The Carr index (also: Carr's index or Carr's Compressibility Index
[Podczeck, Fridun & Brian E. Jones, eds. 2007. ''Pharmaceutical Capsules''111.]) is an indicator of the
compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fl ...
of a
powder
A powder is a dry, bulk solid composed of many very fine particles that may flow freely when shaken or tilted. Powders are a special sub-class of granular materials, although the terms ''powder'' and ''granular'' are sometimes used to distin ...
. It is named after the scientist Ralph J. Carr, Jr.
The Carr index is calculated by the
formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwee ...
, where
is the freely settled
bulk density Bulk density, also called apparent density or volumetric density, is a property of powders, granules, and other "divided" solids, especially used in reference to mineral components (soil, gravel), chemical substances, (pharmaceutical) ingredients ...
of the powder, and
is the tapped bulk density of the powder after "tapping down". It can also be expressed as
.
The Carr index is frequently used in
pharmaceutics
Pharmaceutics is the discipline of pharmacy that deals with the process of turning a new chemical entity (NCE) or old drugs into a medication to be used safely and effectively by patients. It is also called the science of dosage form design. The ...
as an indication of the compressiblity of a powder. In a free-flowing powder, the bulk density and tapped density would be close in value, therefore, the Carr index would be small. On the other hand, in a poor-flowing powder where there are greater interparticle interactions, the difference between the bulk and tapped density observed would be greater, therefore, the Carr index would be larger. A Carr index greater than 25 is considered to be an indication of poor flowability, and below 15, of good flowability.
Another way to measure the flow of a powder is the
Hausner ratio The Hausner ratio is a number that is correlated to the flowability of a powder or granular material. It is named after the engineer Henry H. Hausner (1900–1995).
The Hausner ratio is calculated by the formula
::H=\frac
where \rho_B is the fre ...
, which can be expressed as
.
Both the Hausner ratio and the Carr index are sometimes criticized, despite their relationships to flowability being established
empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
ly, as not having a strong theoretical basis. Use of these measures persists, however, because the equipment required to perform the analysis is relatively cheap and the technique is easy to learn.
References
General Bibliography
Particulates
Pharmaceutics
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