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Particle void fraction

Q: If I use the same material to fill a box with only large or only small particles, which box will weigh more?

A: In a theoretical world, the boxes would have identical weights. However, in practice, the void fraction of the large particles may be different than the small particles and the particles may have different surface characteristics. Also, the individual particle density of the small particles may be different that the large particles due to changes in composition or internal voids. For any particulate solid (as opposed to a bulk solid, like a block of steel), there are three densities to consider: true, individual particle and bulk. Also, bulk density may be a packed or loose density depending on how much pressure is applied, and how that pressure is applied. I'll ignore that difference in this explanation.

The true density is a function of the composition of the solid that makes up the particle. As an example aluminum has a density of 168 lbs/ft³. If you melt the aluminum and spray it into spheres of 100 micron that do not contain any gas, the density of the particles would be 168 lbs/ft³. However, it is usually not possible to exclude voids in a sprayed material and the density of the individual particle would be lower, maybe 150 lbs/ft³ (we need to use a special instrument to measure this individual particle density). Also, the lower density particles may no longer be perfect spheres, which would change how the particles would pack in a container. If these individual particles were put into a box that was large enough to eliminate edge effects of the particles as they packed into the box, the bulk density would go down depending on the fluid around the particles. If the fluid is air at STP and the particles pack to give a void fraction of 50%, the bulk density would be approximately 75 lbs/ft³ since the air has little weight. If the fluid were water, the bulk density would be 106 lbs/ft³. If the particles were of different sizes, but the individual densities, shape and surface characteristics were identical, the void fraction would be the same and the bulk density would be the same as the large particles. Note that this analysis only applies to particle of one size (not a distribution of particle sizes — the real world).

Again, in practice, the void fraction can vary with the average particle size due to the particle size distribution. It is common for the void fraction to decrease as finer particles fill in the voids of larger particles. Thus the bulk density goes up as the average size decreases. Also, finer particles may be more spherical and pack better, which will increase bulk density. However, finer particles may defluidize slow and develop electrical charges on the surface. This will result in a lower bulk density than a mixture of larger particles.

In theory, there is no difference between theory and practice. In practice, however, there is!

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See the data below:

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Chemical formula: Na₂SO₄

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