Johnson's S_B distribution function as applied in the mathematical representation of particle size distributions. Part 1: Theoretical background and numerical simulation

An investigation was carried out of the transformation between the number, length, surface and volume size distributions expressed by Johnson's S_B distribution function – the bounded log‐normal distribution function. As is well known, if any of the number, length, surface and volume distributions is log‐normal, all the others will also be log‐normal. Theoretical analysis suggests that the S_B function may have a similar property. This was confirmed by a computer‐aided numerical simulation, in which emphasis was given to the transformation between successive order size distributions, i.e. ƒ_i(x) → ƒ_{i + 1}(x) or ƒ_i(x) → ƒ_{i − 1}(x). The numerical results can be applied to the particle size distribution transformation because this transformation can generally be made step by step, for example, ƒ_i → ƒ_i−1 (x) → ƒ_{i − 2}(x) → … → ƒ_j(x) for ƒ_i(x) → ƒ_j(x) ( i > j).