Overall Pore Size Distribution

Fig. 7.7 Overall pore size distribution for the sample B2. (From [5])...

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

The determination of the evolution of the permeability of these rocks during acidizing is necessary when attempting to predict the evolution of the skin (Equation 2). Previous studies (6) have tried to model the shift of the pore size distribution due to acid attack. Then, permeability profiles were computed by integrating the contributions to the overall flow of each of the rock pores, all over the considered volume of rock. The main limitation of this method lies in the disregarding of the spatial correlation between rock pores. 

Fast adsorption/desorption kinetics and relatively small (<10 kj/mol) adsorption enthalpies are observed for hydrogen adsorption on many porous materials, which indicates that physisorption on porous materials is suitable for fast recharging with hydrogen [81,82], The narrowest pores make the biggest contribution to hydrogen-adsorption capacity, whereas mesopores contribute to total pore volume, but little to hydrogen capacity, and are detrimental for the overall volumetric capacity. Hence, porous materials with very narrow pores or pore-size distributions are required for enhanced hydrogen capacity at low pressures. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

As stated earlier, CEP and CC are the most common materials used in the PEM and direct liquid fuel cell due fo fheir nature, it is critical to understand how their porosity, pore size distribution, and capillary flow (and pressures) affecf fhe cell s overall performance. In addition to these properties, pressure drop measurements between the inlet and outlet streams of fuel cells are widely used as an indication of the liquid and gas transport within different diffusion layers. In fhis section, we will discuss the main methods used to measure and determine these properties that play such an important role in the improvement of bofh gas and liquid transport mechanisms. 

Eikerling et al. ° used a similar approach except that they focus mainly on convective transport. As mentioned above, they use a pore-size distribution for Nafion and percolation phenomena to describe water flow through two different pore types in the membrane. Their model is also more microscopic and statistically rigorous than that of Weber and Newman. Overall, only through combination models can a physically based description of transport in membranes be accomplished that takes into account all of the experimental findings. 

The overall gain of the multiphase mixture model approach above is that the two-phase flow is still considered, but the simulations have only to solve pseudo-one-phase equations. Problems can arise if the equations are not averaged correctly. Also, the pseudo-one-phase treatment may not allow for pore-size distribution and mixed wettability effects to be considered. Furthermore, the multiphase mixture model predicts much lower saturations than those of Natarajan and Nguyen - and Weber and Newman even though the limiting current densities are comparable. However, without good experimental data on relative permeabilities and the like, one cannot say which approach is more valid. 

Electrical-charge effects can be further exploited by using charged membranes (as referred to above) to increase retention of all species with like polarity. It is important to mention that it may be possible to exploit electrostatic interactions even for solutes with similar isoelectrical points, due to different charge-pH profiles for the different species present. The membrane pore-size distribution also affects selectivity by altering the solute sieving coefficients locally. Narrow pore-size distributions, especially for electrically charged membranes, will impact very positively on membrane selectivity and overall performance. 

Validity of the derived pore size distribution should not be expected unless certain conditions are met and the following practice is recommended for mesopore size analysis if the isotherm is of Type IVa, the desorption branch should be adopted if the isotherm is of Type IVb, the adsorption branch is likely to provide a more reliable overall estimate of die pore size distribution. However, in the latter case the pore shape may be a critical factor. The procedure adopted for mesopore size analysis together with the branch of the hysteresis loop should always be clearly stated. 

Cancellous bone is a very porous material, with an average density of 1.3gcm, implying a porosity of nearly 35%. In practice, the density lies between 5 and 95% varying gradually between cortical and cancellous regions. The pore size distribution is bimodal. The pores are elongated and filled with soft tissues that include bone marrow, blood vessels, and various bone-related cells. It is the overall porosity and the pore size distribution that mostly control the mechanical properties of bone. 

For the micromodel experiments described here, it is felt that the foam sweep efficiency was lower, overall, due to the loss of dimensionality, but that the relative performance by SI, GDS and GDW injection are unaffected by dimensionality. It is not likely, either, that the pore thickness dominated any capillary phenomena that should instead have depended on the two-dimensional pore size distribution. If a typical pore thickness between 200 and 300mm is taken,10>20 then Table I would seem to indicate that the pore diameters were at least comparable if not much smaller, such that the pore diameters would be responsible for any variation in capillary pressure. 

The overall performance of a catalyst is known to depend not only on the inherent catalytic activity of the active phase but also on the textural properties of the solid. The ability to control the specific surface area and the pore size distribution during the synthesis of amorphous silica-aluminas has been described for both surfactant micelle templated syntheses (M41-S (1), FSM-16 (2), HMS (3), SBA (4), MSU (5), KIT-1 (6)) and cluster templated sol-gel syntheses (MSA (7), ERS-8 (8)). 

The overall performance of membranes is related to two main characteristics their permeability and their permselectivity (separation ability). For porous membranes, the selectivity and the membrane cutoff depend on the pore size and the pore size distribution of the separative layer. The membrane permeability and the membrane thickness fix the viscous flux for a given transmembrane pressure. The viscous flux of a liquid, J, across a porous medium is given by Darcy s law ... 

Finally, track-etched MF membranes are made from polymers, such as polycarbonate and polyester, wherein electrons are bombarded onto the polymeric surface. This bombardment results in sensitized tracks, where chemical bonds in the polymeric backbone are broken. Subsequently, the irradiated film is placed in an etching bath (such as a basic solution), in which the damaged polymer in the tracks is preferentially etched from the film, thereby forming cylindrical pores. The residence time in the irradiator determines pore density, and residence time in the etching bath determines pore size. Membranes made by this process generally have cylindrical pores with very narrow pore-size distribution, albeit with low overall porosity. Furthermore, there always is the risk of a double hit, i.e., the etched pore becomes wider and could result in particulate penetration. Such filter membranes are often used in the electronic industry to filter high-purity water. 

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