Description of Two‐dimensional Distributions of Particle Size and Particle Velocity of a flowing discontinuous phase by means of special mathematical functions

As potential approximation functions for measured two‐dimensional distributions, the two‐dimensional normal distribution and the two‐dimensional log‐normal distribution are presented, in addition to mixed forms in which one of the two variables is linearly and the other logarithmically normally distributed. For all four distribution functions, regression curves are calculated, with x being understood as independent and y as dependent variable. The general concept is applied to the specific case of a two‐dimensional distribution of particle size x and particle velocity y . In this context, a number of particularities result from the fact that a distinction has to be made between concentration‐dependent and flux‐dependent measurement.