Transport and Reactions in Special Systems

In what follows, we will not repeat the formal discussions. Rather we exemplify specific and relevant kinetic problems as they are met in practical situations. Reference will be made to previous chapters for the more formal aspects. 

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Like the performance of chemical reactors, in which the transport and reactions of chemical species govern the outcome, the performance of electronic devices is determined by the transport, generation, and recombination of carriers. The main difference is that electronic devices involve charged species and electric fields, which are present only in specialized chemical reactors such as plasma reactors and electrochemical systems. Furthermore, electronic devices involve only two species, electrons and holes, whereas 10-100 species are encountered commonly in chemical reactors. In the same manner that species continuity balances are used to predict the performance of chemical reactors, continuity balances for electrons and holes may be used to simulate electronic devices. The basic continuity equation for electrons has the form... 

The calorimetric measurements in metal oxide-aqueous electrolyte solution systems are, beside temperature dependence of the pzc measurements, the method for the determination of the enthalpy of the reaction in this system. Because of the low temperature effects in such systems they demand very high precision. That is why these measurements may be found only in a few papers from the last ten years [89-98]. A predominant number of published measurements were made in the special constricted calorimeters (bath type), stirring the suspension. The flow calorimeters may be used only for sufficiently large particles of the solid. A separate problem is the calculation of the enthalpy of the respective reactions from the total heat recorded in the calorimeter. A total thermal effect consists of the heat of the neutralization in the liquid phase, heat connected with wetting of the solid, heat of the surface reaction and heat effects caused by the ion solvation changes (the ions that adsorb in the edl). Considering the soluble oxides, one should include the effects connected with the transportation of the ions from the solid to the solution... 

The stiff system of non-linear differential equations describing microbial growth and the related species consumption is solved with the DGEAR-method, a special routine for stiff systems of equations (Hindmarsh, 1974). Transport and reaction are coupled by an iterative multistep-procedure. More details on the TBC model can be found in Schafer et al. (1998). 

So far we have ignored bound states, or composite particles, which may form as a result of the interaction due to an attractive part of the potential. Of course, the behavior of macroscopic systems such as thermodynamic, transport, and optical properties, is essentially influenced by the existence of bound states. A particular problem of special interest in connection with these bound states is the ionization phenomenon, or more general, the problem of chemical reactions. 

Recovery of metals such as copper, the operation of batteries (cells) in portable electronic equipment, the reprocessing of fission products in the nuclear power industry and a very wide range of gas-phase processes catalysed by condensed phase materials are applied chemical processes, other than PTC, in which chemical reactions are coupled to mass transport within phases, or across phase boundaries. Their mechanistic investigation requires special techniques, instrumentation and skills covered here in Chapter 5, but not usually encountered in undergraduate chemistry degrees. Electrochemistry generally involves reactions at phase boundaries, so there are connections here between Chapter 5 (Reaction kinetics in multiphase systems) and Chapter 6 (Electrochemical methods of investigating reaction mechanisms). 

In Section 3.2 we introduced the basic processes of advection, diffusion, and drift, by which material is transported in biophysical systems. In this chapter we focus on a specialized class of transport transport across biological membranes. Transport of a substance across a membrane may be driven by passive permeation, as described by Equation (3.60), or it may be facilitated by a carrier protein or transporter that is embedded in the membrane. Thus transport of substances across membranes mediated by transporters is termed carrier-mediated transport. The most basic way to think about carrier proteins or transporters is as enzymes that catalyze reactions that involve transport. 

In chemistry, labelled compounds are used to elucidate reaction mechanisms and to investigate diffusion and transport processes. Other applications are the study of transport processes in the geosphere, the biosphere and in special ecological systems, and the investigation of corrosion processes and of transport processes in industrial plants, in pipes or in motors. 

Other reactor design considerations may be necessary in special cases. Monomer mass transfer, not normally a problem, can he important if the monomer- aqueous phase interface is small. This is more likely in systems involving gaseous monomers in which the large surface area of the monomer emulsion is not present. In such cases special attention must he paid to gas dispersion and transport. Giher factors that can have a significant effect on reactor design include latex viscosity, heat transfer rates, reaction pressure, and control mechanisms. 

We now pass to the explicit calculation of entropy production. We shall consider here the very important special case in which mechanical and thermal equilibrium are already established. Mechanical equilibrium excludes the production of entropy by viscous flow, while uniformity of temperature, which is necessary for thermal equilibrium, excludes the internal production of entropy arising from the transport of heat between two regions at different temperatures. Similarly we assume that diffusion equilibrium has been attained within each phase of the system. The only production of entropy which can take place in a system of this kind is that associated with chemical reactions, with the transport of matter from one phase to another, or in general with any change which can be expressed in terms of a reaction co-ordinate... 

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