Breakage and Selection Functions

The use of selection and breakage functions is much more cumbersome than working with a single index number. This concept has, therefore, been used only forthe description of comminution processes but not for the description of attrition. 

The assessment of attrition is mainly based on the examination of the behavior of a group of particles. In fluidization technology the total or overall attrition rate Ratot is commonly defined by the relative change of bed weight, Wbed, with time, 

Whether Eq. (2) or Eq. (3) is chosen will normally depend on the type of equipment used. When comparing different authors works, attention should be paid to the definition of Whed. For batch processes it may either be the initial bed mass or the instantaneous inventory of the bed. 

In fluidized bed experiments, most authors assume that all attrition products are elutriated. Consequently, they measure either the decrease in bed mass and use Eq. (2) (e.g.,Kono, 1981 Kokkoris etal., 1991, 1995) or the elutriated mass (e.g., Seville et al., 1992, Werther and Xi, 1993). It should be noted that all these authors used a certain particle size as a threshold below which all particles are assigned to be attrition products provided that all initial particles are clearly larger. Breakage events, which lead to particle sizes above the threshold level are, therefore, not considered. The choice of this threshold is very arbitrary and differs between the various research groups. 

Special attention has to be paid to a definition of attrition rates in the case of continuous processes where fresh solid material is continuously added. This is particularly the case in heterogeneously catalyzed fluidized bed processes where fresh make-up catalyst must be added to compensate for attrition losses. The fresh catalyst may contain elutriable fines which add to the measurable elutriation rate thus leading to an apparently higher attrition rate. 

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BREAKAGE AND SELECTION FUNCTIONS FROM BATCH BALL-MILL TESTS 13.3... 

Within Eq. (7), the selection function S(y) was approximated by Sty) = Kyc with adjustable parameters K and c and the breakage function b(x, y) was simply modeled by a triangular shaped function between a minimal breaking particle size of xq = 25 nm and x with a modal value at... 

In the simulation mns, the design parameters were chosen as d = (u,D), i.e. the kinetic parameters of breakage and the classification function were fixed. The size distribution of particles in the feed stream was constant, selecting 0 for x = xmax/2 and 0.05 for x > xmax/2, while the initial size distribution of the material in the mill was the same in each run. The largest particle size was chosen xmax = 10-3 m, and the values of the kinetic parameters were Ks = 10-4, a = 1.00, /3 = 3.00, y = 0.60,

classification function jump function of the form... 

Determine the breakage functions that pertain to the size fraction of the feed material Cumulative breakage functions can be calculated [1] from the relation Bi J = Fj/Sj. Therefore, in the case of the feed-size selection function 5), the equation is B ,i = Fi/S, and the breakage functions are as follows ... 

Determine the selection and breakage functions for other size fractions of the same material Selection functions for other size intervals may be calculated via the relation... 

Given the feed size distribution, the breakage functions, and the selection functions (probabilities of breakage) for a feedstock to a grinding operation, as shown in Table 13.4, predict the size distribution for the product from the operation. 

Define selection function and breakage function, functions used in the prediction of product size distribution in a size reduction process. 

This class of substances inhibiting nucleic acid synthesis is often found in tissue culture cells to cause chromosome breakage and oflier alterations in the nucleus and nucleolus. They have been selected and studied because they ate powerful antibacterial or antitumour agents. Except for local applications, they are not of great therapeutic use, since they are very toxic. It is difficult to conceive a substance of this type, which would have a selective action because the most regular and vital feature of any type of cell is the presence of a double-stranded DNA, functioning normally. 

Dea lomeration can take place by two methods comminution and ultrasonification. Comminution is the subject of Chapter 4, so it will not be discussed in detail here. In the comminution of aggregates, the popvdation balance can be used to predict the size distribution as a function of time in a batch mill or as a function of mean residence time in a continuous mill. Aggregates have the same type of birth and death fvmctions for particle breakage as polycrystalline particles but the rate constants are much hi er and the size selectivities for aggregates are different than those for the comminution of crystalline materials. The... 

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