Particle-size distribution definition

When a process is continuous, nucleation frequently occurs in the presence of a seeded solution by the combined effec ts of mechanical stimulus and nucleation caused by supersaturation (heterogeneous nucleation). If such a system is completely and uniformly mixed (i.e., the product stream represents the typical magma circulated within the system) and if the system is operating at steady state, the particle-size distribution has definite hmits which can be predic ted mathematically with a high degree of accuracy, as will be shown later in this section. 

The complete mathematical definition of a particle size distribution is often cumbersome and it is more convenient to use one or two single numbers representing say the mean and spread of the distribution. The mean particle size thus enables a distribution to be represented by a single dimension while its standard deviation indicates its spread about the mean. There are two classes of means ... 

For code R8 it commences with a solid with the help of AFNOR standards NF T 20-035 . Handling consists in preparing mixtures of variable compositions of an oxidant to be classified as cellulose. Both substances have to have a definite particle size distribution. The composition which gives the fastest combustion on a moulding of the mixture at a distance of 20 cm is established. This speed is compared with the one of the mixture used as a reference, which has an imposed composition of barium nitrate and cellulose. If the combustion speed of the particular substance is higher than that of the reference, it will bear R8. 

In order to evaluate the extent of attrition and its impact on the particle size distribution, there is a need of a qualitative and quantitative characterization. This, however, is not as simple as it may seem at first. There are many different properties, parameters and effects that manifest themselves and could be measured. In addition, as will be shown, the choice of the assessment procedure is strongly connected with the definition of attrition which, on its part, depends on the degradation mechanism that is considered to be relevant to the process. Hence there are a lot of procedures and indices to characterize the process of particle attrition. Section 3 deals with those which are relevant to fluidized beds and pneumatic conveying lines. 

It should be noted here that the above definition of the attrition rate considers the bed material as a whole. More insights into the influence of elements of the fluidized bed apparatus, e.g., of the cyclone or of the gas distributor may be obtained from the observation of the change in the particle size distribution as has been demonstrated by Zenz and Kelleher (1980) and Lin et al. (1980). 

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

It is possible to define an evaluation index for the mixing state by using the definition of multi-component mixedness in the previous section. The following discussion focuses on the mixing state of the continuous phase and the dispersed phase with a particle size distribution. 

Needless to say, kinetic parameters established in this way are empirical factors dependent on the definition of other variables,e.g., averaging of particle size distribution to determine R. Nevertheless, the model provides a rational approach to the complex physical and chemical phenomena of multistage, multireaction leaching. It is intended to expand the model to include countercurrent operations. 

Example 2.8 Given the particle size distribution shown in the table below, compare values for different diameters, using the definitions in Table 2.1 with values computed with Eq. 2.11. 

Particle Surface Area Determination Methods From the standard definitions of particle surface area, it can be seen that various determination methods are used for surface area measurement, such as adsorption (including Langmuir s equation for monolayer adsorption and the BET equation for multilayer adsorption), particle size distribution, and permeability methods. The different methods are rarely in agreement because the value obtained depends upon the procedures used and also on the assumptions made in the theory relating the surface area to the phenomena measured. The most common methods used for measuring particle surface area are described below. 

By definition, the kinetic curve of a cement is the weighted sum of the curves for its constituent phases as they occur in that cement. The reactivities of individual clinker phases were considered in Section 4.5 and some effects of particle size distribution, which is a particularly important variable, in Section 4.1.4. Although many data relating particle size distribution directly to strength exist, much less is known about its relation to degrees of reaction. Parrott and Killoh (P30) presented data indicating that the rate of hydration, as represented by that of heat evolution, was proportional to the specific surface area during the period of hydration in which the rate was controlled by diffusion. 

Very often one does not require as much detail as presented in Figure 2 and the model can be simplified considerably. For example, one may only be interested in the first few moments of the latex particle size distribution, F(V,t) so as to get a mean and variance of the distribution. This can be readily calculated from the definition of the jth moment ... 

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