Diffusional Length

Confined flows typically exhibit laminar-flow regimes, i.e. rely on a diffusion mixing mechanism, and consequently are only slowly mixed when the diffusion distance is set too large. For this reason, in view of the potential of microfabrication, many authors pointed to the enhancement of mass transfer that can be achieved on further decreasing the diffusional length scales. By simple correlations based on Fick s law, it is evident that short liquid mixing times in the order of milliseconds should result on decreasing the diffusion distance to a few micrometers. 

For a molecule at RTP this is of the order of a few hundred molecular diameters. In our ideal gas there is a distribution of velocities of the molecules about a mean value c. The mean free path defines a length scale in gases. As the density of the gas is increased and the mean free path approaches the molecular dimensions, a short-range molecular order develops and the material condenses to a liquid. The diffusional length scale is now much shorter range as a molecule encounters its... 

Of course, the borderline between the two pictures (the one-phase and the two-phase ones) becomes diffused when the second transforms into the first with the decrease of the typical pore radius. In fact, as will become clear in Chapter 6, 6.4, distinction between the phases becomes meaningless as soon as the typical pore radius becomes shorter than some typical electro-diffusional length scale—the Debye length—to be defined below. 

Nitrogen physisorption of the Ge-ZSM-5 sample revealed a considerable contribution of mesopores to the total pore volume, accompanied by a drop in micropore volume of 20%. In a study of the catalytic activity of these materials it was found that the increased mesoporosity of Ge-ZSM-5 had a beneficial effect on the catalytic activity in a series of acid-catalysed reactions.1771 It was observed that the presence of germanium in the framework does not change the strength of the acid sites but, instead, decreases the extent of deactivation from coke residues formed upon reaction. The microporous domains only have short diffusional lengths, but the shape selectivity ascribed to the zeolitic channels is still fully... 

Using AW devices to monitor dynamic processes such as diffusion and corrosion can dramatically reduce the time required to quantify these processes. For example, as discussed in Section 4.2.2, diffusion equilibration times typically increase with the square of the diffusional length. For a thin film, this length scale, the film thickness (h), is very small. This enables the quantification of diffusion coefficients as low as 10 cm /sec in less than one day, whereas months would be required using many conventional techniques that use thick films or bulk samples. For corrosion monitoring, the dramatic decrease in mass detection limits obtainable using coated AW devices, as compared with conventional balances and sample coupons, allows detectable mass changes to be achieved in minutes or hours rather than days or months (Section 4.4.3). 

In this, g is a geometrical factor, is a diffusional length, v is the velocity of a molecule, and Ea is the activation energy for diffusion. In ordinary gas diffusion the activation... 

For Knudsen diffusion, d is the pore diameter and the activation energy for diffusion is zero. For activated gas translational diffusion d is the diffusional length between adjacent low-energy sites [37] or the pore diameter [38], and the activation energy is between 10 and 60 kJ/mol [37]. The parameter z, the lattice coordination number, depends on the zeolite type, z is equal to 4 for ZSM-5 and to 6 for 5 A, compared to 3 for Knudsen diffusion. 

The results of this Investigation Illustrate the utility of SAW devices in characterizing the properties of thin films formed on the substrate of the device. Using the SAW device as an extremely sensitive microbalance, N2 adsorption isotherms have been obtained directly on thin films. This has allowed the characterization of the surface area and pore size distribution in the film. In general, these measurements are not possible with conventional instrumentation due to the low total surface area present in thin film samples. As another application, SAW device frequency transients can be used to monitor diffusion of species in polymer films in real-time. The short diffusional length scale present in a thin film makes the time required for saturation of the film orders of magnitude shorter than would be required with bulk samples. This allows for a dramatic decrease in the time required for determining diffusion coefficients. 

Figure 3-7 Two mixtures with the same concentration (50% light and 50% dark component), but in (b) the intimacy of contact between the two materials is greater and the diffusional length scale is shorter. More surface area is available for transport in (b) than in (a). If a chemical reaction occurs in each of these systems, the observed reaction rates would be very different.

This measure can be used to characterize the diffusional length scale at all spatial locations. / STD cannot be obtained directly in complex flows, but it is predictable from the stretching field. 

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