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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 thanks to the reduced 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/m3)

ρ_{bulk} : the loose bulk density of the material (kg/m3)

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 1st 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 a full shear cell testing.