Electrical analogy, reaction networks

From the above definitions it follows that the analogy between the electrical and reaction networks is rather exhaustive, the main difference being that the resistance is not a constant. 

There are several advantages in adopting this new viewpoint of a reaction network for its analysis, visualization and reduction. The main advantage is that within this representation a reaction network becomes analogous to a general linear electrical circuit network, so that the procedures of electric circuit analysis are applicable. 

Qualitatively, the analogy between the conventional electrical network theory and the reaction network defined above is quite transparent. To make this analogy quantitative, we introduce several additional concepts ... 

Fig. 3. The electrical circuit analog of the reaction network for the WGSR...

We are now in a position to consider the rate of the overall reaction. First, we write a formal rate equation for the kinetics of the reduced reaction network, Fig. 7d, by employing the electrical circuit analogy and the linear rate law analogous to Ohm s law. Thus, the overall rate (overall current) is the ratio of the affinity of the OR and the overall resistance of the reaction network. The overall resistance of the reduced reaction network is... 

The proposed theoretical methodology has been applied here to study and rationalize a 15 elementary reaction microkinetic mechanism for the WGSR on Cu(lll) for illustrative purposes. A reaction network has been constructed that incorporates all of the 26 direct RRs that have been previously generated using the conventional methods. Using the electrical circuit analogy the reaction network was subsequently simplified and reduced to a reaction network involving only 3 dominant RRs. An overall rate equation has been developed that reproduces the complete microkinetic model precisely. 

The electric analogy also played a major role in evaluating the steady-state species concentration in microfluidic networks. The principle of flow and species balance to a multi-input and multioutput microchannel involving no reaction yields... 

The electrical analogy of reaction networks was first proposed by Nemst in 1926 by suggesting that the rate of a chemical reaction might be represented in analogy to Ohm s law, being equal to a chemical force divided by a chemical resistance. ... 

Fig. 4.23 Electrical analog of the reaction graph in Fig. 4.22. (From S.A. Viiekar, i. Fishtik, R. Datta, The steady-state kinetics of paraiiei reaction networks, Chem. Eng. Sci. 65 (2010) 2921-2933. Copyright 2010 Eisevier).

In the absence of a catalyst the reaction is often immeasurably slow, = Oj then, v = The rate is usually proportional to the concentration of the catalyst. The analogy to an electrical network of parallel resistances (Fig. 32.11a) or to parallel pipes carrying a fluid (Fig. 32.11b) is apparent. In each case the flow through the network is the sum of that passing through each branch. 

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