Size distribution function

By taking special precautions, it is po.ssible to generate aerosols composed of particles that are all the same. size. These are called tnotiodisperse or homof eueotts aerosols. In most practical cases both at emission sources and in the atmosphere, aerosols are compo.sed of particles of many dififerent sizes. These are called polydisper.se or heierodisper.se aerosols. 

The most important physical characteristic of polydisperse sy.stems is their particle size distribution. This distribution can take two forms The first is the discrere dtstrihuiion in which only certain allowed particle sizes are considered. Consider a suspension that consists of aggregates of unitary particles formed by coagulation. All particles will then be composed of integral numbers of these unitary particles, and the size distribution can be 

Usually more useful, however, is the concept of the cominitous sizedismhution. Lei dN be the number of particles per unit volume of gas at a given position in space, represented by r, and at a given time in the particle diameter range dp to dp + d dp)  

This expression defines the particle size distribution function nttidp, r, 0 where the particle diameter may be some equivalent size parameter for nonspherical particles. In theoretical applications, especially coagulation (Chapter 7), it is convenient to introduce a size distribution with particle volume as the size parameter 

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The pore size distribution function (a) appears parametrically in the flux relations of Feng and Stewart, so their models certainly cannot be completely predictive in nature unless this distribution is known. It is... 

Aerosol, monodisperse An aerosol with a size-distribution function described by a geometrical standard deviation less than 1.15. If the deviation is between 1.15 and 1.5, it is classified as a quasi-mono-disperse aerosol. 

The effects due to the finite size of crystallites (in both lateral directions) and the resulting effects due to boundary fields have been studied by Patrykiejew [57], with help of Monte Carlo simulation. A solid surface has been modeled as a collection of finite, two-dimensional, homogeneous regions and each region has been assumed to be a square lattice of the size Lx L (measured in lattice constants). Patches of different size contribute to the total surface with different weights described by a certain size distribution function C L). Following the basic assumption of the patchwise model of surface heterogeneity [6], the patches have been assumed to be independent one of another. 

On the other hand, whenever AV exceeds the value of AVq the formation of a dense monolayer film appears to be the continuous process. It has been demonstrated that the observed crossover between those two regimes is due to the changes in the mechanism of the adsorbate nucleation, as determined by the calculation of the nucleated cluster size distribution functions. For... 

The data in Fig. 2 are compared with a proposed particle-size distribution function / (a, a ) (B4, G5) ... 

Anderson (A2) has derived a formula relating the bubble-radius probability density function (B3) to the contact-time density function on the assumption that the bubble-rise velocity is independent of position. Bankoff (B3) has developed bubble-radius distribution functions that relate the contacttime density function to the radial and axial positions of bubbles as obtained from resistivity-probe measurements. Soo (S10) has recently considered a particle-size distribution function for solid particles in a free stream ... 

Combinatory factors occurring in size distribution functions for nonlinear condensation polymers (see Eqs. IX-18 and -34). 

V. Mishra, S. M. Kresta, J. H. Masliyah 1998, (Self-preservation of the drop size distribution function and variation in the stability ratio for rapid coalescence of a polydisperse emulsion in a simple shear field), J. Colloid Interface Sci. 197, 57. 

Here, Ari) is the size distribution function of the initial solid reagents... 

Gwyn, J. E., On the Particle Size Distribution Function and the Attrition of... 

In order to characterize quantitatively the polydisperse morphology, the shape and the size distribution functions are constructed. The size distribution function gives the probability to find a droplet of a given area (or volume), while the shape distribution function specified the probability to find a droplet of given compactness. The separation of the disconnected objects has to be performed in order to collect the data for such statistics. It is sometimes convenient to use the quantity v1/3 = [Kiropiet/ ]1 3 as a dimensionless measure of the droplet size. Each droplet itself can be further analyzed by calculating the mass center and principal inertia momenta from the scalar field distribution inside the droplet [110]. These data describe the droplet anisotropy. 

The results were obtained for the polydispersed mixtures possessing the following characteristic properties of particle size distribution function (Figs. 14.1-14.2) ... 

The molecular size distribution functions for three-dimensional polymers are derived in a manner analogous to those for linear polymers, but with more difficulty. The derivations have been discussed elsewhere [Flory, 1946, 1953 Somvarsky et al., 2000 Stockmayer,... 

Because of this need to know how the mass, surface, and volume are distributed among the various particle sizes, distribution functions for these parameters (i.e., mass, surface, and volume) are also commonly used for atmospheric aerosols in a manner analogous to the number distribution. That is, Am A log D, AS A log D, or AV A log D is plotted against D on a logarithmic scale, where Am, AS, and AV are the mass, surface area, and volume, respectively, found in a given size interval again the area under these curves gives... 

A knowledge of the size distribution function of the radioactive debris and the specific activity of individual fission product chains as a function of particle size suffice to define many important radiological properties of the land-surface nuclear explosion. If is the function of a radionuclide or fission mass chain distributed between particle sizes Di and D2, then... 

The size distribution function f(D) pertaining to the event as a whole has variously been taken as a log-normal or as a power law distri-... 

Any nonnegative function which has a finite integral over the range of drop sizes may serve as a size-distribution function. However, to form a valid basis for statistical inferences, the distribution of each parameter involved in the chosen distribution must be known. Because the distributions of the parameters often present overwhelming mathematical difficulties, considerable care must be exercised in using various curvefitting techniques which introduce new parameters into the distribution. 

At any time t, a distribution of particle sizes will exist which can be quantified by defining a particle-size distribution function, f(R,t) [units, (length)-4], such that the number of particles per unit volume with radii between R and R + dR, n(R, R + dR t), is given by... 

As the calculations have to be performed numerically the problem has been simplified in so far as only a very simple drop size distribution function is assumed to hold, namely ... 

Packer and Rees [3] extended the work of Tanner and Stejskal by the development of a theoretical model using a log-normal size distribution function. Measurements made on two water-in-oil emulsions are used to obtain the self-diffusion coefficient, D, of the water in the droplets as well as the parameters a and D0 0. Since then, NMR has been widely used for studying the conformation and dynamics of molecules in a variety of systems, but NMR studies on emulsions are sparse. In first instance pulsed field gradient NMR was used to measure sdf-diffusion coefficients of water in plant cells (e.g. ref. [10]). In 1983 Callaghan... 

Fig. 5 Britain and Ireland aerosol overview (location shown in the inset), (a) Histograms of N10o concentration in both stations, (b) Mace Head size distributions, showing 16th, median (thick line), and 83rd percentiles of size distribution functions...

In the applications of gas-solid flows, there are three typical distributions in particle size, namely, Gaussian distribution or normal distribution, log-normal distribution, and Rosin-Rammler distribution. These three size distribution functions are mostly used in the curve fitting of experimental data. 

Characterization of the Bulk Properties of Catalysts Measurements of Particle-size Distribution Functions of Supported Catalysts -... 

In summary the advantage of using neutrons for catalyst particle-size-distribution function measurements, is that, unlike X-rays, they can be applied to catalysts dispersed on high-electron-density supports such as a-Al203. This is because the technique of contrast matching to mask-out one component of the scattering is much more versatile with neutrons than with X-rays. In part this is due to the ready availability of suitable deuteriated solvents. 

Figure 8 The particle-size distribution function for a NiO catalyst determined by small-angle scattering...

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