Pore effective

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

Bernardi, P., Vassanelli, S., Veronese, P., Colonna, R., Szabo, I., and Zoratti, M., 1992, Modulation of the mitochondrial permeability transition pore. Effect of protons and divalent cations, J. Biol. Chem. 

The first term in parentheses in eq 60, together with the preceding factor 3/, is equivalent to eq 51 this represents the pore effectiveness factor whereas the second expression in parentheses denotes the external effectiveness factor rjtM. 

From this figure, it can be concluded that the reduction of the effectiveness factor at large values of becomes more pronounced as the Biot number is decreased. This arises from the fact that the reactant concentration at the external pellet surface drops significantly at low Biot numbers. However, a clear effect of interphase diffusion is seen only at Biot numbers below 100. In practice, Bim typically ranges from 100 to 200. Hence, the difference between the overall and pore effectiveness factor is usually small. In other words, the influence of intraparticle diffusion is normally by far more crucial than the influence of interphase diffusion. Thus, in many practical situations the overall catalyst efficiency may be replaced by the pore efficiency, as a good approximation. 

The intraparticle concentration and temperature gradients in a porous particle can always be neglected, when the pore effectiveness factor rj is close to 1. Assuming that rj... 

The high-pressure and temperature micromodel system has been used in this study to investigate the formation, flow behavior and stability of foams. Micromodel etching patterns were made from binary images of rock thin sections and from other designs for a comparison of pore effects. These experiments show how simultaneous injection of gas and surfactant solution can give better sweep efficiency on a micro-scale in comparison to slug injection. 

For the particle sizes used in industrial reactors (> 1.5 mm), intraparticle transport of the reactants and ammonia to and from the active inner catalyst surface may be slower than the intrinsic reaction rate and therefore cannot be neglected. The overall reaction can in this way be considerably limited by ammonia diffusion through the pores within the catalysts [211]. The ratio of the actual reaction rate to the intrinsic reaction rate (absence of mass transport restriction) has been termed as pore effectiveness factor E. This is often used as a correction factor for the rate equation constants in the engineering design of ammonia converters. 

For this case, the pore effectiveness factor is a function of the so-called Thiele modulus m (Eq. 22) [222] ... 

Two kinds of pitch-based ACFs (P5 and P20 Osaka Gas Co.) were used. The microporous structure was determined by high-resolution N, adsorption isotherms at 77 K using a gravimetric method. The micropore structual parameters were obtained from high-resolution a, -plot analysis with subtracting pore effect (SPE) method. The average slit pore width w was determined from the micropore volume and the surface area. The adsorption isotherms of methanol and ethanol on carbon samples were gravimetrically measured at 303 K. The sample was preevacuated at 10 mPa and 383 K for 2h. 

We introduce another factor for porous bodies, it is called the pore effectiveness factor rjp. This is understood to be the ratio of the actual amount of substance transferred NA0 to the amount which would be transferred NA, if the concentration cao prevailed throughout the porous body. This basically means, if the effective diffusion coefficient DeS, which is used in place of the molecular diffusion coefficient D, was very large DeS — oo, then Ha — 0. Then according to (2.367) the reaction rate of substance A... 

The pore effectiveness factor is valid for pores with constant cross sectional area. It corresponds to the fin efficiency for a straight, rectangular fin, eq. (2.79). The pore effectiveness factor for pores of any cross sectional shape, can also be calculated, as a fairly good approximation using (2.377), as shown by Aris [2.81], if the length L is formed as a characteristic length... 

Simulated profiles are shown in Figure 12b for the case where the tip is positioned between two closely spaced pores. Here the tip and its insulating sheath partially block the pore, effectively reducing the diffusive flux of the electroactive molecule through the pore. The simulated profiles illustrate the complex nature of probing mass transport across membranes at small tip-to-sample separations. 

It may also be that the pore effect is a source of local nonuniformity, which is averaged through the rotation of the wafer (and pad, for rotary tools). Both linear and rotary CMP tools will always present the same trailing edge of any pore to the wafer surface, in contrast to the orbital CMP tools, which will have the opportunity to present more of the pore edge to the shear motion. 

Like zeolites, these materials comprise regular arrays of pores, but they have larger pore sizes, in the range 2-10 nm, and they are amorphous rather than crystalline in structure. These mesoporous materials offer much increased diffusion rates in comparison with zeolites, and yet their channels are small enough to provide useful in-pore effects, such as shape selectivity and the local concentration of reagents. 

The filtration of these primary colloid systems was described in section 5.5. The colloids of a size closest to the membrane pore size resulted in the greatest flux decline, as this was attributed to pore plu ng. In contrast, the smaller colloids were too small to fill up pores effectively at the volumes filtered, and the larger colloids formed a cake on the membrane surface. These su esrions were confirmed with electronmicrographs (see Figure 5.6). 

Volume fraction of i phase in support pores. Effectiveness factor. 

A similar study was carried by Rao et al. [23] in Sibunit carbons. They analyzed the pore effect on the performance of DMFC with carbon supports with a range of surface areas from 6 to 415 m g. Figure 7.7 shows the observed specific activity for methanol oxidation at an anode potential of 0.5 V as a function of the surface area. 

The pore effectiveness factor is given by the ratio of the moles of reactant consumed in the presence of diffusion resistance, to the moles of reactant consumed in the absence of diffusion resistance. The single pore effectiveness is used to calculate the effectiveness factor for the network... 

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