Thiele modulus flat plate geometry

Figure 8.10 (a) Representation of flat-plate geometry (b) concentration profile z) (dimensionless) for various values of Thiele modulus (j>... 

Thiele modulus, O (Equ. 5.251) for enzymatic reactions. Variation of the value are shown in the case of a flat-plate geometry of the solid phase (Pitcher, 1978). This plot is analogous to Fig. 4.36. 

The analyses of simultaneous reaction and mass transfer in this geometry are similar mathematically to those of the straight cylindrical pore model considered previously, because both are essentally one-dimensional models. In the general case, the Thiele modulus for semiinfinite, flat-plate problems becomes... 

The parameter ag= 1, 2, 3, for flat plate, cylindrical, or spherical geometry respectively. In the Thiele modulus, the character distance L = L (a half of thickness of catalyst pellet) for flat plate, L = r<, (the radius of catalyst pellet) for cylindrical, or spherical geometry. 

Figure 6 shows the effectiveness factor for any of the three different pellet shapes as a function of the generalized Thiele modulus p. It is obvious that for larger Thiele moduli (i.e. p > 3) all curves can be described with acceptable accuracy by a common asymptote t] — 1 / p. The largest deviation between the solutions for the individual shapes occurs around p x 1. However, even for the extremely different geometries of the flat plate and the sphere, the deviation of the efficiency... 

The 4>s versus if plot has the same shape as that of (pi versus ij for a flat plate but is shifted by a factor of 3 on the same log-log plot, if Equations 2.60 and 2.63 are used as basis. Aris (29,38] has shown that, for a first-order reaction in various particle geometries, the plots between the Thiele modulus q> and the isothermal internal effectiveness factor ij become identical at high and low values of

size parameter in the Thiele modulus is defined on a common basis. The characteristic size parameter L is, therefore, defined as the ratio of the particle volume to the external surface area available for reactant penetration, which enables its use for any arbitrary particle shape ... 

Figure 4.5.20 shows the effectiveness factor as a function of the Thiele modulus for a slab, a sphere, and a cyclinder. It is apparent that all curves can be described with acceptable accuracy by the exact solution for a slab [ ypore = tanh(0/0) ijpom = 1/0 for 0> 2]. Thus, Figures 4.5.21 and 4.5.22 derived fora flat plate can be used to a good approximation for any particle geometry (with Vp/Ap,ex as characteristic length for 0). 

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