Bifurcations in droplet collisions

TL;DR

This paper investigates how droplet collision rates in turbulence depend on strain rate and settling speed, revealing complex bifurcation phenomena that influence collision dynamics and clustering.

Contribution

It introduces a bifurcation analysis of droplet collision dynamics, explaining non-monotonic collision rates and clustering effects in turbulent flows.

Findings

Collision rate remains non-zero as Kn a0 0, contrary to previous assumptions.

Non-monotonic collision rate dependence explained by grazing bifurcation.

Spatial clustering occurs near saddle points where strain and settling effects cancel.

Abstract

Saffman and Turner (1957) argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. But the numerical simulations of Dhanasekaran et al. (2021) in a steady straining flow show that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity, and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains non-zero in the limit Kn $\to0$, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a non-dimensional measure of the mean free path of air). Second, the non-monotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called "closed trajectories" appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel