Grade Efficiency and Cut Size

If the particle size range on Equation 10.21 becomes infinitesimal, the obtained efficiency corresponds to a single particle size x and it is known as the grade efficiency, defined by 

The grade efficiency has become a very useful definition, since most industrial powders consist of an infinite number of differently sized particles. Thus, a single particle size really corresponds to a range of particles having almost similar sizes. Therefore, the gradeefficiency of most separation equipments is a continuous function of x. This function is seldom expressed analytically but graphically. An S-shaped curve is usually obtained for separators in which inertial or gravity body forces perform the separation. 

Grade efficiency curve (a) without taking into account dead flux effect, and (b) taking into account dead flux effect. 

According to Svarovsky (2000) the combination giving best results is that using both leaving streams in a solid-fluid separation process, that is, overflow and underflow, as represented by Equation 10.28. 

Grade efficiency curves derived for practical applications normally do not pass through the origin. This can be explained bearing in mind that, as has been previously described, some separation devices are flow dividers, and so the underflow always contains a certain quantity of very fine particles which simply follow the flow, and are split in the same ratio as the liquid. In order 

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The degree of cell separation is an important parameter to be evaluated in perfusion systems. This can be done through the use of some concepts as cell separation efficiency, grade efficiency, and cut size. These concepts are applicable to any equipment whose performance remains constant if the operational conditions do not change. They are valid, therefore, for equipment such as sedimenting centrifuges, hydrocyclones, gravitational settlers, etc. 

The solid-liquid separation in hydrocyclones is never complete, because there is always liquid discharging with the solids through the underflow. The term separation efficiency used for the hydrocyclone is usually defined for measuring the capability of the hydrocyclone of separating the solids from the feed into the underflow. There are a number of different terms for the separation efficiency used in the literature. They include total efficiency, reduced total efficiency, grade efficiency, reduced grade efficiency, and cut size. 

Figure 24 Grade efficiency and cut size in hydrocyclone operation. (From Svarosvsky, 1985.)...

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