P diffusion coefficients

P diffusion coefficient of i in a mixture f)K Knud sen diffusion coefficient d diameter of tube... 

Table 7-5. Permeability Coefficient P, Diffusion Coefficient D, and Solubility Coefficient S of Various Gases in Vulcanized cis-1,4-Poly isoprene) at 25° C...

The most recent studies of Sharon Kalia of H and P diffusion coefficients confirm the role of phosphate ion rotation in the conductivity process . The existence of extrinsic and intrinsic regions, however, has not been established with certainty, which leaves the discussion about the effective mechanism open. 

There is experimental evidence to suggest that anion and cation diffusion can have different mechanisms [70]. The temperature variation of the diffusion coefficients of P and Li in oPEO-LiPF shows quite different trends. The P diffusion coefficients follow a VTF-type de-... 

P diffusion coefficient based on thermodynamic driving force (m /s)... 

Sun Y-P and Saltiel J 1989 Application of the Kramers equation to stiibene photoisomerization in / -alkanes using translational diffusion coefficients to define microviscosity J. Phys. Chem. 93 8310-16... 

This complex Ginzburg-Landau equation describes the space and time variations of the amplitude A on long distance and time scales detennined by the parameter distance from the Hopf bifurcation point. The parameters a and (5 can be detennined from a knowledge of the parameter set p and the diffusion coefficients of the reaction-diffusion equation. For example, for the FitzHugh-Nagumo equation we have a = (D - P... 

Note that the diffusion coefficient for a polymer through an environment of low molecular weight molecules is typically on the order of magnitude of 10"" m" sec". If the first subscript indicates the diffusing species, and the second the surrounding molecules, and P stands for polymer and S for small molecules, we see that the order of diffusion coefficients is Ds g > Dp g > Dp P sequence which makes sense in terms of relative frictional resistance. 

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

The mass transport influence is easy to diagnose experimentally. One measures the rate at various values of the Thiele modulus the modulus is easily changed by variation of R, the particle size. Cmshing and sieving the particles provide catalyst samples for the experiments. If the rate is independent of the particle size, the effectiveness factor is unity for all of them. If the rate is inversely proportional to particle size, the effectiveness factor is less than unity and

experimental points allow triangulation on the curve of Figure 10 and estimation of Tj and ( ). It is also possible to estimate the effective diffusion coefficient and thereby to estimate Tj and ( ) from a single measurement of the rate (48). 

Cussler studied diffusion in concentrated associating systems and has shown that, in associating systems, it is the size of diffusing clusters rather than diffusing solutes that controls diffusion. is a reference diffusion coefficient discussed hereafter is the activity of component A and iC is a constant. By assuming that could be predicted by Eq. (5-223) with P = 1, iC was found to be equal to 0.5 based on five binaiy systems and vahdated with a sixth binaiy mixture. The limitations of Eq. (5-225) using and K defined previously have not been explored, so caution is warranted. Gurkan showed that K shoiild actually be closer to 0.3 (rather than 0.5) and discussed the overall results. 

Bailey, R. G. and Chen. H. T., Predicting Diffusion Coefficients In Binary Gas Systems," Chemical Engineering, March 17, 1975, p. 86. 

It is seen from equation (26) that the optimum velocity is determined by the magnitude of the diffusion coefficient and is inversely related to the particle diameter. Unfortunately, in LC (where the mobile phase is a liquid as opposed to a gas), the diffusivity is four to five orders of magnitude less than in GC. Thus, to achieve comparable performance, the particle diameter must also be reduced (c./., 3-5 p)... 

P is fluid density, D is diffusion coefficient, AP is pressure drop... 

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