Local equilibrium concept

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Figure 2,10 Schematic representation of concept of local equilibrium in disequilibrium processes. Reprinted from R F. Sciuto and G. Ottonello, Geochimica et Cosmochimica Acta, 59, 2207-2214, copyright 1995, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1 GB, UK.

Sciuto P. F. and Ottonello G. (1995a). Water-rock interaction on Zabargad Island (Red Sea)., a case study I), application of the concept of local equilibrium. Geochim. Cosmochim. Acta, 59 2187-2206. 

For liquid-vapor interfaces, the correlation length in the bulk is of t he order of atomic distance unless one is close to the critical point Hence the concept of local equilibrium is well justified in most practical circumstances For. solid surfaces above the roughening temperature, the concept also makes sense. Since the surface is rough adding (or removing) an atom to a particular part of the surface docs not disturb the local equilibrium state very much, and this sampling procedure can be used to determine the local chemical potential. This is the essence of the Gibbs-Thomson relation (1). 

Among the basic concepts to be introduced are ionic equilibrium, local equilibrium, local electro-neutrality, etc. 

The vacancy flux and the corresponding lattice shift vanish if bA = bB. In agreement with the irreversible thermodynamics of binary systems i.e., if local equilibrium prevails), there is only one single independent kinetic coefficient, D, necessary for a unique description of the chemical interdiffusion process. Information about individual mobilities and diffusivities can be obtained only from additional knowledge about vL, which must include concepts of the crystal lattice and point defects. 

In other cases, however, and in particular when sublattices are occupied by rather immobile components, the point defect concentrations may not be in local equilibrium during transport and reaction. For example, in ternary oxide solutions, component transport (at high temperatures) occurs almost exclusively in the cation sublattices. It is mediated by the predominant point defects, which are cation vacancies. The nearly perfect oxygen sublattice, by contrast, serves as a rigid matrix. These oxides can thus be regarded as models for closed or partially closed systems. These characteristic features make an AO-BO (or rather A, O-B, a 0) interdiffusion experiment a critical test for possible deviations from local point defect equilibrium. We therefore develop the concept and quantitative analysis using this inhomogeneous model solid solution. 

The basic mechanisms by which various types of interfaces are able to move non-conservatively are now considered, followed by discussion of whether an interface that is moving nonconservatively is able to operate rapidly enough as a source to maintain all species essentially in local equilibrium at the interface. When local equilibrium is achieved, the kinetics of the interface motion is determined by the rate at which the atoms diffuse to or from the interface and not by the rate at which the flux is accommodated at the interface. The kinetics is then diffusion-limited. When the rate is limited by the rate of interface accommodation, it is source-limited. Note that the same concepts were applied in Section 11.4.1 to the ability of dislocations to act as sources during climb. 

To treat solid-solid reactions, Wagner introduced the concepts of local equilibrium and counterdiffusion of cations between the solids. The latter concept forms the basis for Darken s subsequent introduction of the interdiffusion coefficient, which was discussed in Section 2.4. To maintain a state of local equilibrium, the exchange fluxes across the interface must be large compared to the net transport of matter across the boundary. This is analogous to the criterion that the forward and reverse reaction rates be the same, or nearly so, for a reversible reaction to be considered at thermodynamic equilibrium. 

Concepts of local equilibrium and charged particle motion under - electrochemical potential gradients, and the description of high-temperature -> corrosion processes, - ambipolar conductivity, and diffusion-controlled reactions (see also -> chemical potential, -> Wagner equation, -> Wagner factor, and - Wagner enhancement factor). 

Therefore, contributions to methods of data mining are included here. It is uncommon to discuss this topic in the context of reaction processes. However, as we have already discussed, data mining becomes ever more important in analyzing experiments and simulations. In conventional data analyses, the concepts of equilibrium statistical physics have been routinely applied. To the contrary, in situations in which local equilibrium breaks down, established methods do not exist to analyze experiments and simulations. Thus, data mining... 

For many systems it is known that there exist regions or environments in which the time-invariant condition closely approaches equilibrium. The concept of local equilibrium is important in examining complex systems. Local equilibrium conditions are expected to develop, for example, for kinetically rapid species and phases at sediment-water interfaces in fresh, estuarine, and marine environments. In contrast, other local environments, such as the photosyn-thetically active surface regions of nearly all lakes and ocean waters and the biologically active regions of soil-water systems, are clearly far removed from total system equilibrium. 

However, there is no reliable information on transport coefficients, reaction rate constants and concentration ratios that are needed for solving Equations (5) and (6). Hence, a process model based on these equations is not promising. Instead, the process will be modelled on a less detailed level using a cell model, which is based on the concept of local equilibrium. 

The idea of an associated equilibrium state is thus quite general it is a very powerful concept that can be used more accurately and more confidently than the concept of local equilibrium. Confidence comes fi om two sources first we can see that the real nonequilibrium state and the imagined equilibrium state are closely similar, and second, we can bring the exact differences to light—even, in some circumstances, express them quantitatively and demonstrate their smallness. It is the second aspect that brings confidence, and allows us to use associated equilibrium states to define potentials and predict material responses, even in situations where the exact magnitude of the small differences cannot actually be worked out in numbers. 

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