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Section summary |
---|

1. Powder
flowability characterization : Carr Index and Hausner
Ratio |

2. Calculation
formula of Carr Index |

3. Calculation
formula of the Hausner Ratio |

4. Interpretation and relation to
flowability of Carr index and Hausner Ratio |

**The Carr Index and the Hausner Ratio are both meant as being
indicators of the flowability of bulk solids.** The
flowability of solids is **complex** and linked to many
parameters, it is thus not always obvious to characterize
the solid flowability with the few set of data that Engineers
usually have in hand during design or troubleshooting.

Both Carr and Hausner attempted just that : assuming that the
compressibility of a solid is related to its flowability, they
proposed to measure the bulk and
tapped density of bulk materials and **calculate a ratio**
in order to estimate how the material will flow.

**The lower the Carr Index or Hausner Ratio, the more flowable
is a material.**

The Carr Index of a material is calculated with the following formula :

**Carr_Index = (ρ _{tapped}-ρ_{bulk})/ρ_{tapped}*100**

With

ρ_{tapped} : the tapped
bulk density of the material (kg/m^{3})

ρ_{bulk} : the loose bulk
density of the material (kg/m^{3})

It is possible to relate the Carr Index and the Hausner ratio with the following formula :

H = 100/(100-Carr_Index)

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The Hausner Ratio of a material is calculated with the following formula :

**H = ρ _{tapped}/ρ_{bulk}**

With

H : Hausner Ratioρ

ρ

The flowability of a bulk
solids is estimated by 1^{st} calculating the ratio,
then referring to the table below to determine in which class is
the powder studied :

Flowability expected |
Hausner Ratio |
Carr Index |

Excellent / Very Free Flow | 1.00 - 1.11 | <10 |

Good / Free Flow | 1.12 - 1.18 | 11-15 |

Fair | 1.19 - 1.25 | 16-20 |

Passable | 1.26 - 1.34 | 21-25 |

Poor Flow / Cohesive | 1.35 - 1.45 | 26-31 |

Very Poor Flow / Very Cohesive | 1.46 - 1.59 | 32-37 |

Approximatively no flow | > 1.60 | > 38 |

The table was determined by the authors of the method, by testing different material flowability, and calculating the compressibility ratio associated.

**Note that Carr Index and Hausner Ratio are approximate
methods,** the characterization of the flowability and the
determination of physical parameters allowing the design of
hoppers would require more measurement using powder
rheometers or full shear
cell testing.

An Engineer wishes to have an idea of the probable flowability of
a powder. He measures the bulk loose density as 600 kg/m^{3}
and the tapped density as 660 kg/m3. He can then calculate the
Carr Index :

Carr_Index = (ρ_{tapped}-ρ_{bulk})/ρ_{tapped}*100
= (660-600)/660*100 = 9.1

**Refering to the table above, the Engineer concludes the powder
is probably free flowing.
**

With the data above, the Engineer also wishes to define the Hausner ratio, he then makes the following calculation :

H = ρ_{tapped}/ρ_{bulk }= 660/600 = 1.1

The table above is also used, the powder is indeed probably free
flowing.