We are searching for a mathematical correlation for the droplets size distribution of liquid when atomized by air blast.
There are a bunch of models that are used. For example: normal, log-normal, Rosin-Rammler-Sperling-Bennett (RRSB), Nukiyama-Tanasawa distributions. The last 2 are often quoted and you'll see them in the literature from the 1930's to 1950's or 60's. In particular, I am personally skeptical of using RRSB as this involves a log-log approach which constricts the middle part of the distribution. Taking logarithms 5 times (the RRRSB approach where the first R is 'Rawle') will compress the data even further and almost anything can be fitted to such a model. All the above are empirical models, the emphasis being on the word 'model'. However, the data are the data and may not be constrained by a theoretical model.
However, nothing is better than actually measuring the droplet size distribution and using a model-independent approach. This is the modern route and most light scattering measurements process the scattering data in this manner.
You may find useful to check also the following RG discussion: https://www.researchgate.net/post/Is_there_a_way_I_can_estimate_the_droplet_size_distribution_or_mean_size_of_gas_liquid_flowing_in_a_pipe
You should start to read the literature:
ATOMISERS have been in use for almost a century
See for instance the manual of the TSI-atomiser 3076
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