Particle mass distribution

This value falls below the theoretical ratio for these isotopes but is based on the same efficiency and half-life data which were used to derive the atoms/Mg relationships. Therefore, we will find fa and fa so that the ratio of the total 137Cs to the total 155Eu equals 8.14. It is a property of the lognormal form of distribution function that if particle mass distribution is described by x and a, then the surface/volume distribution is given by (4) ... 

For the Rosin-Rammler distribution, the distribution constants (a and f ) are obtained from the particle mass distribution data. To obtain the mass density distribution, the data on... 

Polymers generally have a molar mass distribution. When they associate, a particle-size distribution is produced, which will be different from the molar mass distribution and will vary with the nature of the effective unit. The relationships between the molar mass distributions and the particle mass distributions can be derived by statistical methods. Only the results are given here. 

In a heterodisperse system there is a particle size or, for that matter, particle mass distribution around an average value. We now further elaborate on the particle mass distributions within a heterodisperse population. 

Particle Size Distribution. For many P/M processes, the average particle size is not necessarily a decisive factor, whereas the distribution of the particles of various sizes ia the powder mass is. The distribution curve can be irregular, show a rather regular distribution with one maximum, have more than one maximum, or be perfecdy uniform. 

Analysis of a method of maximizing the usefiilness of smaH pilot units in achieving similitude is described in Reference 67. The pilot unit should be designed to produce fully developed large bubbles or slugs as rapidly as possible above the inlet. UsuaHy, the basic reaction conditions of feed composition, temperature, pressure, and catalyst activity are kept constant. Constant catalyst activity usuaHy requires use of the same particle size distribution and therefore constant minimum fluidization velocity which is usuaHy much less than the superficial gas velocity. Mass transport from the bubble by diffusion may be less than by convective exchange between the bubble and the surrounding emulsion phase. 

Figure 1 shows the particulate loading of a pipe containing gas and particulates where the nonuniformity induced by a disturbance, ie, a 90° bend, is obvious (2). A profile of concentration gradients in a long, straight, horizontal pipe containing suspended soHds is shown in Figure 2. Segregation occurs as a result of particle mass. Certain impurities, eg, metal-rich particulates, however, occur near the bottom of the pipe others, eg, oily flocculates, occur near the top (3). Moreover, the distribution may be affected by Hquid-velocity disturbances and pipe roughness.

Copolymers with butadiene, ie, those containing at least 60 wt % butadiene, are an important family of mbbers. In addition to synthetic mbber, these compositions have extensive uses as paper coatings, water-based paints, and carpet backing. Because of unfavorable reaction kinetics in a mass system, these copolymers are made in an emulsion polymerization system, which favors chain propagation but not termination (199). The result is economically acceptable rates with desirable chain lengths. Usually such processes are mn batchwise in order to achieve satisfactory particle size distribution. 

Tantalum Compounds. Potassium heptafluorotantalate [16924-00-8] K TaF, is the most important tantalum compound produced at plant scale. This compound is used in large quantities for tantalum metal production. The fluorotantalate is prepared by adding potassium salts such as KCl and KF to the hot aqueous tantalum solution produced by the solvent extraction process. The mixture is then allowed to cool under strictiy controlled conditions to get a crystalline mass having a reproducible particle size distribution. To prevent the formation of oxyfluorides, it is necessary to start with reaction mixtures having an excess of about 5% HF on a wt/wt basis. The acid is added directiy to the reaction mixture or together with the aqueous solution of the potassium compound. Potassium heptafluorotantalate is produced either in a batch process where the quantity of output is about 300—500 kg K TaFy, or by a continuously operated process (28). 

Aerosol Dynamics. Inclusion of a description of aerosol dynamics within air quaUty models is of primary importance because of the health effects associated with fine particles in the atmosphere, visibiUty deterioration, and the acid deposition problem. Aerosol dynamics differ markedly from gaseous pollutant dynamics in that particles come in a continuous distribution of sizes and can coagulate, evaporate, grow in size by condensation, be formed by nucleation, or be deposited by sedimentation. Furthermore, the species mass concentration alone does not fliUy characterize the aerosol. The particle size distribution, which changes as a function of time, and size-dependent composition determine the fate of particulate air pollutants and their... 

Particle size distribution determines surface-to-mass ratios and the distance internal moisture must travel to reach the surface. Large pieces thus have higher critical moisture contents than fine particles of the same material dried under the same conditions. Pneumatic-conveyor flash dryers work because very fine particles are produced during initial dispersion and these have low critical moisture contents. 

When a distribufion of particle sizes which must be collected is present, the aclual size distribution must be converted to a mass distribution by aerodynamic size. Frequently the distribution can be represented or approximated by a log-normal distribution (a straight line on a log-log plot of cumulative mass percent of particles versus diameter) wmich can be characterized by the mass median particle diameter dp5o and the standard statistical deviation of particles from the median [Pg.1428]

It calculates one-dimensional heat conduction through walls and structure no solid or liquid ciMiibustion models are available. The energy and mass for burning solids or liquids must be input. It has no agglomeration model nor ability to represent log-normal particle-size distribution. 

FIGURE 5.28 Estimated overall airway deposition as a function of initial particle size and particle hygroscopicity for particles with mass median aerodynamic diameters (MMAD) between 0.1 and 10 p.m. ° Geometric dispersion, a measure of particle size distribution, principally affects only smaller MMAD,... 

Before we go back to Eq. (14.30), we shall evaluate the mass distribution function for the particles whose size distribution is of the form (14.33), i.e., normal probability size distribution. 

Using the same reasoning as with the particle number distribution above, we observe that if the x- and y-axes are provided with the nonlinear scales, n and tf, defined by Eqs. (14.34) and (14.35), the mass distribution m x)/m t) can be described by a straight line... 

The second moment of the particle size distribution used in the mass balances is obtained from... 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

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