Diffusion combined

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

The polydiacetylene crystals (1-4) most strikingly corroborate these conjectures. Along this line of thought is also shown that this electron-phonon interaction is intimately interwoven with the polymerisation process in these materials and plays a profound role there. We make the conjecture that this occurs through the motion of an unpaired electron in a non-bonding p-orbital dressed with a bending mode and guided by a classical intermolecular mode. Such a polaron type diffusion combined with the theory of non radiative transitions explains the essentials of the spectral characteristics of the materials as well as their polymerisation dynamics. ... 

The simulation example DRY is based directly on the above treatment, whereas ENZDYN models the case of unsteady-state diffusion combined with chemical reaction. Unsteady-state heat conduction can be treated in an exactly analogous manner, though for cases of complex geometry, with multiple heat sources and sinks, the reader is referred to specialist texts, such as Carslaw and Jaeger (1959). 

Diffusion, combined three-dimensional and surface diffusion,... 

In order to acquire reliable estimates of metal deposition profiles and catalyst lifetimes, it is of paramount importance to determine intrinsic reaction kinetics and restrictive intraparticle diffusion. Combining these with the percolation approach, reliable estimates can be made for the metal deposition profiles and catalyst life-time. 

A long time ago, Hong, Noolandi, and Street [16] investigated geminate electron-hole recombination in amorphous semiconductors. In their model they included the effects of tunneling, Coulomb interaction, and diffusion. Combination of tunneling and diffusion leads to an S(t) oc t 1/2 behavior. However, when the Coulomb interactions are included in the theory, deviations from the universal t /2 law are observed—for example, in the analysis of photoluminescence decay in amorphous Si H, as a function of temperature. 

Thus, competition is set up between combination and diffusion of the radicals. On the basis of this diffusion-combination model, it is possible to account satisfactorily for the production of hydrogen peroxide and hydrogen. The mathematical treatment permits calculation of the theoretical fraction of the radicals reacting with a solute, and the resulting value is in good... 

Note that, as indicated by Optronic Laboratories, the response of a diffuser/fiber combination is far from uniform or ideal [21], Not only does the fiber/diffuser combination fail to provide the correct measurement area, but also the nonuniform spatial response makes the result highly sensitive to alignment. Therefore, the fiber/diffuser combination should be avoided if the OLED/PLED intensity is to be correctly measured. 

Lewis number Le Sc D = Pr Ratio of molecular thermal and mass diffusivities Combined heat and mass transfer... 

In Chapter 5 we found/ (q, t) = exp — q2Dt for translational diffusion. Combining this with Eqs. (7.2.16) and (7.2.6) gives for combined rotational and translational diffusion... 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

This model has several limitations. The film model assumes that mass transfer is controlled by the liquid-phase film, which is often not the case because the interface characteristics can be the limiting factor (Linek et al., 2005a). The liquid film thickness and diffusivity may not be constant over the bubble surface or swarm of bubbles. Experiments also indicate that mass transfer does not have a linear dependence on diffusivity. Azbel (1981) indicates that others have shown that turbulence can have such a significant effect on mass transfer such that eddy turbulence becomes the controlling mechanism in which diffusivity does not play a role. In most instances, however, eddy turbulence and diffusivity combine to play a significant role in mass transfer (Azbel, 1981). 

Several diffusers having bell-shaped, conical, and straight entry regions with diameters varying from 0.016 to 0.05 m, and different mixing tube diameters and lengths were used. Diffuser combinations denoted as A, B, C, D, and E. Holding vessel diameter, 7 jjy=0.3m and ///7 =3.33. 

The CHF and TRP values can be increased by modifying the pertinent parameters such as the chemical bond dissociation energy and thermal diffusion (combination of the density, specific heat and thermal conductivity). 

The term l3 dvjdy is called the turbulent eddy mass diffusivity Combining Eq. (7.9-15) with the diffusion equation in terms ofZl g, the total flux is... 

In the vicinity of the wall the tracers are submitted to a Taylor dispersion, that is, their diffusion combined with shear enhances the migration speed in the flow direction. This phenomenon seriously complicates all velocimetry methods since to extract the velocity of fluid this effect should be modeled precisely. As shown by analysis of DF-FCS data, large observed values of the apparent slip at the hydrophilic wall are normally fully attributed to a Taylor dispersion of nanotracers (see Fig. 2.6). The data obtained with other velocimetry technique still awaits clarification. We suggest, however, that some very large values of a hydrophobic slip might reflect a Taylor dispersion too. 

Lewis number, Le pCpDA B k density of liquid Cp specific DA—>-B molecular diffiisivity k thermal conductivity molecular diffusivity thermal diffusivity Combined mass and heat transfer... 

Case II No Transfer of Polymer Radicals out of the Particle Through Diffusion Combined with a High Termination Rate... 

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