Size number-density

Ionization associated with the presence of solid particles in flames is small and easily obscured by gaseous ionization of volatile impurities. It can be demonstrated experimentally in certain systems and can be shown to depend on the particle size, number density, and work function as predicted by the theory of Smith or Soo and Dimick. Salts such as the alkali halides volatilize slowly and mix by diffusion. Residual inhomogeneities in ion distribution give the appearance of particulate ionization. 

Dubin SB. Determination of lamellar body size, number density, and concentration by differential light scattering from amniotic fluid physical significance of Afiso. Clin Chem 1988 34 938-43. 

Farmer, W. M., Measurement of particle size, number density and velocity using a laser interferometer. Applied Optics, 11, 2603-2612 (1972)... 

In situ measurements aimed at investigating the gas phase species concentration, temperature field, and particle size offer the best potential for a better understanding of the underlying chemical/transport phenomena that occur during particle synthesis. Laser-based diagnostics offer nonintrusive, sensitive methods for measuring particle size/number density, gas temperature, and species concentration in these reactors (6-9). 

The drop size achieved is important in estimating the mass-transfer surface area developed in the dispersion. In certain situations, the surface area of the dispersion per unit volume of the total liquid phase, a, is available from measurements. The average or mean drop size appropriately defined can then be related to For example, the Sauter mean diameter ( 2 of the drop size number density distribution has been related to via the following relation and the dispersed phase volume fraction... 

Several closures have been proposed to calculate the collision density for molecules in gas mixtures [109] (pp. 52-55). To derive these expressions for the collision density one generally perform an analysis of the particle-particle interactions in an imaginary container [80, 109, 135], called the conceptual collision cylinder in kinetic theory, as outlined in Sect. 2.4.2.5. A fundamental assumption in this concept is that the rate of molecular collisions in a gas depends upon the size, number density, and average speed of the molecules. Following Maxwell [95] each type of molecules are considered hard spheres, resembling billiard balls, having diameter dg, mass ntg and number density These hard spheres exert no forces on... 

Because high quaHty, low cost, and optimum performance are required for spray equipment, improved analytical and experimental tools are iadispensable for increasing productivity ia many competitive iadustries. In most iastances, it is no longer adequate to characterize a spray solely on the basis of flow rate and spray pattern. Information on droplet size, velocity, volume flux, and number density is often needed and can be determined usiag advanced laser diagnostic techniques. These improvements have benefited a wide spectmm of consumer and specialized iadustrial products. 

Mumber Density and Volume Flux. The deterrnination of number density and volume dux requires accurate information on the sample volume cross-sectional area, droplet size and velocity, as well as the number of droplets passing through the sample volume at any given instant of time. Depending on the instmmentation, the sample volume may vary with the optical components and droplet sizes. The number density represents the number of droplets contained in a specified volume of space at a given instant. It can be expressed as follows, where u is the mean droplet velocity, t the sample time, andM the representative cross-sectional area at the sampling location. 

The phase Doppler method utilizes the wavelength of light as the basis of measurement. Hence, performance is not vulnerable to fluctuations in light intensity. The technique has been successfully appHed to dense sprays, highly turbulent flows, and combustion systems. It is capable of making simultaneous measurements of droplet size, velocity, number density, and volume flux. 

Single-component PDA equipment is similar to LDA, but two detectors (not one) are installed with different detection angles. By means of simultaneous processing of signals supplied by the two detectors, information on the velocity and on the size of the scattering objects can be acquired. Therefore, velocity distribution, size distribution, and number density (local concentration)... 

Equation (14.91) contains only the mass flow ratio /u as a characteristic number of the mechanics of similitude of the mixture. All the other irnpor rant factors, such as particle size, solid density, etc., are contained in the additional pressure-loss coefficient of the solid particles, A, which is determined separately for each material. 

Consider the erystal size distribution in a model MSMPR erystallizer arising beeause of simultaneous nueleation, growth and agglomeration of erystalline partieles. Let the number of partieles with a eharaeteristie size in the range L to L + dL be n L)dL. It is assumed that the frequeney of sueeessful binary eollisions between partieles (understood to inelude both single erystals and previously formed agglomerates) of size V to V + dV and L to Ll +dL" is equal to j3n L )n L")dL dL". The number density n L) and the eollision frequeney faetor (3 are related to some eonvenient volumetrie basis, e.g. unit volume of suspension. 

Thus, in the purely agglomerative proeess with a typieal value of the parameter a > 1, the number density distribution n L) aeeording to equation 6.11 is linear when plotted in logarithmie eo-ordinates, i.e. In n L) versus logL, thus exhibits an initial slope equal to —5/2, as shown in Figure 6.12. Note If the population density is defined on a unit solid volume, rather than size, basis, then the eorresponding slope is —3/2, see also Jones etal., 1996.)... 

It is evident that most studies reported to date have used number density, average size or weight per eent as eontrol variables. Often these variables are inferred from other measurements, ineluding density, solution supersaturation, refraetive index ete. Inferential teehniques have been shown to be partieularly suitable for industrial seale applieations where laser seattering deviees for on-line size distribution measurement are not yet praetieal for industrial eontrol purposes, although substantial progress is being made to that end. Even when usable, however, these measurement deviees are often eharaeterized by noise and require operation at very low solids eoneentration. 

Solids usually are more expensive to move and store than liquids and gases. The best equipment to use will depend on a number of factors, including throughput, length of travel, change in elevation, and nature of the solids (size, bulk density, angle of repose, abrasiveness, corrosiveness, wet or dry, etc.). 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

Figure 7 shows the results of measurements of adsorption density by Parsonage, etal. [77] on a series of eighteen block copolymers, with poly(2-vinylpyridine) [PVP] anchors and polystyrene [PS] buoys, adsorbed from toluene (selective for PS) of variable molecular weight in each block. The results are presented as the reciprocal square of Eq. 28, that is, as a dimensionless number density of chains ct (d/Rg A)-2. For all but the copolymers of highest asymmetry, Eq. 28 is in good agreement with the data of Fig. 7. The high asymmetry copolymers are in the regime of the data of curves (a) and (c) of Fig. 3 where the large relative size...

Clearly Fig. 7 must actually have a maximum at high asymmetry since this corresponds to negligible anchor block size and therefore to no adsorption (ct = 0). The lattice theory of Evers et al. predicts this quantitatively [78] and is, on preliminary examination, also able to explain some aspects of these data. From these data, the deviation from power law behavior occurs at a number density of chains where the number of segments in the PVP blocks are insufficient to cover the surface completely, making the idea of a continuous wetting anchor layer untenable. Discontinuous adsorbed layers and surface micelles have been studied theoretically but to date have not been directly observed experimentally [79]. 

This equation gives only the energy required to break up a bubble. The rate of breakage will also involve the number density of eddies of size A and a probability that the bubble will break up [20]. 

The first parameter, which indicates how densely the atoms are packed, will be denoted by D here since it may be called the Density parameter . It should be proportional to the number density (= number of atoms in a unit volume) but must be independent of the size of the atoms, depending only on the relative... 

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