A correction to collision rates of droplets in turbulent flows

TL;DR

This paper revises the collision rate calculations for small droplets in turbulent flows by incorporating fluid rotation effects, leading to a corrected formula that accounts for both distortion and rotation.

Contribution

It introduces a correction to the classical collision rate formula by including fluid rotation effects, enhancing accuracy in turbulent flow modeling.

Findings

Collision rate correction factor is sqrt(2).

Fluid rotation significantly affects droplet collision dynamics.

Enhanced model aligns better with turbulent flow behaviors.

Abstract

This paper makes a correction to the collision rates of small droplets in turbulent fluid derived by Saffman and Turner(1956). Not only the distortion but also the rotation of the fluid is taken into account between two close droplets. A rotation reference is fixed on one drop, and the fluxes of the other drops moving towards the fixed one are carried out based on this new reference. The behaviors of turbulent flow are analyzed within the smallest eddies under the rotation reference, and a correction is made to the collision rates by multiplying a factor sqrt(2).