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Section summary |
---|

1. Powder
flowability characterization : angle of repose |

2. Calculation
formula of the angle of repose |

3. Interpretation
and relation to flowability of angle of repose |

**The angle of repose is used an indicator of the flowability of
bulk solids such as powders or granulates.** It is a quick
method that allows to get an idea of the flowability of granular
materials.

It's actually important to highlight that **there are different
angles of repose, depending on the methodology** that has been
used to measure it. The most common method is to have the material
poured freely through a funnel, the material forming a heap. But
it is also possible to measure an angle by sliding the material on
a plate, using a revolving cylinder, or leaving the powder flow
out of a smaller container through a hole.

**Figure 1 : Different methods for
measuring the angle of repose of powders and granulates**

Those different methods are actually giving different values of
the angle of repose. **It is thus very important to know
according to which protocol the angle of repose has been
measured in order to be able to compare the flowability of
materials.** The funnel method (external funnel) is giving the
lowest measure of the angle of repose :

External funnel method angle | < Internal funnel method angle | < Sliding method angle |

**The lower the angle of repose, the more flowable is a
material.**

**The angle of repose of a material can only be measured through
an actual experience.** The methodology considered here is the
most common, the external funnel method, done by pouring a certain
quantity of solid from a funnel and measuring the angle of the
heap of material formed.

To be noted that even for this funnel method, there are also some variations in methodology. For example, the funnel can be fixed or can be slowly moved up. A specified height of the heap can be the parameter to stop the experience, or it can be the diameter of the heap formed.

If the angle of repose method is used within a lab to characterize the flowability of different components, it is important to chose one protocol and keep it for all measurement.

The formula to calculate the angle of repose is the following :

**Angle_of_repose = arctan(h/r)**

With

h_{} : height of the heap (mm)

r : radius of the heap (mm)

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

Flowability expected |
Angle of repose |

Excellent / Very Free Flow | 25-30 |

Good / Free Flow | 31-35 |

Fair (discharging aid may not be required) | 36-40 |

Passable | 41-45 |

Poor Flow / Cohesive (active discharging aid required) | 46-55 |

Very Poor Flow / Very Cohesive | 56-65 |

Approximatively no flow | > 66 |

The table was determined by the authors of the method, by testing different material flowability, and measuring the corresponding angle of repose.

**Note that it is an approximate method giving trends**, it
can happen that a material behave differently once in the process.
The characterization of the
flowability and the determination of physical parameters
allowing the design of hoppers would require a full shear cell
testing.