Mass distribution of particles

Figure 4. Number mass distribution of particles. (From Liu and Litster, Powder Technol., 74 259-270, 1993, with kind permission from Elsevier Science S.A., P.O. Box 564, 1001 Lausanne, Switzerland.)...

Three distinct methods are therefore available for calculating the mass distribution of particles in suspension for a series of sector-shaped tubes filled to a series of levels. First, the mass fraction of particles larger than a known diameter may be calculated from equation (8.77) and the distribution function determined from the slope of the cumulative mass deposited against S. Secondly, the distribution function may be calculated directly in terms of the first and second derivatives of the fraction sedimented with respect to the length of the column of suspension centrifuged by use of equation (8.77). Thirdly, from the sedimentation -time curve at a series of levels, the distribution functions may be calculated by the use of equation (8.77). 

A total of 5 0 pL of the ARSL dispersions are diluted with 20 mL of filtered buffer (0.22-mm pore size, polycarbonate filters, Millipore, UK) and sized immediately by photon correlation spectroscopy (Model 4700C, Malvern Instruments, UK), which enables the mass distribution of particle size to be obtained, according to the manufacturer. Size distribution measurements are made at 25°C with a fixed angle of 90° and the sizes quoted are the z average mean (dz) for the ARSL hydrodynamic diameter. 

These data are confined to particles fully entrained in the inspired air. When particles are, however, inspired from propellant-based metered-dose or dry-powder inhalers, their velocity is much greater than that of the inspired air, and only a small mass fraction (nonballistic fraction) escapes inertial deposition in the oropharynx and enters the trachea. The mass fraction of particles deposited in the oropharynx (ballistic fraction) can be determined experimentally. It comprises more than 50% of the mass released from inhaler devices and therefore is much larger than that deposited in the larynx. It is usually assumed that the ballistic fraction is equal to the mass fraction collected in an induction port placed in front of a cascade impactor. Collection of particles in the impactor allows the estimation of the mass distribution of particles entering the respiratory tract. Finally, these distributions can be used to calculate regional mass depositions with a deposition model. 

FIGURE 2.2 Histograms for the number and mass distributions of particles in a heterodis-... 

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]

The concentrations and the mass distribution of toluene in the four phases, as calculated from this set of equations, are presented in Table 14.4. As seen in the table, the major part of the toluene, i.e., 68.9%, remains in the vadose zone as free NAPL, 27.6% is adsorbed on the surfaces of solid particles, and only 3.5% is distributed between the aqueous and gas phases. Free NAPL occupies only a small part of the available pore volume, and it is not expected to disturb the movement of air through the contaminated zone. 

In order to use Eq. (6), it is necessary to know what is the initial mass (the measure of size used in Eqs. (5) and (6)) distribution of particles and the growth rate function, G. 

In the LB technique, the fluid to be simulated consists of a large set of fictitious particles. Essentially, the LB technique boils down to tracking a collection of these fictitious particles residing on a regular lattice. A typical lattice that is commonly used for the effective simulation of the NS equations (Somers, 1993) is a 3-D projection of a 4-D face-centred hypercube. This projected lattice has 18 velocity directions. Every time step, the particles move synchronously along these directions to neighboring lattice sites where they collide. The collisions at the lattice sites have to conserve mass and momentum and obey the so-called collision operator comprising a set of collision rules. The characteristic features of the LB technique are the distribution of particle densities over the various directions, the lattice velocities, and the collision rules. 

In this experiment, a solid material, such as pecan hulls, are crushed, ground, and separated into various sizes to observe the effects of the variation of size distribution with screening time and the variation of size distribution on rate of vibration. The size and distribution of particles may be determined by several methods. Screening is commonly used for this purpose. In this method a known mass of material of various sizes is passed over a series of standard screens and the amount of material collected on each screen is determined. The rate of vibrating the screen and the time allowed for vibrating have definite effects on the distribution of particles. 

Organic compounds released into the vadose zone exist in four closely interrelated forms free-phase NAPL, attenuated to surface of soil grains, dissolved in water retained on and between the soil particles, and present as a gaseous phase. The mass distribution of each of these phases is controlled by such factors as concentration gradients, distribution coefficients, and Henry s law constants. 

Large quantities of particles are handled on the industrial scale, and it is frequently necessary to define the system as a whole. Thus, in place of particle size, it is necessary to know the distribution of particle sizes in the mixture and to be able to define a mean size which in some way represents the behaviour of the particulate mass as a whole. Important operations relating to systems of particles include storage in hoppers, flow through orifices and pipes, and metering of flows. It is frequently necessary to reduce the size of particles, or alternatively to form them into aggregates or sinters. Sometimes it may be necessary to mix two or more solids, and there may be a requirement to separate a mixture into its components or according to the sizes of the particles. 

The collection efficiency of a cyclone is 45 per cent over the size range 0-5 xm, 80 per cent over the size range 5-10 xm, and 96 per cent for particles exceeding 10 xm. Calculate the efficiency of collection for a dust with a mass distribution of 50 per cent 0-5 xm, 30 per cent 5-10 pm and 20 per cent above 10 xm. 

Laser diffraction is a fast alternative for analysis of the size distribution of particles in an aerosol cloud. The theory of laser diffraction is well understood [124,125]) but this technique requires special measures to test inhalation devices and to interpret the results correctly. One of the major problems is that flow adjustment through the inhaler is not possible. Furthermore, the presence of carrier particles from adhesive mixtures may disturb the measurement of the fine drug particles and the size distribution obtained is of an unknown dehvered mass fraction of the dose. These practical problems and limitations have been solved by the design of a new modular inhaler adapter for the Sympatec laser diffraction apparatus (Figure 3.6). 

Biological samples such as bacteria and viruses have been studied by SdFFF as well as FIFFF. These two techniques provided bacterial number, density, size, and mass distributions of bacterial cells of diverse shapes and sizes, molecular weights, sizes, densities, and diffusivities of viruses. SdFFF has been used to analyze protein particles, including casein derived from nonfat dry milk, albumin microspheres, and particles in cataractous lenses originating from the aggregation of lens proteins. 

Recently, a miniaturized thermal apparatus, [t-ThFFF, was developed and applied to characterize the molar mass distribution of synthetic polymers in organic solvent as well to determine the particle size distribution of nanoparticles (PSs latex) in aqueous carrier. This 4-ThFFF proved to performed well in both macromolecule and particle analysis [48]. 

Cluster ion sources with different production techniques have been devised [10]. The cluster ions are produced, for instance, by vaporizing the materials using a heated oven, a laser ablation apparatus, or sputtering. Essential features of the cluster ion source are increased intensity and stability of the beam, and control of the mass distribution of the particles. Further development of cluster ion sources is in progress at several facilities [7,11]. 

The species mass extinction efficiency. Eg, can be theoretically determined from Mie s classical solution to light extinction by a sphere in an infinite medium. Computer routines are available to calculate single particle extinction efficiencies, and, hence. Eg ( ). If the mass distribution of each species is... 

Sinha, M. P., and S. K. Friedlander, Mass Distribution of Chemical Species in a Polydisperse Aerosol Measurement of Sodium Chloride in Particles by Mass Spectrometry, J. Colloid Inteface Set., 112, 573-582 (1986). 

The equation in this form states that in the samples analyzed the distribution of any radionuclide, A, can be expressed as a linear combination of the distribution of two species, a refractory and 137Cs. Therefore, we need to determine only refractory distribution, 137Cs distribution, and mass distribution with particle size and the distribution of all other isotopic species for which aA values are known and can be calculated. The refractory species used is 155Eu. It has a half-life of 1.811 years and two easily resolved gamma photopeaks so that its abundance as well as that of 137Cs can be determined readily by gamma spectrometry. 

Nonspherical particles. Little is known about the fall velocity of nonspherical particles. It would be expected that needle-shaped particles would feel less air resistance per unit mass and fall faster but that irregularly shaped particles would, in general, feel more resistance and fall more slowly. The net effect depends upon the distribution of particle shapes, which is also uncertain. 

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