Population balance comminution

In batch comminution, the summation term in equation (4.11) is zero because there are no flows into or out of the mill. Therefore the population balance on a discrete mass basis is simplified to... 

Several classification functions, C(L), are given in Figure 4.20. Here, the fraction of particles by mass reporting to the recycle stream is given as a function of particle size, L, for a screen and a cyclone. Several authors have used empirical classification functions instead of dassifier performance curves with reasonable results for the overall comminution-classification circuit control. The steady state (i.e., dmidt = 0) macroscopic population balance on a discrete mass basis over the grind-... 

In this chapter, the fundamentals of classification and comminution of ceramic powders have been described. Comminution is described by birth and death functions in a population balance. These birth and... 

Consider a continuous comminution process in which the feed consists of large particles and the smaller comminuted particles are being removed at the same mass flow rate as the feed. Following Ramkrishna (2000), the population balance equation may be written as... 

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). 

The size distribution formed in the product of comminution can again be predicted using the population balance methodology (Randolph and Larson, 1988). For a breakage process the population balance becomes... 

Particulate products, such as those from comminution, crystallization, precipitation etc., are distinguished by distributions of the state characteristics of the system, which are not only function of time and space but also some properties of states themselves known as internal variables. Internal variables could include size and shape if particles are formed or diameter for liquid droplets. The mathematical description encompassing internal co-ordinate inevitably results in an integro-partial differential equation called the population balance which has to be solved along with mass and energy balances to describe such processes. 

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