Statistical Approach of Mixing Processes

In the mixing of particulate solid materials the probability of getting an orderly arrangement of particles, which would represent the perfect mixing, is virtually zero. In practical systems the best mixture attainable is that in which there is a random distribution of the ingredients. An ideal random distribution of two solid components in equal proportions would resemble a chess board, that is, white and black squares in a perfect alternate pattern. In practice, however, a perfectly random mixture is commonly defined as one in which the probability of finding a particle of a constituent of the mixture 

2 Blending Quality Mixing Indexes and Mixing Rate 

The degree of uniformity of a mixed product may be measured by analysis of a number of spot samples. Powder mixers act on two or more separate materials to intermingle them. Once a material is randomly distributed through another, mixing may be considered to be complete. Based on these concepts, the well-known statistical parameters mean and standard deviation of component concentration can be used to characterize the state of a mixture. If spot samples are taken at random from a mixture and analyzed, the standard deviation of the analyses s about the average value of the fraction of a specific powder x is estimated by the following relation  

The standard deviation value on its own may be meaningless, unless it can be checked against limiting values of either complete segregation Sq, or complete randomization s,. The minimum standard deviation attainable with 

The numerator on Equahon 6.2 would be an indicator of how much mixing has occurred, while the denominator would show how much mixing can occur. In practice, however, the values of s, even for a very poor mixture, lie much closer to s, than to Sq. Poole et al. (1964) suggested an alternative mixing index, that is. 

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