Macropore diffusion

This type of diffusion takes place when the pore diameter is large compared to the mean free path of the gas molecules. In this case collisions between the molecules represent the main barrier to diffusion. In contrast to micropore diffusion, macropore diffusion, which is largely determined by this mechanism, is not an activated process. The order of magnitude of the diffusion coefficient for a gas A can be estimated by means of the simple kinetic gas theory (Equation 2.1-22)... 

It arises solely because we continue Co describe micropore diffusion in terms of smooch macropore concentration fields and their gradients, even under reactive conditions where these no longer adequately describe Che actual concentration gradients in the micropores. 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

The mesopores make some contribution to the adsorptive capacity, but thek main role is as conduits to provide access to the smaller micropores. Diffusion ia the mesopores may occur by several different mechanisms, as discussed below. The macropores make very Htde contribution to the adsorptive capacity, but they commonly provide a major contribution to the kinetics. Thek role is thus analogous to that of a super highway, aHowkig the adsorbate molecules to diffuse far kito a particle with a minimum of diffusional resistance. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Macropore Diffusion. Transport in a macropore can occur by several different mechanisms, the most important of which ate bulk molecular... 

For a macroporous sorbent the situation is slightly more complex. A differential balance on a shell element, assuming diffusivity transport through the macropores with rapid adsorption at the surface (or in the micropores), yields... 

Also shown are the corresponding curves calculated for the same system assuming a diffusion model in place of the linear rate expression. For intracrystalline diffusion k = 15Dq/v, whereas for macropore diffusion k = 15e /R ) Cq/q ), in accordance with the Glueckauf approximation (21). 

Activated carbons for use in Hquid-phase appHcations differ from gas-phase carbons primarily in pore size distribution. Liquid-phase carbons have significantly more pore volume in the macropore range, which permits Hquids to diffuse more rapidly into the mesopores and micropores (69). The larger pores also promote greater adsorption of large molecules, either impurities or products, in many Hquid-phase appHcations. Specific-grade choice is based on the isotherm (70,71) and, in some cases, bench or pilot scale evaluations of candidate carbons. 

Fig. 10. Catalyst macropores showing D noble metal sites and (a) narrowed micropores after exposure to high temperatures where H represents thermally damaged noble metal sites and (b) pore mouth plugging from poisons where A, if aUowed, diffuses in to be converted to B.

Pore dijfusion in fluid-filled pores. These pores are sufficiently large that the adsorbing moleciile escapes the force field of the adsorbent surface. Thus, this process is often referred to as macropore dijfusion. The driving force for such a diffusion process can be approximated by the gradient in mole fraction or, if the molar concentration is constant, by the gradient in concentration of the diffusing species within the pores. 

In a particle having a bidispersed pore structure comprising spherical adsorptive subparticles of radius forming a macroporous aggregate, separate flux equations can be written for the macroporous network in terms of Eq. (16-64) and for the subparticles themselves in terms of Eq. (16-70) if solid diffusion occurs. 

Liquid phase applications account for nearly 80% of the total use of activated carbon. Activated carbon used in liquid phase applications typically have a high fraction of pores in the macropore (>50nm) range. This is to permit the liquid phase molecules to diffuse more rapidly into the rest of the pore structure [15]. 

Fig. 2. Models of the primary particle (a) and polymer grain (b) for the analysis of the role of monomer diffusion to tbe catalyst surface, (a) 1—catalyst 2—polymer film, (b) 1—micrograin 2—macropore.

The contributions of the individual fluxes were based upon the volume fractions of the respective areas available for diffusion, as would be expected from the simple models given earlier. For low-density pellets only the macropore contribution is significant, and if the macropores are large enough, or the pressure high enough, the Knudsen part of the diffusion in the macropores can be neglected. Under these conditions their expression simplifies to... 

The absorption property exhibited by active carbon certainly depends on the large specific surface area of the material, though an interpretation that it is based solely on this is incomplete. This is borne out by the fact that equal amounts of two activated carbon specimens, prepared from different raw materials or by different processes and having the same total surface area, may behave differently with regard to adsorption. Such differences can be partly explained in terms of the respective surface properties of the carbon samples and partly in terms of their relative pore structure and pore distribution. Every activated carbon particle is associated with at least two types of pores of distinctly different sizes. They are the macropores and the micropores. The macropores completely permeate each particle and act as wide pathways for the diffusion of material in and out of carbon, but they contribute very little to the total surface area. The micropores are more important since they... 

Table 16-4 shows the IUPAC classification of pores by size. Micropores are small enough that a molecule is attracted to both of the opposing walls forming the pore. The potential energy functions for these walls superimpose to create a deep well, and strong adsorption results. Hysteresis is generally not observed. (However, water vapor adsorbed in the micropores of activated carbon shows a large hysteresis loop, and the desorption branch is sometimes used with the Kelvin equation to determine the pore size distribution.) Capillary condensation occurs in mesopores and a hysteresis loop is typically found. Macropores form important paths for molecules to diffuse into a par-... 

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