Comminution efficiency

FIGURE 4M Flviid-particle interaction at grinding media impact. 

1 Macroscopic Population Balance on a Discrete Mass Basis 

In these population balance equations, the volume change term is zero and the internal velocity term is also zero and therefore are not included. When the population balance is performed on a number basis, it is necessary to have a conservation equation, which for grinding is usually the total particle volume. 

The death rate in grinding is also referred to as the breakage rate and, for the population balance on a discrete mass basis, is given by [11] 

The birth fimction for conservation of volume must be consistent with the death function because each particle death results in the birth of smaller particles, resulting from commimition. When particles of size L break, they produce a suite of daughter particles, called the primary progeny, with a size distribution p(x, L). This function applies 

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A novel comminution device, the roll press, has achieved commercial success [Schoenert, International J. Mineral Processing, 22, 401-412 (1988)]. It is used for fine crushing, replacing the function of a coarse-baU mill or of tertiary crushers. Unlike ordinary roll crushers which crush individual particles, the roll press is choke fed and acts on a thick stream or ribbon of feed. Particles are crushed mostly against other particles, so wear is veiy low. Energy efficiency is also greater than in ball mills. 

Although SPME was applied initially for the analysis of relatively volatile environmental pollutants in waters, rapid developments have enabled SPME to be successfully applied for the analysis of pesticides in water, wine and more complex food samples such as honey, fruit juice and pears, vegetables and strawberries. With food samples, most analysts recognize the need for some sample pretreatment in order to minimize matrix effects. The matrix can affect the SPME efficiency, resulting in a reduced recovery of pesticides. The most common method is simply to dilute the sample or sample extract with water. Simpltcio and Boas comminuted pears in water prior to the determination of pesticides. Volante et al. extracted over 100 pesticides... 

In providing an overall picture of the Griffith theory applied to the comminution process, it must be pointed out that the theory requires that a tensile stress should exist across a crack to open it further. While a uniform compressive force can close a crack, a nonuniform one can lead to the occurrence of localized tensile stresses. In a comminution process the particles are subjected to nonuniform loading, and therefore it can be surmised that they normally break in tension and not in compression. However, the tensile component of loading in comminution does not form the major loading component and this contributes towards a lowering of the overall energy efficiency of comminution. 

The efficiency of a classifier is represented by a performance or partition curve, similar to that used for screens, which relates to the particle size to the percentage of each size in the feed that reports to the underflow. The most important industrial application of classifiers is to reduce overgrinding in a mill by separating the milled product output into coarse and fine fractions in order that the fines can be removed as they are produced and the coarse returned for further comminution. 

Modeling of Jet-Induced Attrition. Werther and Xi (1993) compared the jet attrition of catalysts particles under steady state conditions with a comminution process. They suggested a model which considers the efficiency of such a process by relating the surface energy created by comminution to the kinetic energy that has been spent to produce this surface area. The attrition rate, RaJ, defined as the mass of attrited and elutriated fines per unit time produced by a single jet, is described by... 

As is seen from this latter figure, an increase of the solids loading results in a decrease in the cyclone attrition rate. This may be due to a cushioning effect of the increased solids concentration which is well known in comminution processes. This cushioning effect may be interpreted as a decrease in the efficiency T] of the abrasion process. If we assume r] to be a function of jJ and in its simplest form to follow an exponential function,... 

CHARACTERISTICS OF COMMINUTED PRODUCTS. The objective of crushing and grinding is to produce small particles from larger ones. Smaller particles are desired either because of their large surface or because of their shape, size, and number. One measure of the efficiency of the operation is based on the energy required to create new surface, for as shown in Chap. 28, the surface area of a unit mass of particles increases greatly as the particle size is reduced. 

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