Mean Particle Diameters. Part VII. The Rosin-Rammler Size Distribution: Physical and Mathematical Properties and Relationships to Moment-Ratio Defined Mean Particle Diameters




The Rosin-Rammler particle size distribution is used for a broad range of applications. Physical and statistical properties of the Rosin-Rammler distribution and its parameters were investigated to evaluate their suitability in the particulate area. The Rosin-Rammler volume density distribution is identical to the Weibull density distribution describing material failure and fatigue phenomena. The physical meaning of the Rosin-Rammler location parameter depends on the value of its spread parameter. This makes the location parameter physically uninterpretable and less suitable for development of physical models. The distribution can still be used for, e.g., production control purposes. Rosin-Rammler distributions with spread parameter values less than three cannot exist. They can at most give a rough description of size distributions within the measured particle size range. They should not be expected to describe correctly the quantity of small particles outside the measured size range. Their parameters are unsuitable for model development aiming at estimating parameters explaining/predicting physical product or process parameters. Two data sets were used for validation. Mean particle diameters (Moment-Ratio notation) and the Rosin-Rammler parameters are mathematically related, but the relationship is not valid for mean parameter values of a set of size distributions. It is not possible to predict a type of mean particle diameter showing a behavior close to that of the Rosin-Rammler location parameter. For both data sets, the quality of the relationship of physical product property with proper mean particle diameter type is better than that with the Rosin Rammler location parameter. For process control applications a replacement of the Rosin-Rammler location parameter by a mean particle diameter (Moment-Ratio) should be considered. The type of mean particle diameter to be chosen depends on the values of the Rosin-Rammler spread parameter occurring in the process. Two steps in the migration path are identified.