**Follow us on Twitter**** **

Question, remark ? Contact us at **admin@powderprocess.net**

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. This page is proposing an overview of what is the angle
of repose, why it is used and how it is calculated from
experimental measurement.

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 is sometimes confused with the
angle of internal friction used in Jenike's theory to design
hoppers and silos, but the 2 values are not necessarily equal.

**The determination of the angle of repose of a granular
material can only be done 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)

**Top
5 Most Popular **

1.
Pneumatic transport design guide

2. Ribbon
blenders

3. Powder mixing

4. Hoppers design guide

5. Measuring degree of
mixing

--------------

--------------

**Top 5 New **

1. Continuous Dry
Mixing

2. Mixing speed

3. Mixer cycle time
optimization

4.
Batch / continuous mixing comparison

5. Energy Savings

The main application of the angle of repose is to assess the flowability of a granular material (powder, pellets...).

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 |

**Table 1 : angle of repose table**

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.

The angle of repose is also important to calculate the volume of material in hoppers or in stockpiles (for example in large open air or warehouse stock piles, or even in cargo ship transport).