Intraparticle solution processing

Equation (11) is valid for small fractional conversions (F < 0.5). Its main advantage is that the effective diffiisivity, D f, is obtained from the individual diffusivities Dq and D,. The linear dependence of the fractional conversion F versus (Cot) values in the initial stage is typical for intraparticle kinetic processes. Within the approximate solution, the moving boundary velocity is independent of the diffusivity Dy. There is dependence on charge, Zy, and this aspect is considered. 

Solution processes use autoclave, tubular, or loop reactors. As compared to slurry and gas-phase polymerization, solution processes are commonly operated at a much higher temperature to keep the polymer dissolved in the reaction medium, and at much lower average residence times (5-20 min, as opposed to 1-4 h). Since polymerization conditions are more uniform in solutions reactors - there are no inter- and intraparticle heat- and mass-transfer resistances, for instance - this configuration is commonly used for the production of EPDM rubbers with soluble Ziegler-Natta vanadium-based catalysts. Composition homogeneity is a require-... 

The above stagewise analyses provide only the steady state overall mass balances. The design of batch processing equipment requires solution of the dynamic equations (introduced in Chapter 4) which describe the rate of uptake of the adsorbate by the adsorbent. Important matters to consider include the shape of the isotherm, whether V may be considered to be finite or infinite, and the nature of the adsorbent and the intraparticle rate processes (Tien 1994). 

Abstract Removal of catechol and resorcinol from aqueous solutions by adsorption onto high area activated carbon cloth (ACC) was investigated. Kinetics of adsorption was followed by in-situ uv-spectroscopy and the data were treated according to pseudo-first-order, pseudo-second-order and intraparticle drfiusion models. It was fotmd that the adsorption process of these compotmds onto ACC follows pseudo-second-order model. Furthermore, intraparticle drfiusion is efiective in rate of adsorption processes of these compoimds. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundhch models. The fits of experimental data to these equations were examined. 

The film diffusion process assumes that reactive surface groups are exposed directly to the aqueous-solution phase and that the transport barrier to adsorption involves only the healing of a uniform concentration gradient across a quiescent adsorbent surface boundary layer. If instead the adsorbent exhibits significant microporosity at its periphery, such that aqueous solution can effectively enter and adsorptives must therefore traverse sinuous microgrottos in order to reach reactive adsorbent surface sites, then the transport control of adsorption involves intraparticle diffusion.3538 A simple mathematical description of this process based on the Fick rate law can be developed by generalizing Eq. 4.62 to the partial differential expression36... 

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. 

Earlier [26,27,43,46] a phenomenological approach, based on the premise that the thermodynamics of irreversible processes [29] joined with Nemst-Planck equations for ion fluxes, would be useful was applied to the solution of intraparticle diffusion controlled ion exchange (IE) of fast chemical reactions between B and A counterions and the fixed R groups of the ion exchanger. In the model, diffusion within the resin particle, was considered the slow and sole controlling step. 

Rates of ion exchange processes are affected by diffusional resistances of ions into and out of the solid particles as well as resistance to external surface diffusion. The particles are not really solid since their volume expands by 50% or more. For monovalent exchanges in strongly ionized resins, half times with intraparticle diffusion controlling are measured in seconds or minutes. For film diffusion, half times range from a few minutes with 0. N solutions up to several hours with 0.0017V solutions. Film diffusion rates also vary inversely with particle diameter. A rough rule is that film... 

This result may be explained by a combination of intraparticle diffusion and bulk mass transfer processes. As material is extracted from the exposed areas of the seed, the solvent must travel further through the pores to reach the solute. Also, as the entrance portion of the bed becomes depleted of soluble components, the effective bed length decreases until the residence time is insufficient to achieve equilibrium. Similar effects were observed in seed oil extraction by Fattori (1) and Taniguchi et al. (9). 

Catalyst deactivation in large-pore slab catalysts, where intraparticle convection, diffusion and first order reaction are the competing processes, is analyzed by uniform and shell-progressive models. Analytical solutions are provided as well as plots of effectiveness factors as a function of model parameters as a basis for steady-state reactor design. 

The solid supported extractants can be employed in fixed bed contactors to extract metal ions from solutions. Other geometries include slurry extractors and moving bed adsorbers. We consider a fixed bed geometry. In this case the following mass transfer processes may be present (1) interpellet mass transfer, which refers to the diffusion and mixing of metal ion in fluid occupying the spaces between pellets (2) interphase mass transfer, which is the transfer of metal ion across the fluid peUet interface and (3) intraparticle mass transfer, which is the diffusion of metal ions in... 

Since intraparticle diffiision/transport controls the species transport rate, a linear transport rate expression is sought to describe it to focilitate solution of the overall adsorption process taking place in a packed bed. The transient rate of adsorption/desorption of a species i may be described by the time rate of change of a particle-averaged species concentration defined for a spherical particle of radius tp by... 

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