Contents

## Objectives

After completing this lesson students should be able to:

- Demonstrate understanding of various method involved in measuring particle size.
- Explain the importance of particle size analysis and its application.
- Differentiate between the different models used for predicting particle size.
- Explain the different convention followed in measuring particle size.

## Reading & Lecture

### Mineral Particle Sizes

- Particles within a given process stream vary in size and shape.
- Quantifying the amount of material within a given size fraction is often important for design and operational considerations.
- Particles that are either spherical or cubical are relatively easy to characterize.
- However, the majority of particles are often neither of these two shape types.
- Particle size characterization can be determined by:
- Microscopic Analysis
- Sieving
- Sedimentation (Stokes Diameter)
- Optical (Laser deflection or reflection)

### Mean Particle Sizes

- The mean particle size of a distribution is typically measured by either the arithmetic or geometric mean of the maximum (dmax) and minimum (dmin) particle sizes.
- The arithmetic mean is most accurate for symmetric particles such as spheres or cubes.

- The geometric mean is typically preferred when segregation of the particles into various fraction were achieved by passing particles through an opening having a given shape and area, e.g., screening.

N = number of particles or size fractions

### Particle Size Analysis

Sieve Opening Size (mm) | Mean Particle Size (mm) | Weight (#) | Cumul. % Retained | Cumul. % Finer | |
---|---|---|---|---|---|

Passed | Retained | ||||

(1*2^{.5}) | 1.0 | 1.19 | 5.0 | 5.0 | 100.0 |

1.0 | 0.6 | 0.77 | 10.0 | 15.0 | 95.0 |

0.6 | 0.3 | 0.42 | 25.0 | 40.0 | 85.0 |

0.3 | 0.15 | 0.21 | 40.0 | 80.0 | 60.0 |

0.15 | pan | 0.01 | 20.0 | 100.0 | 20.0 |

Total | 100.00 |

- The top size was estimated to be the square root of two times the top sieve size or 1.4mm.
- There is 5% retained on the 1mm screen.
- If the total feed was directed to the 0.3mm screen, 40% of the feed would be retained on the screen.
- 95% of the feed is finer than 1mm and 20% is finer than 0.15mm.
- The mean size of the material passing the 0.15mm screen can be estimated assuming the bottom size is 1 micron.

### Particle Sizes Distribution Models

- There is a common need to determine the amount of material in the feed at a given particle size.
- The desired particle size may not have been included in the original particle size analysis.
- The two common models used include:

- Gates-Gaudin-Schuhmann Model (GGS)
- Rosin-Rammler Model (RR)

- The RR model is typically satisfactory for coarse distributions.
- The GGS model is generally considered more precise for fine particle size distributions.
- It may be needed to perform model fits over more than 2 particle size rangers.

#### Gates-Gaudin-Schumann Model

The GGS model predicts the cumulative percent passing distribution:Y= cumulative percent passing

x= particle size

k= size parameter

m =distribution parameter

The values of k and m can be determined by linear regression:

log y = *m* log x + k

#### Rosin-Rammler Model (RR)

- The Rosin-Rammler model is typically used to predict the % retained.
- The modified equation to predict the % finer is:

R= size parameter

b= distribution parameter

- There is special graph paper available to help determine the correct values of R and b over any size range.

### Volume Mean Diameter

The mean particle size by volume is important when dealing with topics such as material transport, storage and hindered particle settling velocities.

The volume mean diameter, , can be quantified by:

Where is the mass within size fraction *i*.

Mean Size Fraction Diameter (mm) | d_{p}^{3} | Mass, M_{i} (%) | M_{i}/d^{3} |
---|---|---|---|

0.8 | 0.512 | 10 | 19.53 |

0.6 | 0.216 | 40 | 185.19 |

0.3 | 0.027 | 30 | 1111.11 |

0.125 | 0.002 | 20 | 10000 |

Total | 100 | 11315.83 |

### Surface Mean Diameter

- The surface mean diameter is important when considering surface coatings with chemicals, particle agglomeration and dewatering.
- The volume mean diameter, d
_{s }, can be quantified by:

where M_{i}is the mass within the size fraction*i*.

Mean Size Fraction Diameter (mm) | Mass, M_{i} (%) |
|||
---|---|---|---|---|

0.8 | 0.512 | 10 | 20 | 13 |

0.6 | 0.216 | 40 | 185 | 67 |

0.3 | 0.027 | 30 | 1111 | 100 |

0.125 | 0.002 | 20 | 10000 | 160 |

Total | 100 | 11315 | 340 |