Cell models, mixing theory

The incorporation of a third element, e.g. Cu, in electroless Ni-P coatings has been shown to improve thermal stability and other properties of these coatings [99]. Chassaing et al. [100] carried out an electrochemical study of electroless deposition of Ni-Cu-P alloys (55-65 wt% Ni, 25-35 wt% Cu, 7-10 wt% P). As mentioned earlier, pure Cu surfaces do not catalyze the oxidation of hypophosphite. They observed interactions between the anodic and cathodic processes both reactions exhibited faster kinetics in the full electroless solutions than their respective half cell environments (mixed potential theory model is apparently inapplicable). The mechanism responsible for this enhancement has not been established, however. It is possible that an adsorbed species related to hypophosphite mediates electron transfer between the surface and Ni2+ and Cu2+, rather in the manner that halide ions facilitate electron transfer in other systems, e.g., as has been recently demonstrated in the case of In electrodeposition from solutions containing Cl [101]. 

This equation is predicted by the mixing cell model, and turbulence theories put forward by Aris and Amundson130 and by Prausnttz(31). 

Solid materials, in general, are more or less subject to corrosion in the environments where they stand, and materials corrosion is one of the most troublesome problems we have been frequently confronted with in the current industrialized world. In the past decades, corrosion science has steadily contributed to the understanding of materials corrosion and its prevention. Modem corrosion science of materials is rooted in the local cell model of metallic corrosion proposed by Evans [1] and in the mixed electrode potential concept of metallic corrosion proved by Wagner and Traud [2]. These two magnificent achievements have combined into what we call the electrochemical theory of metallic corrosion. It describes metallic corrosion as a coupled reaction of anodic metal dissolution and cathodic oxidant reduction. The electrochemical theory of corrosion can be applied not only to metals but also to other solid materials. 

The modeling of the formation of solutions that we have described assumes that there is no change in volume in mixing. Theories of liquids that consider cell models... 

Detailed models for mixing plus reaction have been presented, and some use computational fluid mechanics to calculate velocities and the local reaction rates throughout the tank [12,13]. Others have developed cell models, with four to six interacting zones to account for different reaction rates [11,14]. These approaches require extensive computations and detailed kinetic data, which may not be available or completely reliable. In industry, multiple reaction systems are generally scaled up from laboratory or pilot-plant data. Mixing theories offer some guidance, but often there is still uncertainty about the correct procedure. 

It appears at present that although crossflow and other macro-mixing models give a more correct description of the flow of a dispersed phase, the dispersion model predicts the conversion data satisfactorily, at least for simple reactions. In future, cell models probably will become more attractive, because they are closer to reality, making allowance for a better modeling of fluid-dynamics via the percolation theory [69]. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

Hoffman and Friedman [106] proposed a mechanism for the induction time in development based on heterogeneous electrochemical theories of corrosion. The model explains the empirical relation derived by Pontius and Willis. In this case the two half-cell reactions of silver and developer give rise to a mixed or corrosion potential, Ecorr, which if electron transfer is rate-limiting can be described by Eq. (74),... 

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