An improvement on the power law for the description of particle size distributions in potable water treatment

In potable water treatment, the use of the power law to describe particle size distributions (PSDs) in particle counting practice is common. The power law is popular because it allows the reduction of numerous data bits to two meaningful parameters that completely describe the size distribution characteristics of a particle suspension. The model is however flawed. This paper presents the further development of an improved model (the variable-β model) first proposed by Lawler (1997). Both the power law model and variable-β model are used to describe the PSDs of a large number of potable water treatment samples taken from full-scale plants and the resulting correlations are compared. The findings from the comparison of data reduction methodologies support the argument that the variable-β model is fundamentally more correct than the power law model and consequently describes the PSDs better.