Binomial expansion, relation

It can be shown that the distribution ratio D of a solute in a CCD process is related to the concentration in the various separatory funnels or stages by the binomial expansion... 

There is a very important difference, however. Notice, particularly, that the width of the three bands in any of the three figures is independent of the D values. You see, in using the binomial expansion to represent the results of a multistage separation process, only the role played by equilibrium considerations was considered. To obtain results that match experimental reality, however, this must be amended to include the effects of diffiision and other related nonequilibrium processes. This will be dealt with in the next section, which concerns chromatography. 

A more general prediction for the intensities of the multiplets can also be made. They are related to the coefficients of the binomial expansion (a -h h)". These can be easily deduced from the Pascal triangle, where each coefficient is the sum of the two terms above it. 

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