Particle population

Distribution Averages. The most commonly used quantities for describing the average diameter of a particle population are the mean, mode, median, and geometric mean. The mean diameter, d, is statistically calculated and in one form or another represents the size of a particle population. It is usefiil for comparing various populations of particles. 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

The mode of distribution is simply the value of the most frequent size present. A distribution exhibiting a single maximum is referred to as a unimodal distribution. When two or more maxima are present, the distribution is caUed bimodal, trimodal, and so on. The mode representing a particle population may have different values depending on whether the measurement is carried out on the basis of particle length, surface area, mass, or volume, or whether the data are represented ia terms of the diameter or log (diameter). 

Field-Flow Fractionation. Field-flow fractionation is a general name for a class of separation techniques that fractionate a particle population into groups according to size. The work in this area has been reviewed (59). 

Thus, for a given particle loading, , the fine fraction in the bimodal assembly is a function of only the diameter ratio, dID a surprisingly simple result for an otherwise complex phenomenon. However, the inclusion of the liquid phase to the above particle assembly should modify the result somewhat. This can be seen very simply by expressing the interstitial particle population of the fines as a function of the continuous phase ... 

Clearly, the inclusion of the liquid phase (xi) will tend to reduce the number of fines in the system. Thus, a diminution in particle size must be effected to provide an equivalent particle population in the fluid-particle assembly. The particle size ratio normally used in practical systems tends to be somewhat lower than the one computed from Eq. (8). 

Flocculation of particles and capture of oligomers to a point of constant particle population... 

As shown in the diagram, do can be calculated from the mean diameter if the distribution is symmetriccil, but they rarely are. Note cdso that a, which is defined as the diameter limits equal to 68% of the total particle population, cannot be obtained, only do. ... 

The slopes of the calibration curves for the HDC and Fractosil systems are 0.512 and 0.289, respectively. This indicates that the "resolution of the peak separation" for the Fractosil system is superior to that of HDC, since resolution is considered to be inversely proportional to the slope of the log particle diameter - AV calibration curve (26). However when peak spreading is taken into account, the actual relative resolution between particle populations is less for the Fractosil system 2k) a result which indicates that overall, for size distribution resolution, the HDC system is superior. 

The micrographs however, revealed that the latex particle standards were not monodispersed as claimed by the suppliers. This can clearly be noted from the micrographs in Fig. U,a-e. They indicate a distinct polydispersity the micrographs of the 2T5 and 312 nm samples in fact reveal two distinct particle populations. 

Trimborn et al. (2000) have developed a mobile system for the on-line analysis of single airborne particles and for the characterisation of particle populations in aerosols, using a transportable laser mass spectrometer. A schematic diagram of their setup is shown in Figure 3.12. 

Mauger et al. [35] used the rotating filter assembly to assess the mass transport kinetics of particle populations of a steroid and demonstrated the applicability of a proposed diffusion model used to interpret the data. 

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

Ray, Y. C., Jiang, T. S., and Jiang T. L., Particle Population Model for a Fluidized Bed with Attrition, Powder Tech., 52 35 (1987b)... 

Wemer, A., Haider, M., and Linzer, W., Modelling of Particle Population in Fluidized Beds of Particles Differing in Size and Physico-chemical Behaviourf Preprint Fluidization VIII, 1 557 (1995)... 

Figure 14.1 Particles commonly used in biological applications can range in size over three orders of magnitude, from as small as macromolecules (—10 nm) to approximately the diameter of cells (10 pm). The diameter of a particle population dramatically can affect its behavior in solution.

Therefore, the total heat content, Q, of the crystal can be expressed as the sum of the number of particles populating each level times the energy of that level. 

FIGURE 19.12 Considerations for the interpretation of SSITKA data. Case 1 Three formates can exist, including (a) rapid reaction zone (RRZ)—those reacting rapidly at the metal-oxide interface (b) intermediate surface diffusion zone (SDZ)—those at path lengths sufficient to eventually diffuse to the metal and contribute to overall activity, and (c) stranded intermediate zone (SIZ)—intermediates are essentially locked onto surface due to excessive diffusional path lengths to the metal-oxide interface. Case 2 Metal particle population sufficient to overcome excessive surface diffusional restrictions. Case 3 All rapid reaction zone. Case 4 For Pt/zirconia, unlike Pt/ceria, the activated oxide is confined to the vicinity of the metal particle, and the surface diffusional zones are sensitive to metal loading. 

Wright, D. L., R. McGraw, and D. E. Rosner (2001). Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering particle populations. Journal of Colloid and Interface Science 236, 242-251. 

Figure 10 shows an example of the large particle population distribution for an abused silica slurry. Steady growth in slurry agglomerates can be detected by looking at the small number of large wafer-scratching particles. This information can be combined with other metrics to assess overall slurry health. 

Differential centrifugation is the simplest form of centrifugation A mixed particle population is subjected to centrifugations with... 

P xcept for tritium, carbon-14, and the long lived rare gases, the radio-active atoms produced by a nuclear detonation are accounted for completely within a population of radioactive particles. The nature of the particle population and the manner in which the individual radionuclides are distributed within it will vary with the conditions under which the detonation occurred. Characterization of the radioactive particle population requires ... 

From the standpoint of particle population all nuclear detonations fall into one of two principal categories ... 

The radioactive particle population consists of environmental materials introduced into the fireball as pre-existing particles. These may be completely or partially melted, but if vaporized, they do not reappear as an identifiable part of the particle population. 

The radioactive particle population consists of metal oxide spheres formed by condensation from the vapor state of metallic constituents of the detonated device. 

Detonations which produce particle populations of the first category are land surface bursts, land subsurface bursts, vented underground bursts, and tower bursts. 

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