Wheeler-Weisz modulus

For lipase, initial activity corresponds to the amount of protein that was adsorbed. Specific activity is constant at 1 mmoFs gE for this carrier-enzyme system, which compares to 27% of the free enzyme activity. The trypsin system shows a lower specific activity that is only 10% of the free enzyme. The reason for the lower recovered activity of this system is not known. To rule out possible internal diffusion limitations, the Wheeler-Weisz modulus was estimated, assuming a carrier layer thickness of 0.1 mm for all carriers. Using the data of the experiments performed at 150 rpm, one finds ... 

While it is the purpose of a study to determine, for example, the intrinsic rate one cannot determine whether this criterion is satisfied. Therefore, the following combination is introduced that yields a procurable quantity (an observable) which is referred to as the Wheeler-Weisz modulus [4, 8]. From series expansion, and since tli is close to 1, the following criterion follows for an nth-order reaction [27] ... 

Figure 12. Isothermal internal effectiveness factor as a function of the Wheeler-Weisz modulus for different reaction orders.

Figure 12 shows the effectiveness factor as a function of the Wheeler-Weisz modulus for different reaction orders, indicating that criterion (33) holds for the generalized Thiele modulus. Due to the definition of L it is fairly independent of the catalyst geometry. 

When 1, strong diffusion limitations occur. Indeed, large values of the Wheeler-Weisz modulus can only correspond to large values of the generalized Thiele modulus, and hence, to strong internal diffusion limitations. 

Analogously to the Wheeler-Weisz modulus, Eqn. (8.78), a dimensionless number featuring only observable quantities can be applied to assess the influence of mass transfer limitations of a homogeneously catalysed reaction ... 

Using the reaction rate observed (in moFs m ataiyst) in experiments performed at 150 rpm, the Wheeler-Weisz modulus was calculated for aU monoUths by estimating the layer thickness (L) from the carbon yield. inside the carbon layers was estimated to be 1 to 3 x 10 ° m /s inside the varions carbons. The valnes for are presented in Table 11.5. For 1-Al, consisting mainly of macroporons carbon, it is likely that internal diffusion limitations are present inside the carbon walls (where the lipase is located). This was also indicated by the decreased activity per gram of enzyme for these monoliths (Table 11.5). For ceramic monoliths, all adsorbed enzyme is used effectively (a constant tnmover freqnency for all carbon types), as confirmed by the low valnes for... 

Finding pore resistance effects from experiment. Here we have a simple trick to help us. Define another modulus which only includes observable and measurable quantities. This is known as the Wagner-Weisz-Wheeler modulus My (lucky for us that the three researchers who first dealt with this problem had last names all starting with the same letter). 

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