Carr Compressibility Index

Ralph Carr published this in Chemical Engineering in 1965 as part of a broader set of powder-flow characterisations, and it is the same tapped-and-loose experiment as the Hausner ratio expressed as a percentage: $CI = 100(1 - \rho_b/\rho_t)$, the fraction of its loose volume the powder gives up when tapped.

The percentage form has one genuine advantage as a teaching number. It is literally the proportion of the loose bed that was air and got squeezed out — 20 per cent means a fifth of what you poured was void that tapping removed. Carr's own classification runs in five-point bands: under 10 excellent flow, 11 to 15 good, 16 to 20 fair, 21 to 25 passable, 26 to 31 poor, 32 to 37 very poor, and above 38 approximately no flow at all. Those bands were established for a much wider range of industrial powders than additive manufacturing deals with, which is worth knowing when a metal powder comes back at 13 per cent and someone treats it as a distinction: nearly all gas-atomised metal powders fit for a powder bed land in the good-to-excellent range, and the interesting variation is finer than Carr's bands can resolve.

Say it once more, because a reader given one index should never have to derive the other: this is the Hausner ratio in different clothes. $CI = 100(1 - 1/HR)$. A Hausner ratio of 1.1548 is a Carr index of 13.40 per cent, and those two statements contain exactly the same information about exactly the same cylinder of powder. The only reason to compute both is that different specifications ask for different forms.

The same limits apply as to its twin. It is a bulk cohesion test rather than a spreadability test; it says nothing about layer uniformity under a moving blade; and the tapping method has to be stated for the number to mean anything. There is a further wrinkle worth knowing for anyone reading powder certificates: the apparent density can be measured by Hall flowmeter, by Carney funnel or by Scott volumeter, and the three do not agree — the Carney funnel has a wider orifice precisely so that powders too cohesive to flow through a Hall funnel can be measured at all, and a powder that will not flow through a Hall funnel is telling you something important before any index is calculated.