Michaelis Thiele modulus

It may also be useful to note that for simple Michaelis-Menten kinetics the Thiele modulus we have been discussing is given, in conventional notation, by... 

Apparent reaction rates with immobilized enzyme particles also decrease due to the mass transfer resistance of reactants (substrates). The Thiele modulus of spherical particles of radius R for the Michaelis-Menten type reactions is given as... 

Numerically calculated values of q are available when only substrate diffusion in Michaelis-Menten type kinetics is considered. They can be presented in graphical form, expressing q as a function of the Thiele modulus and of a dimensionless substrate concentration or occasionally in its reciprocal form as a dimensionless Michaelis constant f) according to Lee and Tsao [84] (reviewed in [82,83] see Table 3 for explanation of symbols), hence ... 

Dimensional analysis of the equations relates the concentration profile, both along the lumen and the radius of the fiber, to seven dimensionless parameters Thiele modulus, X 2, dimensionless length, z, dimensionless Michaelis constant, O and the following dimensionless quantities b/a, d/a, Di/D3 and Di/tt Dj. 

General correlations of bulk concentration as a function of Thiele modulus, dimensionless Michaelis constant and the dimensionless length in the entire range of practical operating conditions are available under the same assumptions as the previously described reactor configuration.47 53... 

The Thiele modulus, calculated from reaction rate data, diffusion length, and diffusion coefficient, can be used to evaluate internal mass transfer effects. Expressed with the Michaelis constant and maximum reaction velocity, the Thiele modulus is given by... 

Kamat et al. have calculated the dependence of the Thiele modulus on particle size and enzyme activity in SCCO2 [57]. For a reaction that obeys Michae-lis-Menten kinetics, any combination of particle radius and that gives... 

Fig. 4.13 Global effectiveness factor (mean integral value) of a membrane immobilized enzyme with Michaelis-Menten kinetics as a function of bulk substrate concentration and Thiele modulus...

Fig. 3.4 The substrate concentration profile with respect to the radial distance predicted by first-order kinetics (solid lines) and Michaelis-Menten kinetics with j3 = 5 (broken lines) for different values of Thiele s modulus ().

Fig. 3.5 Effect of Thiele s modulus on the effectiveness factor for spherical immobilized particles for first-order kinetics and Michaelis-Menten kinetics with p = 5. Thiele s modulus for first-order kinetics is...

Thiele s modulus, (R/3) -Jk / Dg for first-order kinetics, (R/3) / DsK ) for Michaelis-Menten kinetics. 

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