Particle number distribution

Using the same reasoning as with the particle number distribution above, we observe that if the x- and y-axes are provided with the nonlinear scales, n and tf, defined by Eqs. (14.34) and (14.35), the mass distribution m x)/m t) can be described by a straight line... 

By tuning /. to obtain a bimodal particle number distribution, it was possible to locate the point of coexistence between saturated thin and thick films on the adsorbing surface. The prewetting coexistence curve was then obtained through the application of this procedure at each simulation temperature. 

One other form of distribution function which has been suggested as appropriate for condensation particles is the exponential distribution. In terms of a particle number distribution, its form is... 

Birmili W et al (2009) Atmospheric aerosol measurements in the German Ultrafine Aerosol Network (GUAN), - Part 1 soot and particle number distributions. Gefahrstoffe Reinhalt Luft 69 137-145... 

Direct reading ferrography studies were carried out to investigate particle number distribution in large (5//m) and small (1 to 2fam) wear debris (Hunt, 1993). 

Figure 6. Comparison of Particle Number Distribution Curves by DCP, SFFF and TEM a)Sample 68-B b)Sample 8-A...

Figure 13. Particle number distributions for a diesel engine (2.5 L displacement, direct injection, 4-cylinder, 1500 rpm, 7.5 kW) mn with 300 ppm sulfur content diesel fuel. Distributions are measured using a dilution tunnel with conditions simulating those expected in the environment (final dilution ratio of approximately 100 1). From Collings and Graskow (2000). Used by permission of the Royal Society.

Figure 15. Contom plot of monthly average particle number distributions measured in Atlanta, Georgia. SMPS = scanning mobility particle sizer, used to measure numbers of particles with Dp = 20-250 mn. A laser particle counter is employed to measure particles with diameters of 0.1-2 pm. Nanoparticles with Dp = 3-50 mn are measured with a nano-DMA in conjunction with a UCPC. The white boxes without data indicate times of eqipment failure. From Woo et al. (2001). Used by permission of Taylor Francis, Inc.

For flows where compressibility effects in a gas are important the use of the particle mass as internal coordinate may be advantageous because this quantity is conserved under pressure changes [11]. In this approach it is assumed that all the relevant internal variables can be derived from the particle mass, so the particle number distribution is described by the particle mass, position and time. Under these conditions, the dispersed phase flow fields are characterized by a single distribution function /(m, r,t) such that f m,r,t)drdm is the number of particles with mass between m and m+dm, at time t and within dr of position r. Notice that the use of particle diameter and particle mass as inner coordinates give rise to equivalent population balance formulations in the case of describing incompressible fluids. 

Despite the absence of capillary condensation, the one-dimensional hard-rod fluid is still so useful because we have an analytic expression for its partition function [see Eq. (3.12)] that permits us to derive closed expressions for any thormophysical property of interest. One such quantity that is closely related to the Isothermal compressibility discussed in the preceding section is the particle-number distribution P (N), whidi one may also employ to compute thermomechanical properties [see, for example, Eqs. (3.65) and (3.68)]. Moreover, in a three-dimensional system P ) is useful to investigate the sj stem-size dependence of density fluctuations as we shall demonstrate in Section 5.4.2 [see Eq. (5.80)]. 

On the basis of eq. (V. 17), Perrin estimated Avogadro s number from experimental studies of the particle number distribution as a function of height in the gamboge suspensions. His result, 6.7x1023 mol 1, is quite close to the commonly accepted value. 

One can distinguish between the differential and integral (or cumulative) particle size distribution functions. These two types of functions are related to each other by the differentiation and integration operations, respectively. The adequate description of distribution function must include two parameters the object of the distribution (i.e. what is distributed), and the parameter with respect to which the distribution is done. The first parameter may be represented by the number of particles, their net weight or volume10, their net surface area or contour lengthen some rear cases). The second parameter typically characterizes particle size. It can be represented as a particle radius, volume, weight, or, rarely, surface area. Consequently, the differential function of the particle number distribution with respect to their... 

Young K (1998) Population health concepts and methods. Oxford University Press, New York Zhang M, Wexler A (2002) Modeling the number distributions of urban and regional aerosols theoretical foundations. Atmos Environ 36 1863-1874 Zhang M, Wexler A (2004) Evolution of particle number distribution near roadways—Part I analysis of aerosol dynamics and its implications for engine emission measurements. Atmos Environ 38 6643-6653... 

Zhang M, Wexler A, Zhu Y et al (2004) Evolution of particle number distribution near roadways. Part II the road-to-ambient process. Atmos Environ 38 6655-6665... 

Standard quartz is officially designed as DQ12 < 5 (un (Robock 1973). The maximum of the particle number distribution is ca. 0.8 pm that of the surface distribution ca. 1pm while the maximum of the volume or mass distribution is ca. 1.3 pm. The upper size of the quartz particles is between 5 and 6 pm. The specific surface found by the BET-method is 7.4 mVg. 

Analytical solutions for the particle number distribution in the absence of growth and nucleation may be given as... 

The current section of the chapter on numerical methods is devoted to an outline of the most frequently used numerical methods for solving the population balance equation either for the particle number distribution function or for a few moments of the number density function. The methods considered are the standard method of moments, the quadrature method of moments (QMOM), the direct quadrature method of moments (DQMOM), the sectional quadrature method of moments (SQMOM), the discrete fixed pivot method, the finite volume method, and the family of spectral weighted residual methods with emphasis on the least squares method. 

As the diffusion coefficients approach infinity, mixing on the lattices becomes perfect and the particle number distribution will always be binomial. This suggests the construction of an automaton rule where the composition of propagation a nd velocity randomization steps, R- P, is replaced by a new operator B that redistributes the particles at each time step according to a binomial distribution. This well-stirred automaton dynamics has the rule... 

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