Particle size distribution function

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 ... 

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

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

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... 

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... 

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...

The theory of particle clouds proceeds from consideration of the dynamics of the particle size distribution function or its integral moments. This distribution can take two forms. The first is a discrete function in which particle... 

If one focuses on the particle size distribution function as a central framework for describing aerosols, one can conveniently classify the measurement instruments according to the properties of the size distribution function. Organization of instrumentation gives perspective on the ideal requirements as contrasted with the practical limits imposed by current technology. An idealized hierarchy was suggested by S. K. Friedlander in 1977. As an ideal, the modern aerosol analyzer gives a continuous... 

A number of analytical solutions have been developed since that of von Smoluchowski, all of which contain some assumptions and constraints. Friedlander [33] and Swift and Friedlander [34] developed an approach relaxing the above constraint of an initially monodisperse suspension. Using a continuous particle size distribution function, a nonlinear partial integro-differential equation (with no known solution) results from Eq. (5). Friedlander [35] demonstrated the utility of a similarity transformation for representation of experimental particle size distributions. Swift and Friedlander [34] employed this transformation to reduce the partial integro-differential equation to a total integro-differential equation, and dem-... 

The velocity can also be calculated for polydispersed systems with a particle size distribution function, x(<0 (Aldushin et al., 1976a). For a unimodal particle size distribution, an effective particle size, d s, defined as... 

Kamack offered the following solution to equation (8.12). If Q is plotted as a function of v, = rJSy with f = o9-t as parameter, a family of curves is obtained whose shape depends on the particle size distribution function. The boundary conditions are that Q - 1 when f = 0 for all r, (i.e. the suspension is initially homogeneous) and = 0 for r, = S when f>0 (i.e. the surface region is particle free as soon as the centrifuge bowl spins). Hence all the curves, except for f>0, pass through the point Q = 0, S, and they will all be asymptotic to the line / = 0, which has the equation Q = - Furthermore, from equation (8.12), the areas under the curves are each equal to F(r/., ). 

The particle-size distribution function (PSDF) is expressed as the number of particles per milliliter of solution per class size (particles mP pm ) a representative PSDF for the storms (as computed for storm 1) is shown in Figure 10. A cubic regression, determined to be the best fit for the data, was used to compute the PSDF at 4 and 10 pm (1S14 and Nioi ) and dmax, defined as the particle diameter for which only 10 particles were counted. Changes in these three parameters in response to the storms are shown in Figure 11. 

Figure 10. Representative particle-size distribution function (PSDF) for the storms fit with a cubic regression equation.

Surface area(s) and diameter (dp) are also used, so that three particle size distribution functions can be defined ... 

Fiiedlander (1960), Hunt (1980), Filella and Buffle (1993), and others have analyzed the effect of colloid agglomeration by coagulation and particle removal by settling on the shape of the particle size distribution function as expressed by equation 4. The predictions of model calculations are often consistent with the range of values of /3 observed in aquatic systems. 

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... 

The general moment of the particle size distribution function can be defined by the expression... 

Different parts of the particle size distribution function make controlling contributions to the various moments. In a polluted urban atmosphere, the number concentration or zeroth moment is often dominated by the 0.01- to 0, l- um size range, and the surface area is often dominated by the 0.1- to 1.0-/zm range contributions to the volumetric concentration come from both the 0.1 to 1.0- and 1.0- to 10-/xm size ranges (Chapter 13). Muincnts of fractional order appear in the theory of aerosol convective diffusion (Chapter 3). 

More generally, an infinite number of intermediate cases are possible between the internal and external mixture models. To take into account variations in chemical composition from particle to particle, the particle size distribution function must be generalized, and for that purpose the size-composition probability den.sity fimetion has been introduced (Friedlander, 1970). Let r//V be the number of particles per unit volume of gas containing molar quuiititics... 

The contributions to h(k) from a given particle size range depend on the extinction cross section and on the particle size distribution function. The integral (5.16) can be rearranged as follows ... 

GU/p) represents the extinction over ail wavelengths between A. and per unit volume of aerosol in the size range between and dp + d(dp). It is independent of the particle size distribution function. For a refractive index, m = 1.5, G(dp) has been evaluated for the standard distribution of solar radiation at sea level, using Mie scattering functions. The result is shown in Fig. 5.8 as a function of particle size. 

Forpolydisperse aerosols, the simple expression (5.36) for the autocorrelation function must be averaged over the particle size distribution function. In the Rayleigh scattering range... 

Particle collision and coagulation lead to a reduction in the total number of particles and an increase in the average size. An expression for the time rate of change of the particle size distribution function can be derived as follows. 

The change in the particle size distribution function with time for coagulating cigarette smoke has been measured by Keith and Derrick (1960), Smoke issuing from a cigarette was rapidly mixed with clean air, and the mixture was introduced into a 12-liter flask... 

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