## Mathematically Describing the Partition Curve

Corrected partition curves have a sigmoidal shape that can be represented using two-parameter

Figure 2 (A) Axial, (B) tangential and (C) radial velocity profiles in a hydrocyclone. (Reproduced with permission from Kelsall (1953).)

functions such as the exponential sum, the RosinRammler and the log-logistic expressions. The two parameters determine the cut size and the sharpness of separation, respectively. The fishhook partition curve can be modelled using the sum of a corrected partition curve and an inverted partition curve multiplied by a bypass fraction.

The observed partition curve gives a complete description of the selective separation of all sizes of solids entering a cyclone and can be used to predict

1 10 100 Particle size (nm)

1 10 100 Particle size (nm)

Figure 3 The observed (continuous line) and corrected (dashed line) partition curves of a hydrocyclone with a bypass of 20%.

the product size distribution and solids recovery for changes in feed size distribution. If the bypass is assumed to equal the water recovery, the liquid and volumetric balances can also be estimated.

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