Selection-for-breakage

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. 

Industrial examples of adsorbent separations shown above are examples of bulk separation into two products. The basic principles behind trace impurity removal or purification by liquid phase adsorption are similar to the principles of bulk liquid phase adsorption in that both systems involve the interaction between the adsorbate (removed species) and the adsorbent. However, the interaction for bulk liquid separation involves more physical adsorption, while the trace impurity removal often involves chemical adsorption. The formation and breakages of the bonds between the adsorbate and adsorbent in bulk liquid adsorption is weak and reversible. This is indicated by the heat of adsorption which is <2-3 times the latent heat of evaporahon. This allows desorption or recovery of the adsorbate from the adsorbent after the adsorption step. The adsorbent selectivity between the two adsorbates to be separated can be as low as 1.2 for bulk Uquid adsorptive separation. In contrast, with trace impurity removal, the formation and breakages of the bonds between the adsorbate and the adsorbent is strong and occasionally irreversible because the heat of adsorption is >2-3 times the latent heat of evaporation. The adsorbent selectivity between the impurities to be removed and the bulk components in the feed is usually several times higher than the adsorbent selectivity for bulk Uquid adsorptive separation. 

Ito, T. Saito, M. Kobayashi, K. Dissociation of a model DNA compound dApdA by monochromatic soft X-rays in solids and comments on the high selectivity for 3 breakage in the phosphoester bond. Int. J. Radiat. Biol. 1992, 62 (2), 129-136. 

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... 

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... 

Conceptually, the framework of the theory permits description of interphase heat and mass transfer with reaction occurring in either or both phases. In theory one can use this approach to study the affects of partial mixing of the dispersed phase on extent of reaction for non-first-order reactions which occur in the droplets. Analyses can be made for mass-transfer-controlled reactions and selectivity for complex reactions. Difficulties in the solution of the resulting integro-diflferential equations have restricted applications at present to partial solutions. For example, the effects of partial droplet mixing on extent of reaction were studied for uniform drops. Mass transfer from nonuniform drops for various reactor geometries was studied for dispersions with drop breakage only or drop coalescence only. 

This procedure is very easy in the case of simple daughter distribution functions (e.g. symmetric binary breakage), whereas additional random numbers might have to be selected for more complex daughter distribution functions (e.g. beta, uniform, etc.)... 

Also defined are a selectivity for multiple bond breakage... 

Figure 3.5 Graphite models selected for calculation, including three oxygen intermediates. The dashed lines indicate where C-C bond breakage takes place to free CO. (Adapted from ref. 70.)...

A(p) is the rate constant for attrition. The rate of attrition depends on the material to be granulated, the binder, the type of equipment used for granulation and the intensity of agitation. The rate of breakage may also be accounted for by the use of selection and breakage function as used in the simulation of population balances in comminution (see Chapter 12). 

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