flow. Nonetheless, the matching parameter models, which use the activation energy of viscous flow, are more dynamic and predict the thermal diffusion factor better than the non-matching parameter or static models, such as those of Kempers and Haase.

The phenomenological relation of non-equilibrium liquid–gas phase change in a porous medium is described at the macroscopic level using the difference in chemical potentials between the liquid and its vapor. The experiments conducted consisted in lowering the partial pressure of water vapor in the pores of a hygroscopic soil and analyzing the return to equilibrium by two measurements: the macroscopic temperature and the partial pressure of vapor. The central hypothesis of the study is that the characteristic time associated with thermal equilibrium is much lower than the characteristic time associated with mass transfers. From these measurements, it is possible to determine the relation that links phase change rate to the logarithm of the ratio of partial vapor pressure divided by the equilibrium pressure (RH). The representation of this relation according to RH reveals two regimes in the return to equilibrium. The characteristics of these regimes are analyzed according to water content, temperature, and total gas phase pressure.

Within the thermodynamic framework of Rice [J. Mech. Phys. Solids 19: 433–455, 1971], the asymptotic stability of the thermodynamic system of a given material sample in constrained configuration space is addressed in this paper following the work of Edelen [Int. J. Eng. Sci. 11: 819–839, 1973]. As a subspace of the state space, the constrained configuration space is the internal-variable space with fixed stress or strain and temperature. Thermodynamic processes in constrained configuration space are creep or relaxation processes of materials. Using the entropy production rate of the thermodynamic system as a Lyapunov function, sufficient conditions for the asymptotic stability are established in this paper, including that (1) the free and complementary energy functions are convex or concave, respectively, with respect to internal variables; (2) the kinetic rate laws of the internal variables are stress or strain and internal-variable dependent only via their conjugate thermodynamic forces, and (3) the kinetic rate laws are the Ziegler fluxes.

In view of the second law of thermodynamics, the idealized process is usually so selected as to be one of minimum available energy degradation. A measure of departure from this ideal process is the entropy generation rate. In this paper, we shall investigate this aspect concerning an adiabatic peristaltic pump. Our analysis also exhibits the general features of a flow in a contracting tube. It is shown that the dynamics of the system can be reduced to that of a classical Hagen-Poiseuille flow with a source term in the continuity equation and an additional induced force in the momentum equation. In reference to exergy, the analysis reveals that peristaltic pumps generate more entropy than steady walled tubes and are not, from this point of view, competitive devices. The reason for this high-energy degradation is found in the dynamic behavior. The flow rate is not constant along the tube, but increases as sections downstream are reached. This results in high velocity gradients and therefore in strong dynamic irreversibility, which is the prime entropy source of the system. For the classical Hagen–Poiseuille flow, the entropy is mainly generated by heat diffusion.