Damkohler criterion

For reactions following an nth-order kinetic scheme, the reaction rate is often characterized by a dimensionless number the Damkohler criterion [14] ... 

This Damkohler criterion is the Damkohler number of type I (Dof). Other Damkohler numbers were defined [12] type II used to characterize the material transport at the surface of a solid catalyst, type III used to characterize the convective heat transport at the catalyst surface, and type IV used to characterize the temperature profile in a solid catalyst. For batch reactions, the reaction time xr is defined at a reference temperature, the cooling medium temperature, as... 

Occasionally, one could have read about the failures of the Theory of Similarity or of its limits. However, this criticism has arisen when, due to some physical reasons, a complete similarity could not be achieved (see e.g. remarks of Damkohler [113] on p. 183) or the scale-up criterion could not have been worked out with certainty because the measuring conditions did not allow it (false model scale, wanted sensitivity of the target quantity, non-availability of the model material system, ignorance about relevant physical properties, such as in foams and sludges, etc.). 

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