# Flowability of powders: an open issue

##### Powder flowability

There are many techniques to determine the flowability of powders. The propensity of powders to flow under a given consolidation state affects a large number of industrial applications.

However a single, reliable and widely applicable flowability test does not exist. The large variety of granular materials, the influence of handling on the measurements results, the different consolidation states which the material can be subjected to, make impossible to use a universal characterization method.

##### Bulk density ratios

Among the tests working with the material subjected to relatively low consolidation stress, there are those based on bulk density ratios.

In particular when a state of loose packing (obtained by simple pouring of the powder) is compared to a reference state of high packing (obtained by tapping the sample after pouring) the ratio is called Hausner ratio, HR:

Initially developed for metallic powders HR is nowadays used for several different powders. Different combinations of the same two bulk densities are possible creating additional but equivalent indexes. They are the compressibility, Co, (mainly used in pharmaceutics) and Carr’s index, CI:

Sometimes the HR is calculated using the aerated density, instead of the poured one, so attention has to be payed on the exact definition of the ratio. Aerated density can be obtained by packing the powder after fluidization or through a pluviation process (i.e. dispersing the powder through a screen).

We propose an alternative index, the packing ratio, PR, defined as:

where the aerated density appears instead of the the tap density. In this case areated density is measured with a pluviation process allowing the particles to reach their terminal free-fall velocity.

##### Advantages of the new index

This index has demonstrated to be more sensitive to variation in powder flowability than the HR [1]. Resolution of HR is somehow limited since it is able to classify powders in just three flowability groups. This evidence is clear from Figure 1a where HR is measured for a set of powders having different flowability with the static angle of repose, αS ranging from 15° to 80°. For free-flowing powder (angle of repose, αS <45°), HR never departs from values around 1-1.25 and do not distinguish between different powders having a variation of αS from 15° to 45°. The same occurs for cohesive powders with αS ranging from 60° to 80° since HR remains constant around 1.6-1.7.

To improve the limited resolution of HR we  therefore suggest to replace the tap density with the aerated density where the pluviation procedure allows the particles to pack spontaneously according to their mobility. Figure 1b shows that the PR has indeed a much larger resolution than HR for free flowing and cohesive powders. however we observe also that the resolution is smaller for fairly free-flowing powders.

##### An open issue

It is clear that our alternative index is very promising, however it is also evident that further studies are needed to fully clarify the behavior of PR and the differences between the two indexes. Further experimental and numerical studies are going to be undertaken.