STATISTICAL-THEORY OF SPOT OVERLAP IN 2-DIMENSIONAL SEPARATIONS

Equations are derived for the expected numbers of singlet, doublet, and triplet spots in a two-dimensional (2-D) separation bed, in which circular component zones are randomly distributed. The basis of these derivations is the selective interpretation of the radial distribution functions governing 2-D Poisson processes. The equations are sufficient to describe overlap in many 2-D separations and are shown to be adequate in describing the overlap of elliptical zones having aspect ratios less than 2. It is demonstrated that, per unit peak capacity, 2-D separations are considerably worse than their one-dimensional analogues. The equations are verified at low saturations by interpretation of several hundred computer simulations of spot distributions in rectangular beds. Departures of the equations from the simulations are observed at higher saturations. Caution is suggested in overinterpreting the quality of 2-D separations.