Internal Effects

Variables, such as the heat or mass transfer coefficients from or to the interface or the flow friction coefficient for a given geometry, represent variables that can be included in this group. They have a dynamic effect on the process state and generally represent the dependent variables of the process. 

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The size of the cataly.st particle influences the observed rate of reaction the smaller the particle, the less time required for the reactants to move to the active catalyst sites and for the products to diffuse out of the particle. Furthermore, with relatively fast reactions in large particles the reactants may never reach the interior of the particle, thus decreasing the catalyst utilization. Catalyst utilization is expressed as the internal effectiveness factor //,. This factor is defined as follows ... 

The internal effectiveness factor is a function of the generalized Thiele modulus (see for instance Krishna and Sie (1994), Trambouze et al. (1988), and Fogler (1986). For a first-order reaction ... 

In those cases where the internal effectiveness is known in equation form, the steady state rate relation may be written... 

The extremely negative redox potential of Os(OEP)(l-MeIm)2 [29f] is therefore with confidence attributed to an internal effect which is in our opinion the additional 7r-donor effect invoked for the imidazole moiety in Sect. 5.4. Obviously this ligand induces an additional electron density at the Os11 ion which is not transmitted to the porphyrin ring because the a-band of [29f] falls between [29e] and [29i] which both have higher redox potentials than [29f itself. 

To be added in cases of indications for relevance and bioavailability In vivo bioassays with relevant exposure conditions, routes and endpoints Prolonged ELS and metamorphosis In vivo bioassays with sediment extracts In vitro bioassays specific mechanisms Internal effect levels Specific chemicals (e.g. PFACs, HBCDs, PBDEs) ELS not longer than free feeding Chemicals that only are toxic in high concentration (narcotics, nanoparticles) Chemical analysis of lipophillic POPs in water... 

Calculation of the internal effectiveness factor for spherical pellets and fust order reaction The Thiele modulus is... 

Evaluate the effective rate coefficient, i.e. the product of internal effectiveness factor and intrinsic rate coefficient for this reaction... 

The intraparticle phenomena The next step is the evaluation of the internal effectiveness factor. The unknown parameter is the effective solid-phase diffusion coefficient, which is (eq. (3.602))... 

The resulting conversion under the specified conditions is approximately 25%. Evaluate the rate coefficient of the reaction using the Orcutt—Davisdon Pigford model. Assume that the internal effectiveness factor is unity and the expansion factor zero. 

This study employed conventional diffusion-reaction theory, showing that with diffusion-limited reactions the internal effectiveness factor of a heterogeneous catalyst is inversely related to the Thiele modulus. Using a standard definition of the Thiele modulus [100], the observed reaction rate of an immobilized-enzyme reaction will vary with the square root of the immobilized-enzyme concentration in a diffusion-limited system. In this case, a plot of the reaction rate versus the enzyme loading in the catalyst formulation will be nonlinear. 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

Sijm, D. T. H. M., and J. L. M. Hermens, Internal effect concentration Link between bioaccumulation and ecotoxicity for organic chemicals . In The Handbook of Environmental Chemistry, Vol. 2, Part J, B. Beek, Ed., Springer, Berlin, 2000, pp. 167-199. 

Author/s Ito, Yasuhiko Volume 60 Issue 5 Page 1745-1755 Year 2001 Source KIDNEY INTERNATIONAL Effect of the beta (2) agonist clenbuterol on the locomotor activity... 

We notice that stress tensors are not a priori symmetric for (16) and that c)J. symmetric tensors. Further, the 3rd order microstress tensor Ss is normally related to boundary micro tractions, even if, in some cases, it could express weakly non-local internal effects % is interpreted as an externally controlled pore pressure (s includes interactive forces between the gross and fine structures. 

In principle, the two simplest approaches to maximizing the internal effectiveness and efficiency of the scheme are rapidly to phase out free allocations, or to move to relatively uniform output-based benchmarking of allocations, probably based around the performance of best available technology for the sector. 

The typical parameters for the PLD of epitaxial ZnO-based thin films on sapphire including information about target preparation are listed in Table 7.3. Within the range of these software controlled parameters, the properties of the deposited films differ widely, as will be shown in Sect. 7.4. Beside the parameters listed in Table 7.3, the film properties will be influenced furthermore by a few more internal effects, which will be listed and discussed in the following according to the scheme effect/problem-cause-solution. Only the careful consideration of all these hidden effects by experienced operators can ensure the highest quality and reproducibility of PLD grown films. 

The overall process can be affected by pore diffusion and external mass transfer. Molecular diffusion coefficients DPB may be calculated by Aspen Plus. Effective pore diffusion may be estimated by the relation DP = Dpb( j,/tp) = 0.1 DPE, in which ep is the particle porosity and rp the tortuosity. Furthermore, the Thiele modulus and internal effectiveness can be calculated as ... 

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

The derivation of the internal temperature gradient can only be performed numerically, even for simale kinetics. Again the 5% criterion is used for the internal effectiveness factor. Assuming that the rate can be simplified into a temperature and concentration dependent part, this yields... 

Figure 13. Internal effectiveness factor as a function of the Thiele modulus for nonisothermal reactions at different values for the Prater number and y, = 10 (numerical solutions for a first order reaction).

L characteristic catalyst dimension m t, internal effectiveness factor -... 

When the diffusion of a reactant inside the pellet is not fast enough to compensate for its disappearance by reaction a decreasing concentration profile is established in the pellet. For positive partial reaction orders with respect to the reactant this leads to lower reaction rates at positions away from the external surface and hence to a lower reaction rate when averaged over the complete pellet volume. A measure for the degree of internal diffusion limitations is given by the internal effectiveness factor, t, defined as ... 

The sodalite unit (or /J cage), which is a characteristic feature of the A, X and Y zeolites (see Figure 11.13), is made up of both four and six rings arranged in the form of a cubo-octahedron (i.e. a truncated octahedron). The cage has an internal effective diameter of about 0.6 nm. 

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