The Logistic Function and Cyclone Fractional Efficiency

The relationship between fractional efficiency and particle size for a cyclone can be described using a logistic equation: efficiency = 1/(1 + (d ₅₀/d)^β. To use this equation, cyclone cut diameter, d ₅₀, and the logistic slope parameter, β, must be known. Although cyclone cut diameter can be predicted from equations previously published, no method has been available to predict β. Collection efficiency was measured for particles between 1.4 and 7.4 μm in diameter using pilot-scale apparatus to determine the dependence of d ₅₀ and β on cyclone dimensions and operating conditions. An equation for β was developed from a statistical analysis of these data. Although important questions remain concerning the extent to which the p equation can be generalized beyond the experimental conditions for which it was developed, predictions from this equation seem to allow better prediction of fractional efficiency for data presented here and taken from similar experiments in the literature than is found using the efficiency theories of Lapple (1950), Barth (1956), Leith-Licht (1972), or Dietz (1981).