Ratio apparent effective diffusivities

Inhibition of self-diffusion becomes apparent at timescales A short compared jD, where d is the characteristic pore diameter, because a fraction of molecules is always close to the walls, and their diffusion is hindered. This fraction depends on the surface-to-volume ratio (S/V) of the sample and the observation time A of the diffusion. This simple model leads to a fraction of 2DAf 5/V molecules being restricted in their motion. An analytical derivation [Mitl, Mit2, Mit6, Mit7] confirms an approximately linear dependence of the effective diffusion coefficient Deff(A) on... 

As seen in Table 1, the decrease in permeability can be directly attributed to a dramatic reduction in the effective diffusion coefficient, while there is a much smaller effect on the apparent solubility. A similar dependence of the solubility and diffusion coefficients on the draw ratio has been observed in other uniaxially oriented polymers (35-37). Because the glass transition and density of the polystyrene samples were found independent of the draw ratio, they concluded that the reduction in diffusivity was due to anisotropic redistribution of the free volume during drawing. Using an expansion coefficient related to draw ratio, the polystyrene data were successfully correlated using the Cohen-Turnbull free volume theory. However, the situation was found to be more complex for PVC (i ) ... 

SE.16 Considering the same reaction to the previons question, but it is performed in a PFR, with 40 g of catalyst and operating at 550 °C and 10 atm. In this reaction is introduced 5 mol/min of reactant with 20% inert. The catalyst is spherical and has a radius of 1 cm, but it is porous and has an area of the 50 m /g. The effective diffusion coefficient is 0.23cm /s. The density of the catalyst is 2.3 g/cm. Determine the effectiveness factor and apparent activation energy. Check the rate ratio with and without diffusion. 

The ratio of the effective diffusion coefficient in soils or mineral materials to the diffusion coefficient in free water is, however, also influenced by other effects than only the complexity of the diffusion paths in the pore spaces of a soil. For example, the viscosity of water can decrease in narrow pore spaces, with corresponding effects on the diffusion coefficients of the dissolved substances. Apparent tortuosity factors calculated from measured values can therefore be smaller than the value suggested by geometry. It is therefore justifiable to find a conservative estimate of diffusion coefficients for pollutants in soil water, for example when considering mineral landfill liners for which no measured values are available, to use this pure... 

We see on Fig.5 that the apparent effective dif fusivity for hydrogen is higher than for argon and helium.However the ratio of apparent diffusivities for two tracer gases is lower than the ratio of the corresponding diffusion coefficients.This may be due to the influence of intraparticle convective velocity.In fact,let us take a... 

Fig. 17 - Ratio of apparent and effective diffusivities as a function of liquid superficial velocity (75). Reprinted with permission from Chem. Engng. Science 35. Copyright (1980) Pergamon Press.

As mentioned earlier, ascorbate and ubihydroquinone regenerate a-tocopherol contained in a LDL particle and by this may enhance its antioxidant activity. Stocker and his coworkers [123] suggest that this role of ubihydroquinone is especially important. However, it is questionable because ubihydroquinone content in LDL is very small and only 50% to 60% of LDL particles contain a molecule of ubihydroquinone. Moreover, there is another apparently much more effective co-antioxidant of a-tocopherol in LDL particles, namely, nitric oxide [125], It has been already mentioned that nitric oxide exhibits both antioxidant and prooxidant effects depending on the 02 /NO ratio [42]. It is important that NO concentrates up to 25-fold in lipid membranes and LDL compartments due to the high lipid partition coefficient, charge neutrality, and small molecular radius [126,127]. Because of this, the value of 02 /N0 ratio should be very small, and the antioxidant effect of NO must exceed the prooxidant effect of peroxynitrite. As the rate constants for the recombination reaction of NO with peroxyl radicals are close to diffusion limit (about 109 1 mol 1 s 1 [125]), NO will inhibit both Reactions (7) and (8) and by that spare a-tocopherol in LDL oxidation. 

The effects of pore flow in size-exclusion electrochromatography (SEEC) are even more apparent than in reversed-phase CEC. The solutes typically separated in SEEC are slowly diffusing macromolecules such as synthetic polymers. For these solutes the enhanced diffusion effect becomes relevant even at low pore flow velocities and at low pore-to-interstitial flow ratios. 

For comparison of solid and hollow cylinders it is acceptable, as in the previous investigations, to use a modified effectiveness factor, defined as the ratio of the apparent reaction rate to that in a solid cylinder with the same height and radius and in the absence of diffusion limitations. This modified effectiveness factor may be expressed through the usually used effectiveness factor as... 

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