Fine particles other models

Organic compounds, natural, fossil or anthropogenic, can be used to provide a chemical mass balance for atmospheric particles and a receptor model was developed that relates source contributions to mass concentrations in airborne fine particles. The approach uses organic compound distributions in both source and ambient samples to determine source contributions to the airborne particulate matter. This method was validated for southern California and is being applied in numerous other airsheds. ... 

While major components of those aerosols are thought to be oxides of Si, Al, Na, and Ca (5-6), the concentrations of most of the other elements have not been accurately determined. As predicted by models of gas-to-particle deposition (2,7-9), experimental data (8-11) indicate that the concentrations of vapor-deposited species in these very fine particles are often... 

A schematic illustration of the model is shown in Figure 10.2.12, together with that of polyhedral nanoparticles which grow as byproducts of MWNTs (see Fig. 10.2.3). An initial seed of an MWNT is the same as that of a polyhedral nanoparticle. Carbon neutrals [C, C2 (19)] and ions (C+) deposit and coagulate with each other to form atomic clusters and fine particles on a surface of the cathode. Structures of the particles at this stage may be amorphous with high fluidity (liquidlike) because of the high temperature ( 3500 K) of the electrode surface and ion bombardment. 

As fine particles arise from many sources, it would be desirable to replace the fine particle mass concentration in the equations by the concentration of an element borne by the fine particles from coal combustion and no other source. The best candidate for such an element is Se (2.4.17). If coal-fired power plants were the only significant source of Se (probably a good assumption in many areas), one could measure emission rates of SO2, SO4 and Se from the source and their concentrations at a downwind location and plug the values into the equations and solve them to obtain the conversion and deposition rates averaged over the travel time of the plume. The model is a useful first step towards the use of... 

A mathematical model has been proposed to account for the mutual synergistic action of either particle component on the other in increasing the value of the dimensionless time 0 as shown in Fig. 9b. Thus, the dimensionless time 0X for the coarse particles could be assumed to exert a mass-fraction-based influence on the fine particles, proportional to 0 1 — x2), which is affected by certain interaction by the fines, inclusive of their ability to adhere to the surface of the coarse and form clusters among themselves, lumped in certain appropriate form, for instance, [1 + /(x2)], where the function /(x2) may again be assumed to possess certain appropriate form, for instance, exponential, x2, where n1 may be called the interactive exponent. This results in an overall contribution by the coarse particles, suitably corrected for the interaction of the fine particles, 0 1 — x2Xl + x2l). This function has the property of accommodating the following boundary conditions ... 

Experimental Measurements of Reaction Kinetics. The reaction expressions discussed in the following model the intrinsic reaction on the catalyst surface, free of mass-transfer restrictions. Experimental measurements, usually made with very fine particles, are described by theoretically deduced formulas, the validity of which is tested experimentally by their possibility for extrapolation to other reaction conditions. Commonly the isothermal integral reactor is used with catalyst crushed to a size of 0.5-1.5 mm to avoid pore diffusion restriction and heat-transfer resistance in the catalyst particles. To exclude maldistribution effects and back mixing, a high ratio of... 

In another group of stream counters, the fine particles in the inspection zone are monitored with a light beam. Various models of this type of instrument have been developed to count fine particles in liquids others are specialized for the counting of dust fine particles in the... 

Other model distributions used are the normal distribution (Laplace-Gauss), for powders obtained by precipitation, condensation, or natural products (e.g., pollens) the Gates-Gaudin-Schuh-mann distribution (bilogarithmic), for analysis of the extreme values of fine particle distributions (Schuhmann, Am. Inst. Min. Metall. Pet. Eng., Tech. Paper 1189 Min. Tech., 1940) or the Rosin-Rammler-Sperling-Bennet distribution for the analysis of the extreme values of coarse particle distributions, e.g., in monitoring grinding operations [Rosin and Rammler,/. Inst. Fuel, 7,29-36 (1933) Bennett, ibid., 10, 22-29 (1936)]. 

At the other end of the spectrum from FLS in terms of computational requirements lie the simplest models that can be considered, which are the empirical models. These models are usually based on parametric curve fits to in vivo data of aerosol deposition in humans or to data from more complicated lung deposition models. The simplest of all such models is the rule of thumb that inhaled pharmaceutical aerosol should have particle diameters in some fine particle range of, e.g., 1 -5 pm, which is based on observations that lung deposition during tidal breathing (of monodisperse aerosols from tubes inserted partway into the mouth) decreases for particles with diameters on either side of this range (see, e.g., Ref. 4). 

Theoretical modeling tries to give a quantitative explanation of the fines migration mechanism by means of derived mathematical formulations. The mathematical formulations take into account the dynamic interactions of the fines with other suspended particles, the solid substrate of the porous medium, and the liquid phases surrounding the particles. These microscopic theories of fines migration are intended to give insight into the release, transport, and deposition of fines. 

The sol-gel method is also used to make very fine spherical particles of oxides. By structuring the solvent with surface-active solutes, other forms can also be realized during condensation of the monomeric reactant molecules to form a solid particle. Figure 8.16 shows that normal or inverse micelles or liquid crystals (liquids having long-distance order) can be formed in such solutes. Micelles are small domains in a liquid that are bounded by a layer of surface-active molecules. In these domains the solid is condensed and the microstructure of the precipitated solid is affected by the micelle boundaries. Monodisperse colloidal metal particles (as model catalyst) have been made in solvents that have been structured with surfactants. In the concentration domains where liquid crystals obtain highly porous crystalline oxides can be condensed. After calcination such solids can attain specific surface areas up to 1000 m /g. Micro-organisms use structured solutions when they precipitate calcite, hematite and silica particles. 

On the other hand, an analysis of the extreme case of coarse dispersions is more difficult, in a sense, than an analysis of the opposite extreme of fine suspensions. This is due to the mere fact that particles in Ene suspensions interact only hydro-dynamically. Although this means that there is no need to consider direct particle collisions, the problem of formulating both the conservation and rheological equations remains difficult because hydrodynamic interactions involve many particles simultaneously in fine particle suspensions. A sophisticated statistical theory of Brownian suspensions is now being developed by Brady and his co-workers that might help to tackle this problem [11-13]. An attempt to take into account pseudo-turbulent fluctuations in finely dispersed suspensions is described in [14,15]. It is quite evident that any generalization of these models of fine collisionless suspensions to coarse collisional suspensions involves, first of all, the necessity to account for direct collisions, and this is certainly a matter of some difficulty. 

A similar case may be made for the use of density in Stokes law, the buoyancy of particles in the separation zone must be taken into account. The fine particles displace the continuous phase and hence it is the density of the liquid that is used in the model. In any case, the suspension density in the zone is not known but is likely to be much less than that of the feed. The second use of fluid density is in the resistance coefficient, Eu. The density to be used there depends on how we define the Euler number the dynamic pressure in the denominator (equation 6.9) is simply a yardstick against which we measure the pressure loss through a cyclone. We have used the clean liquid density in the dynamic pressure alternatively, the feed suspension density may be used. It is immaterial which of the two densities is used (they are both equally unrealistic) provided the case is clearly defined conversion from one to the other is a simple matter. 

Kinetics models of gas-solid non-catalytic reaction include uniform conversion model (UCN), multiple fine particle model (GPM), crack core model (CCM), phase-change model (PCM), change void model (CVM), thermal decomposition model (TDM), shrinking core model with multi-step reactions, and multi-step reaction model of formation porous structure in reaction etc. Among these models, the shrinking core model (SCM) is the most important and most widely used. For conversion of solid it is also the most simple and practical model. Commonly it is suitable for experimental data. However, it can only be used in some reactions of many solid reactions. A more complex model must be used in other cases. 

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