Size distribution of raindrops

To the Editor:

Villermaux and Bossa¹ (hereafter referred to as VB) presented a model to describe bag break-up of large drops (diameter d ≥ 6 mm), which yields a drop size distribution consistent with Marshall–Palmer's distribution for rainfall². Based on this result, and a laboratory demonstration of bag break-up, VB propose that the equilibrium drop size distribution of natural rainfall is the result of the spontaneous fragmentation of single large drops (d ≥ 6 mm), and that the contribution of drop–drop interactions such as coalescence and collisional break-up is negligible. This proposition is ill-founded. First, the equilibrium Marshall–Palmer distribution is not representative of the variability and transient nature of natural rainfall³. That the VB break-up model yields the Marshall–Palmer distribution is therefore not sufficient to establish that it is physically relevant. Second, field observations show that the number concentration of large drops (d ≥ 6 mm) if observed is extremely small^4,5. VB do not address the physics required to explain the population dynamics of such large drops consistent with the duration, intensity and microstructure of natural rainfall⁶. Third, the laboratory experiments reported by VB do not replicate the free-fall conditions of natural rainfall^7,8.

Whereas evidence of bag break-up is limited⁹, collisional disk break-up that results from the fragmentation of a large drop originated by the near head-on collision of two drops is well documented¹⁰. The transient shape of the large drop evolves to form a 'bag' after collision, and then a 'disk' before breaking to yield a large number of small drops. VB speculate that collisional break-up is unlikely. However, the mean free path for drop–drop collision is of the same order of magnitude as the average distance a drop has to fall before experiencing spontaneous break-up³. Furthermore, spontaneous break-up occurs only once for each (rare) large drop, whereas many interactions can occur among a wide size range of small drops in their downward trajectory. Indeed, surveys of laboratory experiments under free-fall conditions^7,8,9 indicate that collisional disk break-up is responsible for up to 20% of all break-up events^7,8 (other types of break-up being filament and sheet break-up^7,8,10), whereas none or singular observations of spontaneous break-up are reported. VB's thesis that single-drop fragmentation determines the size distribution of raindrops is in conflict with field and laboratory evidence reported so far.