On the products of lognormal and cumulative lognormal particle size distributions

Abstract

The output distributions of particle size which would result when an input aerosol having a lognormal size distribution is passed through a size classifier (e.g. impactor) or control device (e.g. cyclone) having a cumulative lognormal penetration function are investigated theoretically. A computer program is presented for determining these (output) product distributions, their geometric mean sizes ( a′ 8 ), and geometric standard deviations (GSD'). The program was used for forty-five cases having different input aerosol size distributions and different functions of penetration vs particle size. These results are tabulated and used to form regression equations to facilitate predicting a′ 8 and GSD' for conditions not tabulated. The output geometric mean size ( a′ 8 ) is always smaller than the input ( a′ 8 ) and was highly correlated with it. The output aerosol geometric standard deviation (GSD') was also highly correlated with the input aerosol GSD and was never larger. Although the product size distributions are not lognormal, they are approximately so in many instances.