Models for Chemistry

The reactions occurring in chemically reacting flow systems may be represented at different levels of complexity. In the order of increasing complexity, these can be summarized as follows  

These approaches can be divided into two groups. In the first group, fast chemistry (approaches 1 and 2), it is assumed that the rate of chemical conversion is not kinetically controlled. The second group,finite rate chemistry (approaches 3-5), allows for kinetically controlled processes, in that restrictions are put on the chemical reaction rate. Below we discuss these different approaches in more detail. 

The fast chemistry approximation implies that chemical reaction is instantaneous. Consequently the conversion from reactants to products is limited only by mass transport. This way of describing the chemistry is useful in many applications, but obviously it must be used with caution. 

In chemically reacting flow systems, the overall reaction rate may be limited by the mixing rate of the reactants or by the rate of the chemical reaction upon mixing. If mixing is slow compared to chemical reaction, the system is diffusion or mixing controlled, while fast mixing and slow reaction results in a kinetically controlled system (Fig. 13.1). The assumption of fast chemistry is valid if the system is mixing controlled. 

One way to assess the validity of the assumption of fast chemistry is to estimate the Damkohler number (see also Section 6.8.1.1). This number is an important dimensionless parameter that quantifies whether a process is kinetically or diffusion controlled. The 

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Although a separation of electronic and nuclear motion provides an important simplification and appealing qualitative model for chemistry, the electronic Sclirodinger equation is still fomiidable. Efforts to solve it approximately and apply these solutions to the study of spectroscopy, stmcture and chemical reactions fonn the subject of what is usually called electronic structure theory or quantum chemistry. The starting point for most calculations and the foundation of molecular orbital theory is the independent-particle approximation. 

Pople J A 1973 Theoretical models for chemistry Energy, Structure, and Reactivity ed D W Smith and W B McRae (New York Wiley) p 51-67... 

Crutzen and co-workers (Sander and Crutzen, 1996 Vogt et al., 1996) have developed a model for chemistry in the marine boundary layer at midlatitudes, in which autocatalytic cycles involving sea salt particles generate photochemically active gases such as BrCl, Br2, and Cl2. It is likely that such chemistry also occurs in the Arctic as well. In these cycles, reactions (125) and (126) in the condensed phase,... 

In Boerhaave s transformation of chemistry into an accepted academic discipline Hippocrates played a key role. Not only did the Hippocratic Corpus shape Boerhaave s chemistry for medicine, but for Boerhaave, Hippocrates was a perfect role model for chemistry as a discipline. John Powers has argued that Boerhaave chose Hippocrates because in this way he could make chemistry acceptable to a medical faculty oriented towards Hippocratic teaching.4 However this may be, I argue that there was more to it than just political and pragmatic reasons. Like Principe, I maintain that... 

Felder, RM (1996) Active-Inductive-Cooperative Learning An Instructional Model for Chemistry J Chem Educ 73 832-836. 

In this chapter a detailed CFD study of the chemical and electrochemical processes in an internally reforming anode supported SOFC button cell was carried out. Detailed models for chemistry, electrochemistry and porous media transport have been implemented into the commercial CFD code FLUENT with the help of used defined functions (UDF). Simulation results were compared with experimentally reported data. The comparisons lead to the conclusion that precise calculation of surface carbon formation is critical for the accurate prediction of OCVs for hydrocarbon fuels with very low H2O content, and that Nemst equation may not be valid for the calculation of OCV for a fuel composition such as the one considered here. Anodic overpotentials showed remarkable difference from expected behavior. 

At some stage, most scientists benefit by the unreasonable effectiveness of mathematical models in science, but too few look for the cause behind this coinsidence. There is a school of thought that detects a parallel between the subjective choice of topics for analysis and the formulation of matching formulae. At the other extreme, numerical systems are considered to have independent existence in the same way as their physical counterparts. It is, for instance, an undisputed fact that the sophistication of cosmological models faithfully follows developments in number theory. While the concept of infinity remains mathematically unresolved the cosmos remains infinite. However, whether number theories are invented or discovered does not decide their utility in science. If nobody understands the remarkable similarity between Farey sequences. Ford circles and the periodicity of matter, it is no excuse not to exploit this consilience to develop powerful new number-theoretic models for chemistry. 

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