Fuzzy wire model

They treated the system much like a CSTR, with the balance for the gas-phase concentration substituted by the coverage equation for the catalyst. Ray and Hastings then applied the analytical treatment that they had developed for the CSTR in this same publication. Stability analysis revealed that the critical Lewis numbers for oscillations were in a range that did not allow for oscillations on normal nonporous catalytic surfaces. However, as Jensen and Ray 243) showed, a certain model for catalytic surfaces, the fuzzy wire model, with the assumption of a very rough surface with protrusions is able to produce Lewis numbers in the proper range for the occurrence of oscillations. This model, however, included both mass and heat balances as well as coverage equations, thus combining the two classes of reactor-reaction models discussed above. 

Catalytic wires after being used in a catalytic reaction often show increased roughness and the formation of spatial structures [78]. These observations prompted the so-called fuzzy-wire model in which the protrusions on the roughened wire were modelled by interconnected cylinders [78,79]. This study revealed a plethora of complex oscillations of the average rate of reaction resulting from the coupled protruded oscillators. The model however fails to predict the long period of the oscillations usually seen in catalytic reactions. The conclusion to draw is that rough catalysts may lead to different dynamic behavior than smooth ones a conclusion not always supported by experimental fact. 

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