Collision fluctuations of lucky droplets with superdroplets

TL;DR

This paper evaluates the superdroplet algorithm's ability to accurately model fluctuations in droplet collision and growth processes, especially in dilute suspensions, confirming its effectiveness in representing stochastic coagulation driven by gravity.

Contribution

It demonstrates that the superdroplet algorithm accurately captures fluctuation effects in droplet growth due to gravity in dilute suspensions, validating its use for stochastic collision modeling.

Findings

Superdroplet algorithm accurately models fluctuations in droplet growth.

Both spatial distribution and Monte Carlo collision methods independently represent fluctuations well.

The algorithm faithfully captures the subtle increase in fluctuations from multiple lucky droplets.

Abstract

It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space ('lucky droplet model'). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.