A study of particle size distributions

The properties of a size distribution of particulate materials are systematically discussed. In order to avoid possible conceptual problems and difficulty in dealing with a distribution, some boundary conditions are given, based on which the limitations of the distribution functions in the literature are discussed. A search for an alternative to these functions is made. Johnson's S_B function is suggested to be the function that can represent all the unimodal size distributions of particles. Its applicability is proved from the theory of distributions in statistics. It is shown that the normal, log-normal, Rosin-Rammler and even the modified beta distributions can be satisfactorily fitted by the S_B function. The conversion of some commonly used two-parameter distribution functions into the S_B function is presented, which can be used as a general guide in practice. The methods of fitting curves with special reference to their uses in powder technology are also discussed.