Novel approach to estimate quality of binary random powder mixtures: samples of constant volume. I: Derivation of equation.

An equation of the quality of binary random mixtures that applies to powder samples of constant bulk volume was derived from the binomial distribution. In contrast to the Stange-Poole equation for samples of constant mass, this approach can also be used for constituents with large differences in particle size and in bulk density. The validity of this equation was verified with tablets directly compressed from mixtures composed of equal mass proportions of sucrose [volume-weighted/volume-number mean diameter (dv), 504 microns] as the coarse ingredient (A) and of a microcrystalline cellulose (Avicel PH 101)-talc mixture (dv, 60 microns) as the fine constituent (B). Because of the difference in the bulk densities of A and B, the equation estimated a coefficient of the random content variation, which for A was double that for B. The content variations found with the tablets were in excellent agreement with the calculated values and reflected the differences predicted from theory. The Stange-Poole equation yielded identical values of the content variations of A and B, which is in contrast to the experimental results.