Coarse and Fine “Fish Hook” Inflections in Hydrocyclone Efficiency Curves

"The literature contains many cases where the shape of hydrocyclone efficiency curves vary from the ideal “S” shape. These often appear as changes in slope, or inflections. These inflections can be divided into two categories: “coarse” inflections, which are caused by differences in the density of the minerals being separated, and “fine” inflections, for which there are a number of competing hypotheses concerning their cause. The existing literature addresses either the fine inflection or the coarse inflection, but no studies have reported both types of inflection occurring at once in a single hydrocyclone test. This paper presents hydrocyclone results from both in-plant studies and laboratory experiments that show both coarse and fine inflections. The industrial significance of both types of inflections is discussed. Hydrocyclone efficiency curves show the probability of any given particle reporting to the hydrocyclone underflow as a function of its size. Selectivity functions, S(d), are used to represent the fraction of the feed material in size fraction “d” that reports to the hydrocyclone underflow. Plotting this selectivity function against particle size leads to the standard S-shaped efficiency curve shown in Fig. 1. In the “uncorrected” curve, the tail of the curve does not go through 0%, because a portion of the solids are bypassing classification. This happens as a result of their being carried along by the water, and is most important for the finest particles. The curve can be “corrected” based on the fraction of the feed water that reports to the underflow, represented by the bypass fraction, Rf. The corrected curve then normally passes through 0%, as shown in Fig. 1.The act of correcting the curve shifts the value of the d50 size, which is the size that has an equal probability of reporting to either the overflow or to the underflow. Correcting the curve to account for the bypass fraction makes it easier to compare cyclone performance under conditions that cause the quantity of water in the underflow to change, but that do not alter the actual corrected cut size (d50c).The corrected efficiency curve can be expressed closely by equations such as Plitt (1976):"