Diffusion counter

Condition (iv). For equimolar counter diffusion in a binary mixture, the... 

In dilute systems the logarithmic-mean insoluble-gas and nonvolatile-hquid concentrations approach unity, and Eq. (5-261) reduces to the dilute-system formula. For equimolar counter diffusion (e.g., binary distillation), these log-mean factors should be omitted. See Eq. (5-189). 

That is, since the rate of diffusion of B in the liquid film is = bNA for counter-diffusion,... 

Figure 2.29. If the intrinsic barrier for electron transfer is small, the potential range within which the activation control prevails is accordingly narrow and the corresponding asymptote is approximately linear, as represented in the figure, where ks is the standard rate constant (i.e., the rate constant at zero driving force). Under these conditions, redox catalysts that offer a small driving force resulting in counter-diffusion control can be found. This behavior is identified by the value of the slope (F/TIT In 10). The intersection of the counter-diffusion and the diffusion asymptotes provides the value of the standard potential sought, , B.

The reduction of aryl-substituted vinyl halides by electrochemically generated aromatic anion radicals has also been investigated in DMF (Gatti et al., 1987). Counter-diffusion behaviour at low driving forces (pp. 34, 35) does not appear as clearly as in the case of aryl halides (Fig. 11). However, analysis of the log k vs E° plot according to a quadratic activation-driving force relationship gave standard potential and intrinsic barrier values that... 

Figure 10.4 Calculated activation energy of gas diffusion for counter-diffusion CVD modified MFI-type (circle symbols) zeolite membranes and that of counter-diffusion CVD...

Chimie, C.R. (2005) Infrared spectroscopic investigation of diffusion, co-diffusion and counter-diffusion of hydrocarbon molecules in zeolites. Elsevier, Comptes Rendus Chimie, 8, 303-319. 

The crystals of NCPs containing a-satellite DNA palindrome and chicken erythrocyte histones diffracted isotropically to 3.0 A using an in-house rotating anode X-ray source and to better than 2.5 A at a moderate intensity synchrotron beamline [30,31]. The crystals used for structure determination were grown in the microgravity environment using a counter-diffusion apparatus [32]. Ground-based... 

Gelled trials are performed in vapour diffusion, counter diffusion, and in batch. To date, the most simple and speedy procedure for performing trials... 

The main technique employed to set up crystal screens is the vapour diffusion method, either in the hanging drop or sitting drop set up. This method is based on slowly concentrating the droplet solution against a reservoir solution of infinite volmne (ml scale) compared to the volume of the droplet ( xl scale, see Fig. 14.2). Other techniques based on diffusion or counter-diffusion in agarose gels (Biertmnpfel et al., 2002) can also be useful. The... 

In a mixture of two gases A and B provided that the total pressure, and hence the total molar concentration is constant, d[A]/dx and d[B]/dx are equal and opposite and A and B tend to diffuse in opposite directions. In equimolar counter-diffusion, the two components diffuse at equal and opposite rates =- ba- Equation (108) can then be integrated... 

For small values of [A], this reduces to eqn. (110) which was derived from equimolar counter-diffusion and thus, at low concentration, the effect of bulk flow can be neglected. 

Counter diffusion of released solvent from the crystal. 

In the case of multicomponent sorption kinetics the situation becomes even more complex because replacement and counter-diffusion processes as well as film resistances at interfaces could be involved [6,30,31]. 

Investigation of Diffusion and Counter-diffusion of Benzene and Ethylbenzene in ZSM-5-type Zeolites by a Novel IR Technique... 

Fig. 1. Counter-diffusion of (a) Benzene (B) vs. Pyridine (Py) and (b) ethylbenzene (EB) in Hydrogen Mordenite...

The sequence of IR spectra demonstrates that the molecules of the preloaded component A (pyridine, benzene) are displaced by the ingoing component B (benzene, ethylbenzene) when the preloaded sample is contacted with the vapour phase of the second compound. The process is slow because in both cases component A is more strongly held by the sorbent than component B (vide infra). But these experiments showed, that in principle, it should be possible to monitor counter-diffusion in zeolites via the IR method. 

Figure 4 demonstrates the counter-diffusion of ethylbenzene vs. benzene. In this experiment, benzene was first taken up at 415 K from a stream of benzene in helium, with a benzene partial pressure of 1.15 mbar, until a steady state was reached (spectrum No. 0). Subsequently, ethylbenzene was admixed (1.15 mbar) with the benzene partial pressure and the total rate of the gas ilow remaining constant. Counter-diffusion is indicated by the decrease of the typical benzene absorbance at 1478 cm and the development of the typical ethylbenzene bands at 1605,1496 and 1453 cm (spectra Nos. 1-5). 

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