Time average dispersion models

Pheromone propagation by wind depends on the release rate of the pheromone (or any other odor) and air movements (turbulent dispersion). In wind, the turbulent diffusivity overwhelms the diffusion properties of a volatile compound or mixture itself. Diffusion properties are now properties of wind structure and boundary surfaces, and preferably termed dispersion coefficients. Two models have dominated the discussion of insect pheromone propagation. These are the time-average model (Sutton, 1953) and the Gaussian plume model. 

Like frequency estimates, consequence estimates can have very large uncertainties. Estimates that vary by orders of magnitude can result from (1) basic uncertainties in chemical/physical properties, (2) differences in average vs. time-dependent meteorological conditions, and/or (3) uncertainties in the release, dispersion, and effects models. Some... 

Equations in Table IX are written per unit of bed volume (A )g is a time averaged, mean axial bed conductivity. A is a longitudinal diffusivity and Ai allows for particle to particle conductivity. Not all the terms in the model as given in the table are important. For example, Wu et al. (1995, 19%) and Xiao and Yuan (1996) neglect the accumulation and dispersion terms in Eq. (30) and the accumulation and conduction terms in Eq. (28). 

Relaxation dispersion data for water on Cab-O-Sil, which is a monodis-perse silica fine particulate, are shown in Fig. 2 (45). The data are analyzed in terms of the model summarized schematically in Fig. 3. The y process characterizes the high frequency local motions of the liquid in the surface phase and defines the high field relaxation dispersion. There is little field dependence because the local motions are rapid. The p process defines the power-law region of the relaxation dispersion in this model and characterizes the molecular reorientations mediated by translational displacements on the length scale of the order of the monomer size, or the particle size. The a process represents averaging of molecular orientations by translational displacements on the order of the particle cluster size, which is limited to the long time or low frequency end by exchange with bulk or free water. This model has been discussed in a number of contexts and extended studies have been conducted (34,41,43). 

Elkinton, J. S., Card6, R. T., and Mason, C. J. (1984). Evaluation of time-average dispersion models for estimating pheromone concentrations in a deciduous forest. Journal of Chemical Ecology 10,1081-1108. 

In Eulerian-Eulerian (EE) simulations, an effective reaction source term of the form of Eq. (5.32) can be used in species conservation equations for all the participating species. The above comments related to models for local enhancement factors are applicable to the EE approach as well. It must be noted that interfacial area appearing in Eq. (5.32) will be a function of volume fraction of dispersed phase and effective particle diameter. It can be imagined that for turbulent flows, the time-averaged mass transfer source will have additional terms such as correlation of fluctuations in volume fraction of dispersed phase and fluctuations in concentration even in the absence... 

Simple transport models have significant limitations in a complex estuarine setting commonly, sophisticated numerical models are employed to predict transport in estuaries. In long, narrow estuaries, however, a simple onedimensional model, such as is used in rivers, that incorporates a longitudinal dispersion coefficient and a time-averaged seaward water velocity can be useful. The results of such a model must be averaged over the tidal cycle concentrations at each point in the estuary may be expected to vary significantly with the state of the tide. See Fischer et al. (1979) for a more complete discussion of transport in estuaries. 

The turbulent gas/liquid flow in baffled tanks with turbine stirrer can be predicted. A mathematical model has been developed for turbulent, dispersed G/L flow. The time-averaged two phase momentum equations were solved by using a finite volume algorithm. The turbulent stresses were simulated with a K-fi-model. The distribution of gas around the stirrer blades is predicted for the first time. This model also enables an a priori prediction of the drop in the power dissipated by the stirrer in the presence of gas. Predicted flow characteristics for the gas/liquid dispersion show good agreement with the experimental data. 

At an axi-symmetric boundary Neuman conditions are used for all the fields, except for the normal velocity component which is zero because the flow direction turns at this point. The assumption of cylindrical axi-symmetry in the computations prevents lateral motion of the dispersed gas phase and leads to an unrealistic radial phase distribution [73, 66[. Krishna and van Baten [73] obtained better agreement with experiments when a 3D model was applied. However, experience showed that it is very difficult to obtain reasonable time averaged radial void profiles even in 3D simulations. 

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