E----------------------------------------Eddy diffusion

The value of 0/ is calculated from Eq. (14-142). The term Dg is an eddy-diffusion coefficient that is obtained from experimental measurements. For sieve plates, Barker and Self [Chem. E/ig. Sci., 17,, 541 (1962)] obtained the Following correlation ... 

For the following we assume that the atmospheric variations in C02 and in its carbon isotopic composition are entirely due to atmospheric system disturbances, such as the input of 14C-free C02 from fossil C02 production, and deviations from the average rate of 14C production by cosmic radiation. The system dynamics, i.e., the exchange coefficients and the eddy diffusivity are kept constant. We approximate the fossil C02 input p(t) by... 

The mean profiles of velocity, temperature and solute concentration are relatively flat over most of a turbulent flow field. As an example, in Figure 1.24 the velocity profile for turbulent flow in a pipe is compared with the profile for laminar flow with the same volumetric flow rate. As the turbulent fluxes are very high but the velocity, temperature and concentration gradients are relatively small, it follows that the effective diffusivities (iH-e), (a+eH) and (2+ed) must be extremely large. In the main part of the turbulent flow, ie away from the walls, the eddy diffusivities are much larger than the corresponding molecular diffusivities ... 

CE is a technique with a very high power of resolution. This is attributed to low diffusion and high plate numbers obtained from the absence of band-broadening factors (e.g., eddy diffusion, equilibrium dynamics, etc.) other than diffusion, which is also minimized by short analysis time. 

D Molecular diffusivity D, Diameter of screw Db Diameter of barrel E Eddy difiusivity e Flight width in a twin-screw extruder... 

We will apply equation (5.20) to solve for the concentration profile of suspended sediment in a river, with some simplifying assumptions. Suspended sediment is generally considered similar to a solute, in that it is a scalar quantity in equation (5.20), except that it has a settling velocity. We will also change our notation, in that the bars over the temporal mean values will be dropped. This is a common protocol in turbulent transport and will be followed here for conformity. Thus, if an eddy diffusion coefficient, e, is in the transport equation,... 

The eddy diffusion coefficients that we introduced in Chapter 5 were steady quantities, using mean turbulence quantities (e.g., the temporal mean of u C). This temporal mean character of eddy diffusion coefficients can be misleading in determining the thickness of a diffusive boundary layer because of the importance of unsteady characteristics. We will review some conceptual theories of mass transfer that have been put forward to describe the interaction of the diffusive boundary layer and turbulence. 

The relative importance of gas-phase and surface resistances depends on the nature of the pollutant and the surface as well as the meteorology (Shaw, 1984 Unsworth et al., 1984 Chameides, 1987 Wesely and Hicks, 1999). The gas-phase resistance (rgas) is determined by the vertical eddy diffusivity, which depends on the evenness of the surface and the meteorology, for example, wind speed, solar surface heating, and so on. The surface resistance (rsur[) depends on the detailed characteristics of the surface (e.g., type, whether... 

Particles in the accumulation range tend to represent only a small portion of the total particle number (e.g., 5%) but a significant portion (e.g., 50%) of the aerosol mass. Because they are too small to settle out rapidly (see later), they are removed by incorporation into cloud droplets followed by rainout, or by washout during precipitation. Alternatively, they may be carried to surfaces by eddy diffusion and advection and undergo dry deposition. As a result, they have much longer lifetimes than coarse particles. This long lifetime, combined with their effects on visibility, cloud formation, and health, makes them of great importance in atmospheric chemistry. 

Turbulent flow means that, superimposed on the large-scale flow field (e.g., the Gulf Stream), we find random velocity components along the flow (longitudinal turbulence) as well as perpendicular to the flow (transversal turbulence). The effect of the turbulent velocity component on the transport of a dissolved substance can be described by an expression which has the same form as Fick s first law (Eq. 18-6), where the molecular diffusion coefficient is replaced by the so-called turbulent or eddy diffusion coefficient, E. For instance, for transport along the x-axis ... 

DESIGNER also contains different hydrodynamic models (e.g., completely mixed liquid-completely mixed vapor, completely mixed liquid-vapor plug flow, mixed pool model, eddy diffusion model) and a model library of hydrodynamic correlations for the mass transfer coefficients, interfacial area, pressure drop, holdup, weeping, and entrainment that cover a number of different column internals and flow conditions. 

The second stage realizes a two-step procedure that re-calculates the ozone concentration over the whole space S = (tp, A, z) (, A)e l 0atmospheric boundary layer (zH 70 km), whose consideration is important in estimating the state of the regional ozonosphere. These two steps correspond to the vertical and horizontal constituents of atmospheric motion. This division is made for convenience, so that the user of the expert system can choose a synoptic scenario. According to the available estimates (Karol, 2000 Kraabol et al., 2000 Meijer and Velthoven, 1997), the processes involved in vertical mixing prevail in the dynamics of ozone concentration. It is here that, due to uncertain estimates of Dz, there are serious errors in model calculations. Therefore the units CCAB, MFDO, and MPTO (see Table 4.9) provide the user with the principal possibility to choose various approximations of the vertical profile of the eddy diffusion coefficient (Dz). 

In order to convert point efficiencies to Murphree tray efficiencies, the Chan and Fair correlation uses the same general mixing model as the AIChE model (125). This model uses Lewis case 1 (Sec. 7.1.3), i.e., mixed vapor and plug flow of liquid. In addition, some liquid back-mixing is assumed and correlated via an eddy diffusion coefficient. The model gives... 

It must, of course, be clearly understood that e and e are not, like v and a, properties of the fluid involved alone but depend primarily on the turbulence structure at the point under consideration and hence on the mean velocity and temperature at this point and the derivatives of these quantities as well as on the type of flow being considered. The use of e and e does not, in itself, constitute the use of an empirical turbulence model. It is only when attempts are made to describe the variation of 6 and eh through the flow field on the basis of certain usually rather limited experimental measurements that the term eddy viscosity turbulence model is applicable. In fact, even when advanced turbulence models are used, it is often convenient to express the end results in terms of the eddy viscosity and eddy diffusivity. 

MECC separations are conducted in open capillaries, hence eddy diffusion is not problematic. However, the columns behave in many ways like packed columns, with the micelles functioning as uniformly sized and evenly dispersed packing particles. In packed columns, resistance to mass transfer in the mobile phase is reduced (i.e., efficiency improved) when smaller particles are used because the "diffusion distance" between particles is decreased. Average inter-micellar" distance is the analogous parameter in MECC. This distance can be decreased by increasing surfactant concentration. 

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