Linear thermodynamics of irreversible

We consider a system made of a solid phase (denoted by s) containing a liquid phase (denoted by L). The latter is composed by water (denoted by e) and by two kinds of ions (denoted by + and —). An electric field is applied. The methods of the linear thermodynamics of irreversible processes permits the description of transport phenomena by linear relations. For the liquid phase [9] (in this paper, the indices or exponents k and m refer to cartesian coordinates) ... 

In the domain of validity of linear thermodynamics of irreversible processes, the contribution of the time change of forces to the entropy production is negative or zero... 

All electrokinetic phenomena include the coupled action of an electrical force (with the respective electrical current) and a hydrodynamic force (with the respective hydrodynamic flux). Therefore, we can apply the general approach of the linear thermodynamics of irreversible processes to... 

The Use of Linear Thermodynamics of Irreversible Processes (LTIP) for Calculation of Parameters Related to Conservative Mechanisms in the Process of Light-to-Chemical Energy Conversion P/2e Calculation and Analysis Thermodynamic Efficiency and Energetic Coupling Analysis Experimental Validation of the Proposed Model for Different Simple Geometric Structures of a Photobioreactor... 

It follows that within the domain of validity of linear thermodynamics of irreversible processes, t of should be independent of current density. Actually such a behaviour was observed by earlier workers [29, 63]. However, abnormalities at very low current densities have been noted, the reason for which is obscure. Marked dependence of electro-osmotic water transport on current has also been observed at higher current densities [48], which may be due to non-linear effects discussed below. 

In the earlier chapters, transport phenomena involving a barrier have been discussed from the angle of (i) basic understanding of the physico-chemical phenomena and (ii) test of the linear thermodynamics of irreversible processes. Similar phenomena in continuous systems such as thermal diffusion (Soret effect)/Dufour effect are of equal... 

Using the linear thermodynamics of irreversible processes, one can write the phenomenological relations as follows. 

In view of the complexity in biological systems, different theoretical techniques have to be applied for different non-equilibrium regions. The range of applicability of linear thermodynamics of irreversible processes is quite limited on account of very thin... 

When the gradients are small, theoretical results based on linear thermodynamics of irreversible processes agree well with experimental results. However, when the gradients of intensive variables are large, there are deviations as would be clear from the discussion of experimental studies in Chapters 3-5. The exact domain of applicability of LET and useful information for non-equilibrium region close to equilibrium can be easily ascertained from experimental data as discussed in these chapters. 

For simpler phenomena such as thermo-osmosis, electro-kinetic phenomena, thermal diffusion and Dufour effect, the linear thermodynamics of irreversible processes is valid in a wide range as indicated by the experimental results discussed in Chapters 3-5. It may be noted that Onsager relations for thermal diffusion can be proved by ETT [2]. 

Thus, in the formalism of extended irreversible thermodynamics by inclusion of gradients in the basic formalism of linear thermodynamics of irreversible processes, a small correction in the local entropy due to flow appears. With this modification, the new formalism can be applied to the systems such as shock waves, where there are large gradients. 

If the steady state concentrations of the components are shifted, but not too far from their equilibrium values, the interconnection between the fluxes and chemical forces (chemical affinities, in our case) should satisfy the well-known linear relationships that are usually postulated in the linear thermodynamics of irreversible processes [15-18]. We do not consider here the phenomenological equations of nonequilibrium thermodynamics. For details the reader can refer to numerous excellent monographs and review articles devoted to the applications of nonequilibrium thermodynamics in the description of chemical reactions and biological processes (see, for instance, [22-30]). In many cases, the conventional phenomenological approaches of linear and nonlinear nonequilibrium thermodynamics appear to be useful tools for the... 

This result is in the frame of the traditional approach of phenomenological linear thermodynamics of irreversible processes. It follows from (2.61) that in the case of two consecutive reactions the ratio of the affinities for two partial reactions, s abI bc = is determined not only by thermodynamic... 

Let us discuss main ideas of the above mentioned methods on an example of thin film growth kinetics for structureless gas flux under the conditions when diffusion processes are faster than those of adsorption-desorption (see. (8.3.7)). On the initial stage of film formation a role of diffusion is restricted to the promotion of two-dimensional nucleation (two-dimensional vapor of adatoms is assumed to be supersaturated). The study of growth kinetics at all stages of film formation can be done on the base of (8.3.7). On the other hand, if one is interested in the film growth description on large time scale (when nuclei are large and can be treated thermodynamically) methods of linear thermodynamics of irreversible processes can... 

Chapter 6, entitled Applications to the Peltier Effect, relates to the thermoelectrical effects observed with the formalism of linear thermodynamics of irreversible processes, or TIP, also known as classic irreversible thermodynamics (CIT - see [PRU 12]), in the bulk (the phenomenological relations for a metal are recapped in the Appendix), and then considering the jvmction as an interface. 

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