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

Abstract

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.

CFD analysis of the impact of physical parameters on evaporative cooling by a mist spray system

“…3a. The RosineRammler volume density distribution of the droplets can be calculated as follows [53,54]: Fig. 3b shows the results according to Eq.…”

Digital micro-mirror device-based detector for particle-sizing instruments via Fraunhofer diffraction

“…It was defined as the ratio of root-mean square error of the retrieved distribution to the original distribution [23] s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi…”

Mean Values, Moments, Moment Ratios and a Generalized Mean Value Theorem for Size Distributions

“…Probably the most important milestones in this field are Herdan's classical book on Small Particle Statistics [1], the German school of particle sizing [2][3][4] and Alderliesten's profound and authoritative treatment of mean particle diameters [5][6][7][8][9][10][11][12]. The latter has clearly emphasized the insufficiency of the German DIN 66141 [13] and European ISO 9276-2 [14] notation, which is based on the moment notation, and has proposed an alternative in the form of the so-called moment-ratio notation, which has been the basis of the British standard BS 2955 [15].…”