A Comparison Study to Determine the Mean of Particle Size Distribution for Truthful Characterization of Environmental Data (part 1)

One of the most important steps in environmental studies is to get an accurate distribution of the pollutants in terms of its quantity and qualities. Some environmental studies are acquiring a good classification of the particle size including the average mean of the particle. Many researchers use the median size (x50) or until the size passing 80% cumulative undersize (x80) as a measure for evaluation of the particle size distribution resulted from different mineral processing operations such as crushing, grinding, classification, sedimentation, and/or solid-liquid separation or even during the study of the pollutant settlement. These measures are not so accurate to differentiate between different particle size distributions (PSDs) because many PSDs data sets may have the same values of x50 or x80 if these data sets are represented between the particle size, x and the cumulative undersize distribution, F (x). This paper is a trial to introduce a new methodology to determine the mean of a particle size distribution (MPSD) accurately using GatesGaudin-Schuhmann and Rosin-Rammler models. The value of this measure takes into consideration all particle sizes and their corresponding distributions. The results showed that the different PSD, which have the same values of median (x50) have different values of this measure, especially with Rosin-Rammler model. In this paper, the expressions of different types of means of a particle size distribution (arithmetic, quadratic, cubic, geometric, and harmonic) were derived mathematically using the two mentioned models. It is recommended to select RR model to be applied in estimation of the different means of a particle size distribution because it fits the available data better than the GGS model, as well as, it determines the correct values and exerts the actual differences between the different means of different particle size distribution data sets. This work will be continuing by demonstrating a case study using real environmental data in Part (2).