Dispersion factor

Other Factors Affecting the Viscosity of Dispersions. Factors other than concentration affect the viscosity of dispersions. A dispersion of nonspherical particles tends to be more viscous than predicted if the Brownian motion is great enough to maintain a random orientation of the particles. However, at low temperatures or high solvent viscosities, the Brownian motion is small and the particle alignment in flow (streamlining) results in unexpectedly lower viscosities. This is a form of shear thinning. 

A dispersion factor, defined as the ratio of the number of surface atoms to the total number of atoms ia the particle, is commonly used to describe highly dispersed systems that do not exhibit a particularly high surface-area-to-volume ratio (22). Representative values for 10-, 100-, and 1000-nm particles are, respectively, on the order of 0.15—0.30, 0.40, and 0.003—0.02, depending on the specific dimensions of the atoms or molecules that comprise the particles. Other quantities can be used to describe the degree of dispersion (6,7), but these tend to assume, at least, quasi-equUibrium conditions that are not always met (7,23). 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

In practice, experimental peaks can be affected by extracolumn retention and dispersion factors associated with the injector, connections, and any detector. For hnear chromatography conditions, the apparent response parameters are related to their corresponding true column value by... 

The distance traveled by a cloud of flammable vapor is site specific mid relies on several dispersion factors, wliich are discussed in Part 111 of this book. It is not likely tliat a vapor cloud would travel far in any industrial or urban area. In open areas wifli few sources of ignition, a vapor cloud may drift several miles. The time before ignition can range from 10 seconds to 15 minutes. 

Because this is an unwieldy quantity, for the characterization of the unsym-metrical scattering of the results the dispersion factor (scattering factor) v is used ... 

In case of unsymmetric distributed measured values, the dispersion factor v can be used to estimate a relative dispersion measure that has the character... 

Geometrical means have unsymmetrical uncertainty intervals which are characterized by a dispersion factor v (see Sect. 4.1.2, Eq. (4.20)) and a covering factor k (see Sect. 4.2). Corresponding results should be given in the form... 

Example Uranium has been found in wine in a concentration of 2.0 ng/L. The dispersion factor v has been estimated v = 1.2 and the coverage factor has been chosen k = 2. Then the uncertainty factor amounts vA = 1.45 and the analytical result has to be presented in one of the following ways ... 

In general, exact analytic solutions are available only for the linear (R = 1) and irreversible limits (R —> 0). Intermediate cases require numerical solution or use of approximate driving force expressions (see "Rate and Dispersion Factors ). 

Source-dispersion and receptor-oriented models have a common physical basis. Both assume that mass arriving at a receptor (sampling site) from source j was transported with conservation of mass by atmospheric dispersion of source emitted material. From the source-dispersion model point of view, the mass collected at the receptor from source j, Mj, Is the dependent variable which Is equal to the product of a dispersion factor, Dj (which depends on wind speed, wind direction, stability, etc.) and an emission rate factor, Ej, 1. e. , ... 

Each pollution source s contribution to a receptor sample is the product of an emissions factor and a dispersion factor in the source model formulation. The total concentrations measured at the receptor is the linear sum of this product. 

A source model incorporates measured or estimated values for an emission rate factor and the dispersion factor. Whenever either of these enter the receptor model as observables, we call it a hybrid model. The three applications considered here are emission inventory scaling, micro-inventories, and dispersion modeling of specific sources within a source type. 

Emission Inventory scaling, proposed by (24), uses the relative emission rates of two source types subject to approximately the same dispersion factor (e.g., residential heating by woodstoves and natural gas) to approximate the source contribution from the source type not included in the chemical mass balance (e.g., natural gas combustion). The ratio of the emission rates is multiplied by the contribution of the source type which was included in the balance. 

Two more sets of observables are Introduced Into the hybrid models the emissions factors and the dispersion factors. It Is the difficulty of quantifying these that led to the use of a receptor model over the source model In the first place, so It would seem there Is little advantage In reintroducing them. The advantage of the hybridization Is that the number of Individual emission and dispersion factors can be considerably reduced and that the relative values rather than the absolute values are used. These relative values are more accurate In most cases. Still, the uncertainties of emission and dispersion factors need to be evaluated and Incorporated Into any source/receptor hybrid model. 

Dispersion Normalization. Atmospheric dispersion is greater in winter than in summer in New York City and, in addition, varies from year to year. Thus, for a constantly emitting source of particles, atmospheric concentrations of TSP observed in winter would be lower than in summer. In order to relate ambient concentrations of particulate species to their sources Kleinman, et al. ( 5), suggested the use of a dispersion normalization technique based on the dispersion factor proposed by Holzworth ( ). Ambient concentrations of aerosol species are multiplied by the ratio of the dispersion factor for the sampling period to an average dispersion factor of 4200 m /sec. 

The use of dispersion-normalized data is equivalent to adjusting all ambient concentrations to the same dispersion conditions and assuming that the remaining variations in concentrations are due to variations in source emissions. Although this is a logical approach conceptually, it is not known at present what uncertainties are associated with the use of a dispersion factor calculated from a 7 A.M. determination of mixing height and wind-speed. 

From XPS, it is possible to define a dispersion factor which is roughly proportional to the true dispersion ... 

Here (fVs/S)xps is the ratio of the number of surface W atoms to the number of atoms of the cationic element of the support (S) (for instance S = Ti for Ti02) determined by XPS, and (WVS)bulk is the ratio of total W atoms to the total number of atoms of cationic element of the support determined by chemical analysis. This dispersion factor increases in the following order (Table 18.3) ... 

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