Local effectiveness factor

This approach is analytically correct for isothermal reactors and first-order rate laws, since concentration does not appear in the expression for the Thiele modulus. For other (nonlinear) rate laws, concentration changes along the reactor affect the Thiele modulus, and hence produce changes in the local effectiveness factor, even if the reaction is isothermal. Problem 21-15 uses an average effectiveness factor as an approximation. 

Once the local effectiveness factor y has been found, the new value of r is used in equation (7.19) for the next integration step to find ys and so forth. 

The analysis will be done in three steps. In the fist step, differential equations will be developed by combining enzyme kinetics and mass transfer to obtain the substrate (and product) profile within the biocatalyst particle in the second step, local effectiveness factor profiles will be obtained from the previous step in the third step a global effectiveness factor will be obtained by adequately averaging that distribution. This global effectiveness factor describes the behavior of the biocatalyst particle as a whole and will be obtained in terms of measured and calculated parameters, being a useful way of incorporating IDR into enzyme reactor design and performance evaluation, as considered in section 5.3. 

The second step is the determination of the local effectiveness factor profile that by definition (see Eq. 4.18) is ... 

The final step is the determination of a global effectiveness factor from the profile of local effectiveness factors that adequately describe the behavior of the biocatalyst particle (membrane in this case) as a whole. Since the distribution of r values is... 

Substrate (and product) profiles are obtained from the numerical resolution of the above differential equations (system of differential equations in the case of product inhibition). The corresponding local effectiveness factors (ratio of effective and intrinsic reaction rates) are then calculated and the global effectiveness factor determined from their profiles, as in the case of simple Michaels-Menten kinetics. Results are represented in three-dimensional plots in Figs. 4.15 to 4.18 respectively. 

The concentration profile throughout the particle can be attained numerically by integrating Equation 4.57. The extent of mass transfer is commonly expressed by a local effectiveness factor, q, defined as the ratio between local reaction rates inside the catalyst particles and the reaction rate at the surface with bulk substrate concentration, as given by Eqnation 4.63. This can be rearranged to give Equation 4.64. The mean, or overall, effectiveness factor of the enzyme particles can be evaluated by an average integration of local effectiveness distribution inside the particle. 

The reaction order m is generally taken as 1 (see Section 2.1.1 for details of reaction order). The active surface area per unit volume of the solid reactant changes during the reaction. The local effectiveness factor (ij,) is included into the equation to take into account the local product layer diffusion resistance in the porous solid. It is the ratio of actual local reaction rate to local reaction rate without product layer diffusion resistance. 

Swallowing. If it is sufficiently irritant or caustic, a swallowed material may cause local effects on the mouth, pharynx, esophagus, and stomach. Additionally, carcinogenic materials may induce tumor formation in the alimentary tract. Also, the gastrointestinal tract is an important route by which toxic materials are absorbed. The sites of absorption and factors regulating absorption have been reviewed (42,43). 

Experiments were conducted with air through micro-channel A = 319 (friction factor. The relative surface roughness was low k /H = 0.001) and Kn < 0.001, thus the experiments were effectively isolated from the influence of surface roughness and rarefaction. The local friction factor is plotted versus Ma in Fig. 2.25 for air. The experimental A increases about 8% above the theoretical A as Ma increases to 0.35. 

Analyzes should be conducted on more than one sample, when available, to determine whether inferred environmental factors are indeed regional or global, and not related to specific local effects. 

In general, no matter what the route, certain characteristics will predispose a material to have local effects (and, by definition, if not present, tend to limit the possibility of local effects). These factors include pH, redox potential, high molar concentration, and the low flexibility and sharp edges of certain solids. These characteristics will increase the potential for irritation by any route and, subsequent... 

These studies indicate that the charge transfer at the metal-oxide interface alters the electronic structure of the metal thin film, which in turn affects the adsorption of molecules to these surfaces. Understanding the effect that an oxide support has on molecular adsorption can give insight into how local environmental factors control the reactivity at the metal surface, presenting new avenues for tuning the properties of metal thin films and nanoparticles. Coupled with the knowledge of how particle size and shape modify the metal s electronic properties, these results can be used to predict how local structure and environment influence the reactivity at the metal surface. 

Eor illustration purposes, we consider here a simple scenario of this interplay. We evaluate the effectiveness factor at a fixed cell voltage and thus at a fixed rig. We can express the corresponding current density as a two-variable function, jg =f f, Sqi), where the reaction penetration depth, CL/ depends on rjg. This function can be used to determine the effectiveness factor, rcL- In the case of severely limited oxygen diffusion, the following relations for local oxygen partial pressure and current density can be obtained ... 

For local effects, in contrast, the determining factor for effects to occur at the site of first contact (mucous membrane of the respiratory tract, the eyes, or the skin) is generally the concentration of the chemical in the air rather than the total dose at the site of first contact. In such cases, a tolerable concentration (expressed as mg/m ) is estabhshed from the NOAEC, or LOAEC, derived in the inhalation smdy without an adjustment to a continuous exposure. 

For substances with local effects on the respiratory tract, no general approach for interspecies scaling can be given. Anatomical and physiological differences in the airways between experimental animals and humans contribute to interspecies differences in local effects observed between animals and humans, see Section 4.7.8. It should be noted, however, that for local effects the determining factor for effects to occur in the respiratory tract is generally the concentration of the chemical in the air rather than the total dose and thus allometric scaling is not relevant. 

For local effects, a default assessment factor of 1 for interspecies extrapolation for water-soluble gases and vapors was considered to be sufficiently conservative, as well as for aerosols since the respiratory rate of rodents leads to a greater respiratory tract burden as compared to humans. 

For systemic effects, ECETOC (2003) recommended a default assessment factor of 6 for extrapolation from subacute (28 days) to chronic exposure, and a factor of 2 from subchronic (90 days) to chronic exposure. For local effects, no additional assessment factor is needed for duration of exposure extrapolation for substances with a local effect below the threshold of cytotoxicity. 

A lower assessment factor may be applied if there is evidence that the exposure duration is of no or low importance. If it is assumed that the effect is concentration-dependent rather than dose-dependent, which might be the case for certain local effects, no assessment factor for duration of exposure may be considered necessary. 

WHO/IPCS (1994, 1996, 1999) did not consider an extrapolation factor for duration of exposure specifically, but the uncertainty related to this element is included in a broader defined additional factor addressing the adequacy of the overall database (Section 5.9). The US-EPA (1993) has adopted the 10-fold factor to account for the uncertainty involved in extrapolating from less than chronic NOAELs to chronic NOAELs. This default value has later on been reconfirmed (US-EPA 2002) when only a subchronic duration smdy is available to develop a chronic reference value no chronic reference value is derived if neither a subchronic nor a chronic smdy is available. For systemic effects, ECETOC (2001) recommended a default assessment factor of 6 for extrapolation from subacute (28 days) to chronic exposure, and a factor of 2 from subchronic (90 days) to chronic exposure. For local effects, no additional assessment factor is needed for duration of exposure extrapolation for substances with a local effect below the threshold of cytotoxicity. KEMl (2003) suggested that extrapolation from subchronic to chronic exposure should be based on the distribution of NOAEL ratios reported by Vermeire et al. (2001) with an assessment factor of 16 covering 95% of the substances compared and for extrapolation from subacute to chronic exposure, with an assessment factor of 39 covering 95% of the substances. 

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