Specific breakage rate

Specific breakage rate Specific conductivity Specific ion electrode Specific properties... 

Table 1 summarizes typical data the specific breakage rate, 3), for particles in size class 1 is 0.6, and the breakage product mass in size classes 2—6 is as shown. The corresponding values of b and B are given. 

The function S(L) is the specific breakage rate, which is dependent on particle size because smaller particles are usually stronger than larger ones, see Figure 4.4. This death rate has been shown by Sedlatschek and Bass [12] to be in accord with probability theory. The specific breakage rate, S(L), has several definitions in the literature. The simplest is [13]... 

The resulting particle size distribution therefore depends to a large degree on the primary progeny function p(x, y) and to a lesser extent on the specific breakage rate. Much effort has been extended in describing the primary progeny function in a cumulative form ... 

In addition, several other two-parameter residence time distributions have been formulated [24]. With these or any other residence time distribution, the specific breakage rate, and the progeny array, the mill output can be determined ftnm the mill input thus the comminution step is mathematically described. 

If breakup of particles occurs independently of each other, we let fo(x, r, Y, t) be the specific breakage rate of particles of state (x,r) at time t in an environment described by Y. It represents the fraction of particles of state (x, r) breaking per unit time. Then we have... 

It is evident that most future work with irradiated polynucleotides will have to employ techniques such as these. Many pertinent observations were made about the effect of irradiation of the poly U upon enzyme specificity and rate. Irradiation of the polynucleotide drastically reduced the rate of hydrolysis of poly U by RNase. It was observed that RNase could not split the phosphodiester bond on the 3 -OH end of uridylic acid dimer. It was also shown that dehydration of irradiated poly U was accompanied by marked phosphodiester bond breakage and degradation of the polynucleotide. 

Taking the Gaussian average in gi (0, T) with the chain breakage rate (7.6), we find that a modulus-frequency curve at any temperature T can be superimposed onto a single curve at the reference temperature To, if it is horizontally and vertically shifted properly. Specifically, we have... 

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. 

Klimpel, R.R. and Austin, L.G., 1984. The back-calculation of specific rates of breakage from continuous mill data. Powder Technology, 38, 77-91. 

Cleland (160), steady-state kinetics of a Theorell-Chance mechanism can generally apply also to a rapid-equilibrium random mechanism with two dead-end complexes. However, in view of the data obtained with site-specific inhibitors this latter mechanism is unlikely in the case of the transhydrogenase (70, 71). The proposed mechanism is also consistent with the observation of Fisher and Kaplan (118) that the breakage of the C-H bonds of the reduced nicotinamide nucleotides is not a rate-limiting step in the mitochondrial transhydrogenase reaction. 

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