Particle size distribution number

Numerous techniques have been applied for the characterization of StOber silica particles. The primary characterization is with respect to particle size, and mostly transmission electron microscopy has been used to determine the size distribution as well as shape and any kind of aggregation behavior. Figure 2.1.7 shows a typical example. As is obvious from the micrograph, the StOber silica particles attract a great deal of attention due to their extreme uniformity. The spread (standard distribution) of the particle size distribution (number) can be as small as 1%. For particle sizes below SO nm the particle size distribution becomes wider and the particle shape is not as perfectly spherical as for all larger particles. Recently, high-resolution transmission electron microscopy (TEM) has also revealed the microporous substructure within the particles (see Fig. 2.1.8) (51), which is further discussed in the section about particle formation mechanisms. 

It has been found that the particle-size distribution, number, and shape of the contaminations falling out of the flow depend on the direction of gas flow. Thus, small particles stick in the rear zone. The shape of edge contaminations depends on the manner in which the dust-laden stream flows around the obstacles. The frontal part of the pipes is subjected to the impact of the large particles hence, sticking to this part only occurs at low velocities. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Continuous emulsion copolymerization processes for vinyl acetate and vinyl acetate—ethylene copolymer have been reported (59—64). CycHc variations in the number of particles, conversion, and particle-size distribution have been studied. Control of these variations based on on-line measurements and the use of preformed latex seed particles has been discussed (61,62). 

Mechanical Properties. Mechanical properties (4,6,55) are important for a number of steps in coal preparation from mining through handling, cmshing, and grinding. The properties include elasticity and strength as measured by standard laboratory tests and empirical tests for grindabiUty and friabihty, and indirect measurements based on particle size distributions. 

Injection moulding compositions have a number of requirements with regard to granule flow and cure characteristics not always met by conventional formulations. For example, granules should be free-flowing (i.e. of a narrow particle size distribution and not too irregular in shape). There are also certain requirements in terms of viscosity. 

The electrical low-pressure impactor was used to measure the number concentrations of diesel exhaust particles. The particle size distribution ranges from 30 nm upward were then determined using the aerodynamic diameter as the characteristic dimension. ... 

In order to use Eq. (14.30) we need to know the particle size distribution. In many cases it has been observed that the size distribution obeys normal probability distribution, or at least can be well approximated by it. In fact, the number of particles dN whose logarithm of diameter... 

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 ... 

At the crystallization stage, the rates of generation and growth of particles together with their residence times are all important for the formal accounting of particle numbers in each size range. Use of the mass and population balances facilitates calculation of the particle size distribution and its statistics i.e. mean particle size, etc. 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

There have been few discussions of the specific problems inherent in the application of methods of curve matching to solid state reactions. It is probable that a degree of subjectivity frequently enters many decisions concerning identification of a best fit . It is not known, for example, (i) the accuracy with which data must be measured to enable a clear distinction to be made between obedience to alternative rate equations, (ii) the range of a within which results provide the most sensitive tests of possible equations, (iii) the form of test, i.e. f(a)—time, reduced time, etc. plots, which is most appropriate for confirmation of probable kinetic obediences and (iv) the minimum time intervals at which measurements must be made for use in kinetic analyses, the number of (a, t) values required. It is also important to know the influence of experimental errors in oto, t0, particle size distributions, temperature variations, etc., on kinetic analyses and distinguishability. A critical survey of quantitative aspects of curve fitting, concerned particularly with the reactions of solids, has not yet been provided [490]. 

A dynamic ordinary differential equation was written for the number concentration of particles in the reactor. In the development of EPM, we have assumed that the size dependence of the coagulation rate coefficients can be ignored above a certain maximum size, which should be chosen sufficiently large so as not to affect the final result. If the particle size distribution is desired, the particle number balance would have to be a partial differential equation in volume and time as shown by other investigators ( ). 

---