Uptake Rate Measurement

Oxygen Uptake Rate Measurements of Bulk Water... 

Equation 9.15, when solved for the case of macro-pore diffusion gives us, in the low loading Hmit, the famihar relationship that mass uptake is proportional to the square root of time. The same relationship can be derived for micro-pore diffusion as well. The solution to this equation can be used with the appropriate particle sizes to estimate diffusivity from uptake rate measurements. 

Schweitzer, F., L. Magi, P. Mirabel, and C. George, Uptake Rate Measurements of Methanesulfonic Acid and Glyoxal by Aqueous Droplets, J. Phys. Chem. A, 102, 593-600 (1998). 

NMR Sorption Comparison Diffusion of the large tri-ethylamine molecule is sufficiently slow that reliable dif-fusivities can be determined from uptake rate measurements in 50]jm crystals(57) at least over a limited range of conditions. A comparative study, carried out with the same zeolite samples showed good agreement between the sorption and PFG NMR measurements, both as to the magnitude of the diffusivity ( 10 cm2.s- at 445K) and the trends with concentration and temperature(41). 

The relationship between irradiance and N uptake in the Southern Ocean is unclear and often contradictory, and most of our earher understanding is based on comparison of specific N uptake rates measured at various depths throughout the euphotic zone using either in situ or simulated in situ irradiance fields. Although... 

When pubhshed reports of the diffusivity of paraffins in ZSM-5 catalysts obtained from uptake rate measurements appeared grossly inconsistent with catalytic behavior. Werner participated in resolving the problem by determining diffusivities from catalytic behavior of catalysts of very different particle sizes. The analysis not only confirmed the many orders of magnitude higher true diffusivities but also allowed Werner to extend the technique to demonstrate that shape selectivity could occur due to lack of fit of a reactant (e.g., diffusion of a dimethyl paraffin) in the structure or lack of fit of a reaction complex (transition state) that must be created on the active site (e.g., the methyl paraffin/propyl cation complex). 

Bedner, E., Melamed, M.R., and Darzynkiewicz, Z. (1998) Enzyme kinetic reactions and fluorochrome uptake rates measured in individual cells by laser scanning cytometry (LSC). Cytometry, 33, 1-9. 

A new experimental technique (ZLC) has been developed and applied to study the diffusion of a range of hydrocarbons (xylene, benzene, cyclohexane and linear paraffins) in unaggregated crystals of zeolites A and X. The validity of the method was confirmed by varying the crystal size and the nature and flowrate of the purge gas. The method has advantages of speed and simplicity but the major advantage is that the intrusion of extraneous heat and mass transfer resistances is much less significant than in conventional uptake rate measurements. As a result, the new method can be applied to systems in which diffusion is too rapid to follow in a conventional sorption experiment. 

Monitoring urban air quality and uptake rates measurements... 

Transient uptake rate measurements are subject to intrusion of heat transfer hmitations, especially in batch measurements at low pressures. Membrane permeation, frequency response, and ZLC measurements should not be subject to serious heat transfer limitations but, especially in frequency response and ZLC, there is always a danger of intrusion of extracrystalline resistances to mass transfer, although in principle these can be eliminated by reducing the sample size and ensuring that the crystals within the sample are dis-... 

Fig. 2 Experimental uptake curves for CO2 in 4A zeolite crystals showing near isothermal behavior in large (34 and 21.5 Jim) crystals (D 9 x 10 cm s at 371 K and 5.2 X 10 cm s at 323 K). The solid lines are the theoretical curves for isothermal diffusion from Eq. 2 with the appropriate value of Ddr. The uptake curves for the small (7.3 jim) crystals show considerable deviation from the isothermal curves but conform well to the theoretical nonisothermal curves with the values of Dc estimated from the data for the large crystals, the value of p calculated from the equilibrium data, and the value of a estimated using heat transfer parameters estimated from uptake rate measurements with a similar system under conditions of complete heat-transfer control. The limiting isothermal curve is also shown by a continuous line with no points. From Ruthven et al. [8]...

Uptake rate measurements with large oriented crystals have been used by Caro [24] to demonstrate the nonisotropy of silicalite. Diffusion coefficients for the longitudinal and transverse directions differed by a factor of about three. 

Regardless of the way in which progress of the sorption is followed, all uptake rate measurements are subject to the intrusion of heat transfer resistance, and such effects are more severe for strongly adsorbed and rapidly diffusing species. To circumvent this problem Grenier et al. [27] introduced... 

The striking discrepancy between the results of sorption rate measurements with large (100 xm, 250 xm) crystals, and the PFG NMR data for the xylenes in NaX was pointed out in 1989 [72]. The behavior of benzene in NaX is similar [55]. Diffusion of benzene is about an order of magnitude faster than the xylenes, and direct derivation of diffusivities from uptake rate measurements is therefore possible only over a very limited range of conditions. This system... 

Kyung, Y.-S., Peshwa, M. V., Giyte, D.M., and Hu, W.-S. (1994) High density culture of mammalian cells with dynamic perfusion based on on-line oxygen uptake rate measurements. Cvtot hnol. 14 183-190... 

The method has the advantage that it depends on a steady-state measurement and it is not affected by finite heat transfer. Effective intraparticle diffusivities determined in this way are commonly somewhat smaller than the values derived for the same adsorbent under simitar conditions from transient uptake rate measurements. This is because blind pores, which contribute to the flux in a transient measurement, make no contribution in a Wicke-Kallenbach system. 

NMR techniques provide a somewhat more convenient and widely used method for the measurement of self-diffusivities. The method is, however, restricted to species such as hydrocarbons which contain a sufficiently hi concentration of unpaired nuclear spins. In comparing the results of NMR and uptake rate measurements it follows from Eqs. (5.6) and (5.9) that one should compare the NMR self-diffusivity with the corrected diffusivity from the uptake rate measurements. Exact agreement can be expected only when the cross coefficient is zero, but this is normally a good approximation at low concentrations. 

Results of a series of uptake rate measurements performed with different crystal size fractions are summarized in Figures 5.7-5.9. For butane in both 27.5 and 55 jam 5A crystals and for COj in 21.5 and 34 pm 4A crystals the uptake rate is relatively slow and is evidently controlled by intracrystalline diffusion since the time constants show the expected dependence on the... 

FIGURE 5.16. Diffusivity data for n-butane and propane in 5A zeolite crystals showing comparison between NMR sclf-diffusivities ( ) and corrected diffusivilies from uptake rate measurements (Dq)- X, 0. 55- and 27.5-jam diameter crystals synthesized by Yucel O, , 34-and 7.3-/xm crystals synthesized by Yucel +, 3.6-ftm Linde crystals A 2l.5- im crystals synthesized by Shdanov ( ). (From ref. 54, with permission.)... 

Despite the large difference in the apparent diffusivities derived from uptake rate measurements, measurements of the intracrystalline self-diffusivity (for C2H6-5A) by the NMR (PFG) method show little difference between the large laboratory synthesized crystals and the small Linde crystals, thus favoring the surface barrier hypothesis. The increase in activation energy, which is observed for this system on severe hydrothermal pretreatment of the smaller crystals, is also consistent with a change from intracrystalline diffusion to surface barrier control. Detailed sorption rate studies with the system n-butane-5A, however, support the opposite conclusion that the differences in... 

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