Mass transfer intraparticle

Linear Driving Force Approximation Simplified expressions can also be used for an approximate description of adsorption in terms of rate coefficients for both extrapai ticle and intraparticle mass transfer controlling. As an approximation, the rate of adsorption on a particle can be written as ... 

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

The aerobic mineralization of a-hexachloro[aaaacc]cyclohexane by endemic bacteria in the soil is limited by the rate of its desorption and by intraparticle mass transfer (Rijnaarts... 

Rijnaarts HHM, A Bachmann, JC Jumelet, AJB Zehnder (1990) Effect of desorption and intraparticle mass transfer on the aerobic biomineralization of alpha-hexachlorocyclohexane in a contaminated calcareous soil. Environ Sci Technol 24 1349-1354. 

One often finds that either external or intraparticle mass transfer effects are significant in reactors of this type. Although the treatments... 

Schematic representation of shift in activation energy when intraparticle mass transfer effects become significant.

The Influence of Intraparticle Mass Transfer Limitations on Catalyst Selectivity... 

The present section deals with the influence of intraparticle mass transfer processes on catalyst selectivity following the basic pattern established by Wheeler (64, 65) in his classic papers. 

In the presence of intraparticle mass transfer limitations, the rate per particle is expressed in terms of the species concentrations prevailing at the exterior of the catalyst. However, when external mass transfer limitations are also present, these concentrations will differ from those prevailing in the bulk. Since bulk concentrations are what one measures in the laboratory, exterior surface concentrations must be eliminated to express the observed conversion rate in terms of measurable concentrations. In the paragraphs that follow, the manner in which one eliminates surface concentrations is indicated in some detail for a specific case. 

Since our calculations indicate that intraparticle mass transfer limitations are significant, we must now consider the possibility that temperature and concentration differences will exist between the bulk fluid and the external surface of the catalyst. Appropriate mass and heat transfer coefficients must therefore be determined. 

Novel Bioparticle Research. Two major thrusts have been seen in recent particle research—the area of density manipulation so that particle density suits the desired fluidization mode, and the development of magnetic particles for use in magnetically stabilized fluidization. Intraparticle mass transfer is also of interest. Table 18 lists several novel particles developed in recent years to address these and other concerns. 

Improvement of intraparticle mass transfer is the goal of some particle research efforts. One novel approach that has been recently tested is the co-immobilization of algae with bacteria the algae produced oxygen and the bacteria produced the desired product (Chevalier and de la Noue, 1988). Another method used microporous particles entrapped within alginate bead bioparticles to prevent excess biomass growth that could hinder intraparticle mass transfer (Seki et al., 1993). 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

Adsorbents for biomacromolecules such as proteins have special properties. First, they need to have large pore sizes. A ratio of pore radius to molecule radius larger than 5 is desirable to prevent excessive diffusional hindrance (see Intraparticle Mass Transfer in this section). Thus, for typical proteins, pore radii need to be in excess of 10-15 nm. Second, functional groups for interactions with the protein are usually attached to the adsorbent backbone via a spacer arm to provide accessibility. Third, adsorbents based on hydrophilic structures are preferred to limit nonspecific interactions with the adsorbent backbone and prevent global unfolding or denaturation of the protein. Thus, if hydrophobic supports are used, their surfaces are usually rendered hydrophilic by incorporating hydrophilic coatings such as dextran or polyvinyl alcohol. Finally, materials stable in sodium hydroxide solutions (used for clean-in-place) are... 

Intramolecular chain transfer, 20 220 Intramolecular cycloacylations, 72 177 Intramolecular self assembly, 20 482 Intramolecular stretching modes, 74 236 Intraoperative auto transfusion, 3 719 Intraparticle mass transfer, 75 729-730 Intrapellet Damkohler number, 25 294,... 

Chromatographic columns packed with conventional porous particles meet these requirements only to a limited extent. Slow diffusion of large molecules limits the speed of the separation due to the low rate of intraparticle mass transfer [7]. New approaches have been introduced to overcome this problem including ... 

The usual experimental criterion for diffusion control involves an evaluation of the rate of reaction as a function of particle size. At a sufficiently small particle size, the measured rate of reaction will become independent of particle size. The reaction rate can then be safely assumed to be independent of intraparticle mass transfer effects. At the other extreme, if the observed rate is inversely proportional to particle size, the reaction is strongly influenced by intraparticle diffusion. For a reaction whose rate is inhibited by the presence of products, there is an attendant danger of misinterpreting experimental results obtained for different particle sizes when a differential reactor is used, because, under these conditions, the effectiveness factor is sensitive to changes in the partial pressure of product. 

Recently, Pacheco et al developed and validated a pseudo-homogeneous mathematical model for ATR of i-Cg and the subsequent WGS reaction, based on the reaction kinetics and intraparticle mass transfer resistance. They regressed kinetic expressions from the literature for POX and SR to determine the kinetic parameters from their i-Cg ATR experimental data using Pt on ceria. 

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