Interparticle transport

Numerical simulations of the coarsening of several particles are now possible, allowing the particles to change shape due to diffusional interparticle transport in a manner consistent with the local interphase boundary curvatures [17]. These studies display interparticle translational motions that are a significant phenomenon at high volume fractions of the coarsening phase. 

Whether particles sinter by migration or by an atomic interparticle transport process is less important in a catalytic sense than is the rate at which particles reconstruct. If reconstruction is slow, as it might be with large particles, then unusual surface structures will be present and these may affect catalytic properties. Wynblatt and Gjostein23 have estimated the relative... 

In all the models discussed so far, the support surface was assumed to be flat. In fact, very many case studies, particularly of supported metals, have used flat, low-surface-area substrates. However, Wynblatt and Ahn [36] have demonstrated that surface curvature does affect the surface free energy, the growth of particles (sintering) via particle migration and interparticle transport. Therefore, the sintering process of practical supported catalysts which frequently use high-surface-area, porous supports must be significantly more complex than described by the simple models. 

Sintering of supported solids can occur by two distinct mechanisms particle migration and coalescence as already mentioned above and interparticle transport of atoms or molecules (Ostwald ripening)... 

Interparticle transport may be possible either by surface diffusion across the support or by vapor phase transport. Depending on the supported systems and on the sintering conditions the particles may grow predominantly via one of these possible routes. Supported PcFe deposits have been sintered in experimental conditions close to that of the condensation process (T = 235°C, residual pressure 10 torr). The surface areas of PcFe after 2 and 3 hours of sintering are shown in Table IV. It is seen that the sintering effect is more pronounced with a homogeneous carbon support. 

From the above it follows that in most practical situations a model, that takes into account only an intraparticle mass and an interparticle heat transfer resistance will give good results. However, in experimental laboratory reactors, which usually operate at low gas flow rates, this may not be true. In the above criteria the heat and mass transfer coefficients for interparticle transport also have to be known. These were amply discussed in Section 4.2. 

It is also interesting to note that HD may play two additional roles during miniemulsion polymerization. It may hinder (or retard) the interparticle transport of monomer during polymerization by two different mechanisms ... 

Under these circumstances, the interparticle transport resistances can be neglected. What are left are the intraparticle resistances, i.e. the heat and mass transfer effects inside the catalyst particles. Since the current case reflects the situation that few reactant and product molecules exist in an environment of solvent molecules, the simplest Fick s law approach with effective diffusion coefficients can be considered as sufficient for the description of molecular diffusion. 

Table 12.2 Some models for interparticle transport the reactor field equations...

The adsorption isotherms for both pesticides were Type I of the BET classification (Figure 7.27) and fitted very well to the Langmuir equation. The amount of the two pesticides adsorbed on different activated carbons varied between -18 and 36% for diquat, and between -6 and 14% for paraqnat, depending upon the surface area of the activated carbon (Table 7.10). These workers also carried out calculations for thermodynamic quantities, such as differential heat of adsorption AH and activation energy E, which indicated that the rate of removal of these pesticides by activated carbons is an endothermic process, which agreed with the suggested interparticle transport rate control mechanism. However, the eqnUibrium... 

Table 8.1 Some Models for Interparticle Transport The Reactor Field Equations...

We compare the intrinsic rate of adsorption of nitrogen with an experimentally observed rate of adsorption of nitrogen at 6 bar and 25°C (Crittenden et al. 1995). Appropriate substitution of numerical values into equation (4.1) gives the maximum intrinsic rate of adsorption as 2 x 10 kg m s" . On the other hand, the experimentally observed rate is approximately 4 x 10 kg s (c. 0.33 mol s" at 6 bar, 25°C onto a surface of 250 m g ). Thus the intrinsic rate of adsorption is some 10 times faster than the observed rate of adsorption. It is generally acknowledged throughout the literature on physical adsorption processes that the dominant rate-controlling step is not the actual physical attachment of adsorbate to adsorbent (normally referred to as very rapid) but rather intraparticle transport of gas within the porous structure of the adsorbent to its available surface. Interparticle transport from bulk fluid to the external surface of the porous adsorbent may also have an effect on the overall rate of adsorption under some circumstances. 

In Chapter 4, two different transport regimes were identified transport inside the particles and transport between the bulk fluid and the surface of the catalyst particles. Transport inside the catalyst particles is known as internal or intraparticle transport, or as pore diffusion. Transport between the bulk fluid stream and the external surface of the catalyst particles is known as external or interparticle transport. The mechanisms of transport are different fiar these two regimes, and the rates of transport are influenced by different variables. Internal transport will be treated first, followed by extmial tranqiort. These discussions will be preceded by a brief overview iff the physical nature of heterogeneous catalysts. 

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