External surface concentrations estimation

In Illustration 12.5, we considered the problem of estimating the concentration differences that exist between the bulk fluid and a catalyst used for the oxidation of sulfur dioxide. If the reported temperature is that of the bulk fluid, determine the external surface temperature corresponding to the conditions cited. Additional useful data are ... 

An additional difficulty in the determination of actual TOF values for zeolite catalysed reactions deals with the accessibility by reactant molecules to the narrow micropores in which most of the potential active sites are located. The didactic presentation in Khabtou et al.[37] of the characterization of the protonic sites of FAU zeolites by pyridine adsorption followed by IR spectroscopy shows that the concentration of protonic sites located in the hexagonal prisms (not accessible to organic molecules) and in the supercages (accessible) can be estimated by this method. Base probe molecules with different sizes can also be used for estimating the concentrations of protonic sites located within the different types of micropores, which are presented by many zeolites (e.g. large channels and side pockets of mordenite1381). The concentration of acid sites located on the external surface of the... 

Here, is the experimental mean rate of reaction per unit volume of catalyst, L is a characteristic length of the porous photocatalyst (i.e., the film thickness), t is the pore tortuosity (taken as three), D is the diffusion coefficient of the pollutant in air, Cg is the mean concentration at the external surface, and e is the catalyst grain porosity (0.5 for Degussa s P25). Such a treatment was performed by Doucet et al. (2006) while taking D of the pollutants to be approximately 10 m s. The estimated Weisz modulus ranged between 10 and 10, depending on the type of pollutant, that is, some three to five orders of magnitude smaller than the value of unity, which is often taken as a criterion for internal mass transport limitation. 

Fig. 5 shows the low pressure adsorption isotherms of n-nonane by the micropore entrance modified ACF and the pristine ACF. These adsorption isotherms were determined under the almost equilibrium conditions. A remarkable enhancement of n-nonane adsorption with the micropore entrance modification is observed in the low P/Po region, although the adsorption amounts at high P/Pq region almost coincide with each other. The fractional filling of n-nonane at saturation is almost constant irrespective of the surface modification with TTS the ratios of the saturation n-nonane adsorption Wo(nonane) to the saturation Nj adsorption Wo(N2) for the modified ACF and ACF were 0.72 and 0.70, respectively. Thus, the low pressure uptake depends sensitively on the chemical state of the external surface, while the fractional filling at saturation does not change. Consequently, the slight uptake of the pristine ACF should be caused by the limitation of micropore diffusion. The diffusion limitation can be removed by application of n-nonane pressure of P/Pq >0.1 according to the result shown in Fig. 5. Accordingly, a marked enhancement of low pressure adsorption by the micropore-entrance modification is associated with enrichment of n-nonane molecules at the entrance of the micropore due to favourable interaction of n-nonane with hydrocarbon chains of TTS. The amount of the n-nonane enrichment can be estimated from the comparison of both adsorption isotherms in Fig. 5. With the adsorption amount indicated by the horizontal broken line, the equal amount of adsorption for both samples is obtained at different relative pressures of 0.065 (for ACF) and 0.02 (for TTS-modified ACF). That is, application of P/Pq = 0.065 is necessary for the prescribed adsorption in the case of ACF, whereas the TTS-modified ACF does not need such a high P/Pq. Application of P/Po = 0.02 is sufficient for the adsorption by the TTS-modified ACF. Thus, the TTS-modification increases the concentration...

Estimate the dimensionless concentration gradient on the external surface of the catalyst at = 1 or f = 0 which yields a zero gradient at the center of the catalyst for the following set of important dimensionless parameters when the chemical kinetics are first-order and irreversible in porous catalysts with rectangular symmetry Aa, intranet = 2, = 0.65, y = 8-6. 

Prediction of the fiber surface concentration during brief exposure to the saturated vapor of a strong swelling agent. The model parameters are estimated for the system PET/methylene chloride vapor at room temperature. The combination k k/Uq is the dimensionless external mass transfer coefficient k k/Uo = corresponds to a constant surface concentration. 

The Weisz-Prater criterion makes use of observable quantities like -Ra)p, the measured global rate (kmol/kg-s) dp, the particle diameter (m) pp, the particle density (kg/m ) Dg, the effective mass diffusivity (m /s) and the surface concentration of reactant (kmol/m ). The intrinsic reaction rate constant ky need not be known in order to use the Weisz-Prater criterion. If external mass transfer effects are eliminated, CAb can be used, and the effective diffusivity can be estimated using catalyst and fluid physical properties. The criterion can be extended to other reaction orders and multiple reactions by using the generalized Thiele modulus, and various functional forms are quoted in the literature [17, 26, 28]. 

An estimation of the temperature gradient in a particle is given in Example 4.5.7, indicating that notable gradients can only occur for gas-phase reactions. For an exothermic reaction, overheating of the particle (to a certain mean temperature f > Ts) leads to an increase in the intrinsic rate constant compared to the one reached at the temperature of the external surface of the particle. This effect can overcompensate for the lo ver concentration compared to the bulk phase caused by dif-fusional limitations, and the effectiveness factor may reach values above unity... 

If we assume that external mass transport has no influence (thus the concentration of oxygen at the external surface equals the gas-phase concentration), we can use Eq. (4.5.99) to estimate the maximum temperature difference between the external surface and the center of the spherical coke particle ... 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

Figure 2.4. In vivo measurement of blood-brain barrier (BBB) permeability, (a) Internal carotid artery perfusion technique (i) in the rat. Other branches of the carotid artery are ligated or electrically coagulated (o, occipital artery p, pterygopalatine artery). The external carotid artery (e) is cannulated and the common carotid artery (c) ligated. Perfusion time may range from 15 s to 10 min, depending on the test substance. It is necessary to subtract the intravascular volume, Vo, from (apparent volume of distribution), to obtain true uptake values and this may be achieved by inclusion of a vascular marker in the perfusate, for example labelled albumin. Time-dependent analysis of results in estimates of the unidirectional brain influx constant Ki (pi min which is equivalent within certain constraints to the PS product. BBB permeability surface area product PS can be calculated from the increase in the apparent volume of distribution Vd over time. Capillary depletion, i.e. separation of the vascular elements from the homogenate by density centrifugation, can discriminate capillary uptake from transcytosis. (b) i.v. bolus kinetics. The PS product is calculated from the brain concentration at the sampling time, T, and the area under the plasma concentration-time curve, AUC.

Chl and CHS are the hydrogen concentration in the liquid and the external pellet surface, respectively. H is the Henry s constant, estimated to be 2.3 x 104 kPa/(kmol/m3) (9). kLaL and ksas are the gas-liquid and liquid-solid mass... 

The external dose to an inadvertent intruder who is assumed to be exposed to uncovered waste for a period of 1,000 h at the time of facility closure can be estimated as follows. For a 137Cs source assumed to be uniformly distributed in surface soil with its decay product 137mBa in activity equilibrium, and taking into account the decay branching fraction of 0.946 (Kocher, 1981), the external dose rate per unit concentration is 2.9 X 10 11 Sv s 1 per Bq g 1 (Eckerman and Ryman, 1993). Multiplying this external dose coefficient by the assumed concentration of 137Cs (4.8 Bqg ) and exposure time (1,000 h) gives a total dose for the assumed scenario of 5 X 10 4 Sv. 

The limiting Sherwood number of 2.0 corresponds to an effective film thickness of DJ2 if the mass-transfer area is taken as the external area of the sphere. The concentration gradients actually extend out to infinity in this case, but the mass-transfer area also increases with distance from the surface, so the effective film thickness is much less than might be estimated from the shape of the concentration profile. 

In the above equation, q represents the specific growth rate (d ), Cg is external CO2 (aq) concentration (pM/kg), V is cell volume (pm ) and A is the cell surface area (pm ). Popp et al. (1998) estimated surface area to volume ratios for cells of different geometry, with cell dimensions ranging from a radius of 0.68 pm (Synechococcus sp.) to 14 pm Porosira glacialis). Isotopic fractionation for the prokaryotic species Synechococcus sp.) employed in this study exhibited little variation with growth conditions, and did not conform to the relationship observed for the eukaryotic species. Thus, Synechococcus was not included in the development of Equation (2) data from this study are shown in Figure 2. 

---