Intraparticle transport mechanisms

Intraparticle Transport Mechanisms Intraparticle transport may be limited by pore diffusion, solid diffusion, reaction kinetics at phase boundaries, or two or more of these mechanisms together. 

Comparison of the values of E for the various pesticides and the neutral and anionic species of the simple nitrophenol indicates that a much higher activation energy is associated with adsorption of neutral molecules (parathion and the neutral nitrophenol) than with adsorption of anions (2,4-D, DNOSBP, and the anionic nitrophenol). This observation suggests the possibility of two different rate-limiting steps in the intraparticle transport mechanism. Current studies are being directed toward more detailed exploration of the observed thermokinetic phenomena. 

For uptake of solute from solution by porous solids the rate will be endothermic rather than exothermic if intraparticle transport is the rate-limiting mechanism. Because diffusion is an endothermic process while adsorption is exothermic, rate of uptake of solute by porous solids will often increase with increasing temperature while for the same system the equilibrium position of adsorption or adsorption capacity will decrease with increasing temperature. 

Let us now deal with "large-pore" catalysts (e.g., a-alumina supports) in which intraparticle convection is a mass transport mechanism which cannot be ignored. 

Generally, the overall kinetics is primarily governed by the external and internal diffusion (also called the two-step mass transport mechanism Steps 2 and 3 above). The intraparticle diffusion model described below can therefore be used for calculation of ion uptake by IX resins. When the mass transfer is due only to the diffusion of adsorbate molecules through the pore liquid, a pore diffusion model is often used. On the other hand, in the case where the intraparticle mass transfer is contributed by the diffusion... 

As a first estimate, it would appear that most combinations of deactivation mechanism and intraparticle transport processes have been investigated, at least theoretically. We still would benefit from additional experimental studies in this area, especially in systems where thermal effects are of importance. We also tend to forget that sometimes important physical properties such as porosity and effective difiusivity change significantly with time-on-stream. The basics of such studies, however, are well-established fi om work dating back even twenty plus years, as seen here, so unfortunately research of this kind is probably not considered very glamorous. In addition, although the topic has not been discussed here, more work on reaction/difiusion/deactivation in biochemical systems, in many instances similar to that done for chemical systems, is much needed and is an important area for future study. 

Considering the intraparticle, the convective and the diffusive mass transport mechanisms in the pores of the particles as separate mass transport mechanisms, each one characterized by its own individual and proper driving force, rather than as a convective flux augmented of a diffusive flux in the pores of the particles... 

The solid particles in the bed always have a degree of porosity, regardless of whether the solid is a catalyst or not. The pores contained in each particle may have different characteristics (size, etc.). Thus, the diffusion of molecules on the solid surface is very important, which has various transport mechanisms, such as intraparticle diffusion, Knudsen diffusion, or surface diffusion. The latter, for example, depends on the surface characteristics, such as high or low surface area. Typically, one determines the effective diffusion encompassing both characteristics. 

The external fluid film resistance (the corresponding mass-transfer coefficient ki from equations (3.4.32a,b)) is in series with the intraparticle transport resistance. The flux of a species through a porous/mesoporous/microporous adsorbent particle consists, in general, of simultaneous contributions from the four transport mechanisms described earlier for gas transport in Section 3.1.3.2 (for molecular diffusion, where (Dak/T>ab) 2> 1) ... 

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. 

A quantitative answer to above questions may be given through the theoretical modeling of non-isobaric, non-isothermal single component gas phase adsorption. External heat and mass transfer, intrapai ticle mass transport through Knudsen diffusion, Fickian diffusion, sorbed phase diffusion and viscous flow as well as intraparticle heat conduction are accounted for. Fig. 1 presents the underlying assumption on the combination of the different mass transport mechanisms in the pore system. It is shown elsewhere that the assumption of instantaneous... 

The major difference between the various GRM models is due to the mechanism of intraparticle diffusion that they propose, namely pore diffusion, siuface diffusion or a combination of both, independent or competitive diffusion. The pore diffusion model assumes that the solute diffuses into the pore of the adsorbent mainly or only in the free mobile phase that impregnates the pores of the particles. The surface diffusion model considers that the intraparticle resistance that slows the mass transfer into and out of the pores proceeds mainly through surface diffusion. In the GRM, diffusion within the mobile phase filling the pores is usually assumed to control intraparticle diffusion (pore diffusion model or PDM). This kind of model often fits the experimental data quite well, so it can be used for the calculation of the effective diffusivity. If this model fails to fit the data satisfactorily, other transport formulations such as the Homogeneous Surface Diffusion Model (HSDM) [27] or a model that allows for simultaneous pore and siuface diffusion may be more successful [28,29]. However, how accurately any transport model can reflect the actual physical events that take place within the porous... 

Mass transport in an adsorbent particle can be viewed as a combination of several mechanisms, as shown in Figure 14.8. Macropore and micropore diffnsion are shown and conld be considered as examples of intraparticle diffusion. Bulk flow or conveyance through the particle (e.g., via connected pores) is shown in that figure but, to be significant, requires high porosity or a large... 

Optimal reactor design is critical for the effectiveness and economic viability of AOPs. The WAO process poses significant challenges to chemical reactor engineering and design, due to the (i) multiphase nature of WAO reactions (ii) temperatures and pressures of the reaction and (iii) radical reaction mechanism. In multiphase reactors, complex relationships are present between parameters such as chemical kinetics, thermodynamics, interphase/intraphase intraparticle mass transport, flow patterns, and hydrodynamics influencing reactant mass transfer. Complex models of WAO are necessary to take into account the influence of catalyst wetting, the interface mass-transfer coefficients, the intraparticle effective diffusion coefficient, and the axial dispersion coefficient. " ... 

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