Bulk density will decrease, as the size of the voids will increase with increasing particle size.
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In the case of equal sized spherical particles packed on a cubic grid, the bulk density is independent of particle size (neglecting boundary effects).
e.g. 1 sphere in a 1 x 1 x 1 cubic container: volume of sphere (= bulk density) ≈ 0.524
For 8 spheres, volume per sphere x 8 ≈ 0.524
The same goes for 27, 64, 125 etc.
The more variation in particle size there is for a given sample, the higher the bulk density will be, as the smaller particles will tend to fill in the interstices between the larger ones.
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