Diffusion interparticle

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

Fig. 34 Kinetics of association and dissociation for conventional and self-protected interactions, (a) Conventional scheme (Fig. 33a). Red lines and right axis represent temperature as a function of the elapsed time, while symbols and the left axis are the corresponding particle singlet fraction at fast (blue) or slow black) temperature quench. The insets show microscopy images of isolated or aggregated particles, (b) Self-protected scheme (Fig. 33c). Particle singlet fraction as a function of time at fixed temperature profile (red line), but at different overall particle concentrations for dilute colloids, intra-particle hybridization prevents aggregation, while at higher c the interparticle diffusion competes with hairpin formation. Adapted with permission from [140]...

A two-site model has been used (18) to model cesium transport in soils. In this model a Langmuir-type model, Equation 3,was used to represent surface sorption and a first-order model, Equation 1, was used to approximate interparticle diffusion. Extraction with CaC was used to verify the exchangeable site inventory. 

Hydraulic cements are excellent examples of accelerated chemical bonding. Hydrogen bonds are formed in these materials by chemical reaction when water is added to the powders. These bonds are distinct from the bonds in ceramics in which high temperature interparticle diffusion leads to consolidation of powders. 

Krishna R (1993) Problems and Pitfalls in the use of the Pick Formulation for Interparticle Diffusion. Chem Eng Sci 48(5) 845-861... 

Colloidal support such as small Si02 particles restrict interparticle diffusion of silver atoms when formed by radiolysis of the ions at their surface. The silver oligomers absorbing at 290 and 330 nm are observed by pulse radiolysis. They are stable with respect to coalescence but they are oxidized by MV, O, Cu and RufNHj)/. Alumino-silica gels with silver ions give after irradiation optically clear xerogels containing silver clusters from 2.5 to 4.5 nm. 

For sufficiently small particles 0 0 and 1, so the measured rate constant approaches the intrinsic rate constant (k). By making replicate measurements under similar conditions, with different particle size fractions it is possible to determine both the intrinsic rate constant and the effective interparticle diffusivity. Haag [67] suggested that this approach could be used to determine intracrystalline diffusivities in zeolite crystals. A more complete experimental study in which the diffusivity of 2,2-dimethyl butane in HZSM-5 was determined both chromatographically and from measurements of the cracking rate under diffusion-limited conditions was reported by Post et al. [68] - see Fig. 11. This approach has the advantage that it makes steady-state rather than transient measurements, but it is limited to sorbates for which a suitable catalytic reaction occurs. 

Combined intraparticle and interparticle diffusion of oxygen has been taken into account in a model of a tray bioreactor [122]. A complete bioreactor... 

In the case of battery materials, the interparticle diffusion effects within a normally starved electrolyte cell design force standard voltammetric or coulometric experiments to be extremely time consuming. However, when working with small... 

Figure 16.1.3 Schematic diagram depicting the effect of interparticle diffusion coupling (or IDC) on particle size dispersion at three deposition rates diffusion control (top), activation control (bottom), and an intermediate reaction rate (middle). Reprinted with permission of the American...

Theoretical studies have been published by Gondo (13) and by Ramachandran and coworkers (14,15,16). Gondo showed that the effects of diffusion on multiple immobilized enz3nne systems were such that mass transfer resistances are expected to improve the yield of final product. Ramachandran has applied the interior collocation technique of Villadsen and Stewart (17) to account for the expected influences of intraparticle and interparticle diffusion on the kinetics of immobilized two step enz3nne systems. 

Figure 8 illustrates the sintering and coarsening of a three particle array where the smaller particle is sandwiched between two identical, larger particles. Sintering without interparticle diffusion (each particle retains... 

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