# DROP SIZE DISTRIBUTIONS IN LIQUID SPRAYS

**Tuomas Paloposki**

## Abstract

A comparative study was carried out on the applicability of various distribution functions to describe drop size distributions in sprays. Six different distribution functions were compared; they were the upper-limit, log-normal, Nukiyama-Tanasawa, Rosm-Rammler, log-hyperbolic and three-parameter log-hyperbolic distribution functions. The comparison was based on experimental data consisting of twenty-two data sets from seven different experimental studies. The x^{2}statistical test was employed as a criterion for the goodness-of-fit.

It was found that the best fit to the experimental data was provided by the Nukiyama-Tanasawa and log-hyperbolic distribution functions. The upper-limit and log-normal distribution functions were reasonable but clearly inferior to the Nukiyama-Tanasawa and log-hyperbolic distribution functions. The Rosin-Rammler and three-parameter log-hyperbolic distribution functions did poorly in this study.

The Nukiyama-Tanasawa and log-hyperbolic distribution functions are mathematically rather complex and problems occurred in the determination of the best-fit values of the parameters. The log-normal distribution function is particularly simple and easy to use and can perhaps be used in applications where the accuracy requirements are less stringent.

It is not clear why the Nukiyama-Tanasawa and log-hyperbolic distribution functions were the best. Further work is needed to develop drop size distribution functions based on theoretical understanding of the break-up of bulk liquid into drops.

Some problems were encountered when the x^{2} test was applied to experimental drop size distribution data and the interpretation of the test results is therefore difficult. A more advanced statistical theory would be rather useful.