Diffusion transition region

In the specific instance of A diffusing through a catalytic pore and reacting at the end of the pore to form gaseous component B, equimolar counterdiffusion can be assumed, and an effective transition region diffusivity, D a is independent of concentration and can be calculated from the Knudsen and binary diffusion coefficients ... 

Using equivalent values of 3 for t and r, and 0.5 for e and e, determine the range of pore radius for which transition-region diffusion will exist in the following systems at room temperature and 1 atm. 

The transition-region diffusion equation can be derived by adding the momentum loss due to molecule-wall collisions in Eq. (7.6-4) and that due to molecule-molecule collisions in Eq. (7,6-7) on a slice of capillary. No chemical reactions are occurring. The final differential equation is (Gl) = ... 

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

Diffusion Flames in the Transition Region. As the velocity of the fuel jet increases in the laminar to turbulent transition region, an instabihty develops at the top of the flame and spreads down to its base. This is caused by the shear forces at the boundaries of the fuel jet. The flame length in the transition region is usually calculated by means of empirical formulas of the form (eq. 13) where I = length of the flame, m r = radius of the fuel jet, m v = fuel flow velocity, m/s and and are empirical constants. 

Other Considerations In general, dry ESPs operate most efficiently with dust resistivities between 5x10 and 2 x lO ohm-cm. In general, the most diffieult particles to collect are those with aerodynamie diameters between 0.1 and 1.0 / m. Particles between 0.2 and 0.4 m usually show the most penetration. This is most likely a result of the transition region between field and diffusion charging. 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

When the radius of an aerosol particle, r, is of the order of the mean free path, i, of gas molecules, neither the diffusion nor the kinetic theory can be considered to be strictly valid. Arendt and Kallman (1926), Lassen and Rau (1960) and Fuchs (1964) have derived attachment theories for the transition region, r, which, for very small particles, reduce to the gas kinetic theory, and, for large particles, reduce to the classical diffusion theory. The underlying assumptions of the hybrid theories are summarized by Van Pelt (1971) as follows 1. the diffusion theory applies to the transport of unattached radon progeny across an imaginary sphere of radius r + i centred on the aerosol particle and 2. kinetic theory predicts the attachment of radon progeny to the particle based on a uniform concentration of radon atoms corresponding to the concentration at a radius of r + L... 

It should be noted here that since the original work done at Mobil was completed, there have been new developments published in the literature. Ishida and Wen (1968) analytically solved a special case for the transition region when the reaction rate does not depend on the local solids (coke) concentration. Wen (1968) has also numerically solved the more general problem for certain kinetic forms, and Amundson and co-workers have done much work on the diffusion and reaction in the boundry layer about a carbon particle (Caram and Amundson, 1977). We will not attempt to review the literature or compare the more accurate numerical solutions with our ad hoc approximation technique. However, we note that our technique was simple, fit the experimental and commercial data extremely well, and provided us with valuable insight and understanding... 

Overall Diffusion Control in the Glass Transition Region... 

For K very large, the right-hand side of Eq. (13) will be negligibly small, except in a very thin transition region where the newly diffused molecules are reacting with holes previously not in contact with molecules. In this case a sharp boundary will prevail between the region where the... 

If equimolecular counterdiffusion takes place N = -N B (see Volume 1, Chapter 10) and the total pressure is constant, we obtain from equation 3.5 an expression for the effective self-diffusion coefficient in the transition region ... 

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