Mechanical Sieving Model

The Mechanical Sieving Model (Ferry) suggests hindered transport of solute due to convection, limited by steric effects (Braghetta (1995)). Rejection is determined by the ratio of solute macromolecular diameter to pore diameter, X. 

In the performance data of various polyamide and related membranes published to date there should be valuable information for molecular design of more excellent barrier materials. But at present a means for their evaluation and optimization is still not clear. One of the reasons may at least come from the competitive flood of proposals for the detailed mechanisms of reverse osmosis, e.g. the solution-diffusion model, the sieve model, the preferential sorption model and so on. 109)... 

As seen in other chapters, the Ogston sieving model also does not describe sedimentation or diffusion through polymer solutions (cross-linked gels are a separate question not considered here), so its invocation in electrophoresis seems problematic. Conclusions about transport mechanics, drawn from relationships between measurements and a hypothesized Ogston model, are therefore subject to reservations. 

The oxidation of thiophene and its derivatives with H202 was studied using a Ti-Beta molecular sieve. The oxidation product is very dependent from the aromaticity of model compounds. The thiophene oxidation product was mostly sulfates and the benzothiophene oxidation product was benzothiophene sulfone. Oxidation of mono and di-alkyl thiophenes also produced sulfates and sulfones. The diffusivity and aromaticity of the relevant sulfur compounds, intermediates and stable product, as well as the proposed new mechanism of oxidation will be discussed. This proposed new reaction pathway is different from current literature, which reports the formation of sulfones as a stable oxidation product. 

As described above, a number of empirical and analytical correlations for droplet sizes have been established for normal liquids. These correlations are applicable mainly to atomizer designs, and operation conditions under which they were derived, and hold for fairly narrow variations of geometry and process parameters. In contrast, correlations for droplet sizes of liquid metals/alloys available in published literature 318]f323ff328]- 3311 [485]-[487] are relatively limited, and most of these correlations fail to provide quantitative information on mechanisms of droplet formation. Many of the empirical correlations for metal droplet sizes have been derived from off-line measurements of solidified particles (powders), mainly sieve analysis. In addition, the validity of the published correlations needs to be examined for a wide range of process conditions in different applications. Reviews of mathematical models and correlations for... 

The Brunauer type I is the characteristic shape that arises from uniform micro-porous sorbents such as zeolite molecular sieves. It must be admitted though that there are indeed some deviations from pure Brunauer type I behavior in zeoHtes. From this we derive the concept of the favorable versus an unfavorable isotherm for adsorption. The computation of mass transfer coefficients can be accompHshed through the construction of a multiple mass transfer resistance model. Resistance modehng utilizes the analogy between electrical current flow and transport of molecular species. In electrical current flow voltage difference represents the driving force and current flow represents the transport In mass transport the driving force is typically concentration difference and the flux of the species into the sorbent is resisted by various mechanisms. 

The sharp iron profiles in Fig. 38 are thought to be due to deposits from rust and scale, not to organometallic compounds. Their removal likely occurs by a sieving process and thus delineates the edge of the pellet. The Ni and V internal maxima cannot be predicted by simple first- or second-order reaction kinetics. Rather, these profiles are a consequence of the consecutive HDM mechanism involving metal deposition from an intermediate not originally in the oil. This mechanism has been demonstrated in model oil systems (Section IV, A, 4) and now has evidence with real oils. 

The isotherm model of Schirmer et al. (T.) for sorption in molecular sieves is based on statistical thermodynamics in which the configuration integrals describing the sorption behaviour are extracted from the available data. The model does not presuppose any specific kind of sorption mechanism. The multi-component form of this isotherm derived by Loughlin and Roberts (8 ) is also not limited to any particular sorption mechanism,... 

The overall design obtained wasverysuccessful. With theavailability of comprehensive chemical equilibria data it was possible to develop an accurate mathematical model to aid the design calculations. The sieve tray and mechanical column design were both straightforward and appeared to be efficient. 

Although Knudsen diffusion, shape selectivity, and molecular sieving play an important role in the separation of mixtures, the mechanisms which control the majority of the multicomponent separations in zeolite membranes are surface diffusion, and sometimes, capillary condensation. In addition, molecular simulations and modeling of M-S diffusion in zeolites [69,70] show that the slower moving molecules are also sped up in some mixtures [71,72] in the presence of fast-diffusing molecules and other times, slower molecules inhibit diffusion of faster molecules because molecules have difficulty passing one another in zeolite pores [73]. 

Water molecules attack high-alumina zeolites by a acid hydrolysis of the Al-O-Si bonds. The framework is decomposed inside the bulk of the crystals. High-silica zeolites are dissolved by an alkaline mechanism starting at the crystal surface. Non-framework aluminium directly formed during the dealumination or generated subsequently by a surface alumination stabilizes high-silica zeolites. Mathematical models allow the prediction of the long-term stability of molecular sieves on the basis of experimental data. 

Mechanical pulverizing and sieving procedures reduced the particle size to 100 x 200 and 200 x 325 mesh, although the data presented here are largely for the former size range. The mineral and elemental composition as a function of shale richness were determined from X-ray diffraction measurements (Phillips APD-3500) and energy dispersive X-ray fluorescence data (Kevex Model 0700). Low-temperature ash samples were prepared using a 13.56 MHz radio frequency asher (LFE Corp., Model LTA 504). 

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