PARTICLE MIXING


If particles are to be mixed, starting out from segregated groups and ending up with the components randomly distributed, the expected variances (s2) of the sample compositions from the mean sample composition can be calculated.
Consider a two-component mixture consisting of a fraction p of component P and a fraction q of component Q. In the unmixed state virtually all small samples taken will consist either of pure P or of pure Q. From the overall proportions, if a large number of samples are taken, it would be expected that a proportion p of the samples would contain pure component P. That is their deviation from the mean composition would be (1 - p), as the sample containing pure P has a fractional composition 1 of component P. Similarly, a proportion q of the samples would contain pure Q, that is, a fractional composition 0 in terms of component P and a deviation (0 - p) from the mean. Summing these in terms of fractional composition of component P and remembering that p + q = 1.



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