Grade centrifugal sedimentation

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. 

Gravity sedimentation equipment, hydrocyclones, sedimenting centrifuges or flotation cells have also been extensively used in mineral processing for separation of minerals according to density or affinity to water. In such separations, the efficiency is expressed by the Tromp curve which, similar to the grade efficiency curve, shows probability of separation as a function of material density or mineral composition. The steepness of the curve is a measure of the sharpness of the separation. 

It is for these same reasons that the grade efficiency value cannot be determined by a physically exact calculation. If, under certain simplifying assumptions, such a calculation is carried out, the results have to be corrected by coefficients determined experimentally, values of which may be very different from 100% according to the degree of the simplification adopted. Such a procedure can be used with separators that employ inertia principles, sedimentation, centrifugation, etc., where the particle trajectories in the separator can be estimated. 

For any separator with a size-dependent performance, such as a hydrocyclone, a sedimenting centrifuge or a settling vessel, the grade efficiency varies with particle size, and a graphical representation of this is called the grade efficiency curve (see section 3.2.2). As the value of the grade efficiency has the character of probability, it is sometimes referred to as the partition probability the curve then becomes the partition probability curve or Tromp curve. 

There are many other assumptions made in the following analysis (these are stated where they are introduced) but despite their often obvious oversimplicity the final results give a reasonable estimate of equipment performance. The analysis is made for a simple tubular centrifuge but the same approach, with slight modifications, may be used for other types of sedimenting centrifuges. An attempt is first made to derive the whole grade efficiency... 

The only way to describe fuUy the performance of a sedimenting centrifuge is by the grade efficiency curve knowledge of this curve allows accurate and reliable (subject to the operation characteristics, the state of dispersion of solids and other variables remaining constant) predictions of total efficiencies... 

The size corresponding to 50% on the reduced grade efficiency curve G (x) is referred to as the "reduced cut size" - see Fig.l. Most mathematical descriptions of the performance of hydrocyclones or sedimenting centrifuges are in terms of the reduced cut size. 

The reduced grade efficiency curves of some dynamic separators, including hydrocyclones and sedimenting centrifuges, can be fitted by a cumulative log-normal function in the following form ... 

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