Turbulent diffiisivity

There are many ways of categorizing air quality models. One differentiation is between statistical and deterministic models. The structure of statistical models is based on the patterns that appear in the extensive measured data. The structure of deterministic models is based on mechanistic principles wherever possible. Most deterministic models contain some degree of empiricism. For example, few models, if any, use turbulent-diffiision formulations that are based on first principles, but rather use measured values of dispersion. The same is true in regard... 

We have now derived two fundamentally different expressions for the mean concentration of an inert tracer in a turbulent flow Eqs. (2.7) and (2.19). To compute the mean concentration c from Eq. (2.7) requires only that p(x, y, z, t x, y, z, t ), the transition probability density, be specified, whereas the mean velocities and eddy diffiisivities must be prescribed to obtain c from Eq. (2.19). In the next section we see how forms of c are obtained from Eqs. (2.7) and (2.19). 

Saffman, P. G. (1960). On the effect of molecular diffiisivity in turbulent diffusion. J. Fluid Mech. 8, 273-283. 

Equations (7.1-45) and (7-1-46) show that the two-film theory predicts that the mass transfer coefficient is directly proportional to the molecular diffiisivity to the power unify. The complexity of flow normally prevents evaluation of Zf, but it will decrease with increasing turbulence. 

Gudmundsson [1981] has quoted a correlation for the dimensionless mass transfer coefficient K in terms of the particle Schmidt number for particles in the diffiision regime in turbulent pipe flow. 

The Higbie penetration model for mass transfer compensates for transient behavior. It assumes that mass transfer occurs during brief phase contacts that do not allow enough time for steady-state conditions. In other words, the phases collide but do not have a definitive and continuous interface with respect to time. The mass transfer is prompted by turbulence that refreshes the interface, and the refresh rate is the limiting step in mass transfer. Eddies approach the surface at which point mass transfer by molecular diffiision is initiated and is described by Azbel (1981) ... 

The mass transfer coefficient in the near-interfacial region of the liquid Ki generally has a value of 10 -10 m/sec (3.6-36 cm/h). It depends on two factors, the level of turbulence in the region (which is mainly controlled by the prevailing wind speed) and the molecular diffiisivity of the solute molecule (which is mainly controlled by molecular size). 

The last two relations show that the inteifacial turbulence is suppressed (1) by large bulk viscosities and diffiisivities or (2) by large interfacial viscosity and diffiisivity. 

By using present two-equation model, both the diffiisivity profiles of acetylene and acetic acid along the reactor can be obtained as shown in Fig. 7.4. As shown in the figure, the turbulent mass dififusivity of acetylene A,ac in axial direction becomes steady after traveling from inlet to a distance about 20-fold of effective catalyst diameter d in present case is 3.3 mm). As shown in Fig. 7.4b, the distribution of A,AC in radial direction in the main flow region increases gradually to a maximum until to about r R — 0.8 and then decreases sharply toward the column wall. Such tendency is in consistent with the experimental measurement. It is as a result of the uneven distribution of porosity, velocity, temperature, and concentration near the wall region. 

In particular, horizontal advection and horizontal diffusion in the Chesapeake Bay are comparable while vertical difiiision is a fast process that acts over short distances, and a model must account for all three. In this environment, atrazine that is discharged to the surface waters could be horizontally distributed over a distance of 1 km over a period of one week, since the time scale of horizontal advection-difiusion processes is 10 -10 s (approximately 3 hours). As atrazine is distributed horizontally, it also mixes vertically down the water coluitm. With the estimates of verticd diffiisivity for the Bay that are available in the literature, for a depth of 10-20 m the time scale for vertical diffusion processes is on the order of 15 minutes, and can be as short as 3 minutes. The sidfidic vraters are in the sediment porewaters and atrazine needs to be transported to the water-sediment inter ce in order to encounter and react with reduced sulfiir species. The characteristic horizontal and vertical scales that describe the flow in the Bay indicate that it is possible for atrazine to reach the depth of the water-sediment interface before it is horizontally transported out of the system. The subsequent exchange at the water-sediment interface depends on many factors, including half-life of atrazine, the hydraulic residence time of the bottom layer, turbulent processes, and other characteristics of the water column above the sediment layer. Simple box models cannot capture the dynamics necessary to describe these exchanges that ultimately govern the te of atrazine in the Bay. 

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