Product size distribution

The summation term is the mass broken into size interval / from all size intervals between j and /, and S is the mass broken from size internal i. Thus for a given feed material the product size distribution after a given time in a mill may be deterrnined. In practice however, both S and b are dependent on particle size, material, and the machine utilized. It is also expected that specific rate of breakage should decrease with decreasing particle size, and this is found to be tme. Such an approach has been shown to give reasonably accurate predictions when all conditions are known however, in practical appHcations severe limitations are met owing to inadequate data and scale-up uncertainties. Hence it is stiH the usual practice to carry out tests on equipment to be sure of predictions. 

FIG. 18-63 Calculated product -size distribution for a crystallizer operation at different fine-crystal-separation sizes. 

Crusher Product Sizes Table 20-10 relates product size to the discharge setting of the crusher in terms of the percent smaller than that size in the product. Size-distribution curves differ for various types of materials crushed, and a general set of curves is not vahd. 

Swaroop et al. [Powder Technology, 28, 253-260 (Mar.-Apr. 1981)] found that the material holdup is higher and the vessel dispersion number Dl/L (see subsection on Continuous Mill Simulation) is lower in the rod mill than in the ball mill under identical dimensionless conditions. This indicates that the known narrow-product-size distribution from rod mills is partly due to less mixing in the rod mill, in addition to different breakage kinetics. 

The industrial importance of the nucleation lies in its effects on the yield and product size distribution of alumina crystals. The yield is significant for plant economic reasons while off-target product size distribution adversely affects the downstream operations (e.g. washing and separation) as well as not meeting the customers product specifications. 

First the particle size and shape should mentioned. As columns packed with nominally 5 or 10 pm particles are used most commonly in HPLC, the particle size distribution has become an important characteristic of the packing because with such small particles it is difficult to obtain a monodisperse product. Size distribution of the particles can be represented in many different ways. Most commonly the cumulative particle size distribution curve obtained with an instrument such as the... 

Most polymerisation reactions occur via a complex reaction scheme. Relatively few reactant species are involved (sometimes only one) and these are usually well-defined. However, the reaction products can be described in a number of ways. The polymer molecules produced in these reactions vary in size in some cases the size distribution can be very wide. In effect, a polymerisation reaction produces a large number of reaction products and reaction selectivity requires special treatment. For some purposes, the polymer molecules can be treated as a combined group which is referred to generally as polymer . However, the physical properties of any given type of polymer depend on its molecular weight distribution. Therefore, it is often necessary to obtain a quantitative description of the product size distribution. This will depend on both the kinetic scheme for the polymerisation reaction and the mixing conditions in the polymerisation reactor. 

Recently, crushing has been widely used in chemical industries. Although the crushed product size distribution in the operation has been expressed by various PSD functions, the most utilized PSD function is the log-normal PSD function. However, there is no physical background for applying the log-normal PSD function to the crushed product size distribution. Additionally, when the crushed product size distribution is expressed by various PSD functions, it becomes difficult to discuss the relationship between the parameters in the PSD and the operation condition. This fact is one of the obstacles in the development of particle technology. 

To examine whether the new PSD defined by Eq. (5.18) can sufficiently express the crushed product size distribution in the grinder. 

A fixed weight feed is fed in the ball mill and the ball mill is rotated at a fixed rotational speed. After the rotation has begun, the crushed product is removed at constant time interval, and the crushed product size distribution is measured by using a Tyler standard sieve. 

F. Luciani and A. Zaikin. Mathematical models of the proteasome product size distribution. 2006. (submitted). 

A. Zaikin and J. Kurths. Optimal length transportation hypothesis to model proteasome product size distribution. Journal of Biological Physics, 2006. (in press, DOI 10.1007/sl0867-006-9014-z). 

Narrow product size distribution, in part due to a classification effect at the top of the annulus which allows the outlet pipe to be located so as to remove primarily the largest granules. 

PREDICTING PRODUCT SIZE DISTRIBUTION FROM FEEDSTOCK DATA 13.4... 

Size interval Total-product size distribution, percent... 

Cumulative product size distribution for two identical runs, with and without seeding, is shown in Fig. 21. The results obtained by Schlichtkrull from three seeded runs are shown in Fig. 22. In curve (a) it is assumed... 

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