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Single-drop fragmentation determines size distribution of raindrops


Like many natural objects, raindrops are distributed in size. By extension of what is known to occur inside the clouds, where small droplets grow by accretion of vapour and coalescence, raindrops in the falling rain at the ground level are believed to result from a complex mutual interaction with their neighbours. We show that the raindrops’ polydispersity, generically represented according to Marshall–Palmer’s law (1948), is quantitatively understood from the fragmentation products of non-interacting, isolated drops. Both the shape of the drops’ size distribution, and its parameters are related from first principles to the dynamics of a single drop deforming as it falls in air, ultimately breaking into a dispersion of smaller fragments containing the whole spectrum of sizes observed in rain. The topological change from a big drop into smaller stable fragments—the raindrops—is accomplished within a timescale much shorter than the typical collision time between the drops.

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Figure 1: Raindrops collected at the ground level, and their size distribution.
Figure 2: Topological changes of falling drops and fragmentation.
Figure 3: Bag inflation.
Figure 4: Distribution of single-drop fragments.


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This work has been supported by the Office National d’Études et Recherches Aérospatiales (ONERA) under contract F/20215/DAT-PPUJ and Agence Nationale de la Recherche (ANR) through grant ANR-05-BLAN-0222-01.

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E.V. designed and carried out the experiments, analysed the data and wrote the paper; B.B. helped in the experiments and image processing.

Corresponding author

Correspondence to Emmanuel Villermaux.

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Villermaux, E., Bossa, B. Single-drop fragmentation determines size distribution of raindrops. Nature Phys 5, 697–702 (2009).

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