Particle size distribution various systems

Many properties of disperse systems, such as those described above and those analyzed in subsequent chapters, are defined by the degree to which substance is dispersed and by the type of particle size distribution. Various methods for the investigation of dispersion composition of dispersed phase (idispersion analysis) have been developed. Many of these methods utilize the concepts of transfer phenomena discussed in previous sections of this chapter. 

These relations can be spread to the systems of particles of one form, but of various sizes, D. The specific surface area of such PS is equal to the sum of surface areas of particles related to the entire mass. At known particle size distribution (PSD), v(D), one has... 

The analysis of the autocorrelation function data by the Coulter Model N4 is carried out by the Size Distribution Program (SDP), which gives the particle size distribution in the form of various output displays (see Section 10.4). The SDP analysis utilizes the computer program CONTIN developed by S.W. Provencher (ref. 467-470 see also Section 10.2). (This program has been tested on computer-generated data, monomodal polystyrene samples, and a vesicle system (ref. 466-468,471).) Since the SDP does not fit to any specific distribution type, it offers the ability to detect multimodal and very broad distributions. 

Colloidal systems are generally of a polydispersed nature - i.e. the molecules or particles in a particular sample vary in size. By virtue of their stepwise build-up, colloidal particle and polymer molecular sizes tend to have skew distributions, as illustrated in Figure 1.2, for which the Poisson distribution often offers a good approximation. Very often, detailed determination of relative molecular mass or particle size distribution is impracticable and less perfect experimental methods, which yield average values, must be accepted. The significance of the word average depends on the relative contributions of the various molecules or particles to the property of the system which is being measured. 

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. 

For a given size distribution, various averaged diameters can be calculated, depending on the forms of weighing factors. The selection of an appropriate averaged diameter of a particle system depends on the specific needs of the application. For instance, in a pulverized coal combustion process, the surface area per unit volume may be important. In this case, Sauter s averaged diameter should be chosen. 

Figure 1. Particle size distributions for emulsion system A with various emulsifier concentrations (in g/lOOg oil phase) (a) 3.5, (b) 5, (c) 10. Each figure is an average of 15 distributions, each of which was obtained using quadratic spacing with 20 particle sizes per pass and 5 passes.

Other important physical measurements are bulk densities used to estimate hopper contents and circulation factors, and particle size analysis. The correct distribution of fine particles (30 - 180 microns) is essential to proper fluidization and transfer within the FCC unit. Generally, particles less than 30 microns are lost to the atmosphere or fines recovery system and are destined for a landfill. If the catalyst is too coarse, it may not circulate through the unit, necessitating a shutdown. Both problems are costly to the refiner and must be avoided. In addition, observation of particle size distribution changes at various points within the unit can pinpoint equipment malfunctions that might otherwise go undetected. 

This was developed by Aerometrics in 1983, in collaboration with Lewis Research center, for research into pollution reduction from gas turbines. It is particularly relevent to measurements of small, spherical particles such as are found in fuel injection systems, medical nebulizers and bubbles in water. Aerometrics was later acquired by TSI who currently produce the TSI/Aerometrics PDPA 2D System. This instrument measures sizes in the 0.5 to 10,000 pm range using various optical configurations. The optical transmitter and receiver can be traversed together to move the location of the optical probe for spatial mapping of the flow field and the particle size distributions. 

Furthermore, it was recently demonstrated that the release of a drug, such as propranolol, from the multilaminate adhesive-based TDD system can be maintained at zero-order kinetics by controlling the particle size distribution of drug crystals in the various laminates of adhesive matrix. ... 

The ratio of the Sauter mean diameter to the drag diameter appears as a shape factor. It is noted that for non-spherical particles or for systems with a particle size distribution, the various shape factors may not be unity. However, for a distribution of spherical particles, the shape factor, is unity regardless... 

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