Modelling of hydrocyclone classifiers: A critique of 'bypass' and corrected efficiency

In early 1950s, Kelsall visualised the classification process in which a fraction of feed solids reaches underflow without undergoing classification in a hydrocyclone. We bring to light that this notion of 'bypass' is beyond experimental reach and is purely imaginary. This implies that the corrected efficiency, which is a key performance characteristic in all the successfully used hydrocyclone models and for which bypass is the foundation is also hypothetical. We discuss the reasons for the continued acceptance of a physical meaning to 'bypass' among the hydrocyclone practitioners. Following a discussion on why the classification process as visualised by Kelsall is purely notional, we bring to light the lack of an experimental basis for 'bypass' and why no physical meaning can be attributed to it. A mathematical interpretation of the method suggested by Kelsall for calculating corrected efficiency is also presented. A general method for normalising any function y = f(x) where x and y vary between x(min) to x(max) and Y-min to y(max) respectively into Y-n (x)where the range of Y-n is from 0 to 1, is then proposed. We show that this normalisation can be done in an infinite number of ways by choosing user defined normalising functions and demonstrate our method with a numerical example. Taking into consideration that classifications function is a special case of y = f(x), we show that it too can be normalised in an infinite number of ways. While illustrating our method with examples, we show that the procedure suggested by Kelsall is the simplest method to normalise actual efficiency curves. The similarity between bypass and normalising functions is illustrated with examples; it is shown that both of them are purely notional and have no physical significance. We bring to light the possibility of development of improved hydrocyclone models using a normalised cut size other than Kelsall cut size. Finally, we propose that the corrected efficiency be denoted as Kelsall efficiency and the corrected classification size as Kelsall cut size, as a tribute to the landmark contribution of Kelsall towards modelling of hydrocyclones. (C) 2016 Elsevier B.V. All rights reserved.