Effect of gravitational settling on the collisions of small inertial particles with a sphere

TL;DR

This paper investigates how gravity-induced settling influences collision rates of small inertial particles with a sphere, revealing critical Stokes numbers and complex flow effects that alter collision efficiencies.

Contribution

It introduces a detailed analysis of gravitational effects on particle-sphere collisions, identifying new critical Stokes numbers and flow mechanisms affecting collision outcomes.

Findings

Sedimentation alters the critical Stokes number for collisions.

Existence of a secondary critical Stokes number where collisions cease.

Flow disturbances can cause collision efficiencies exceeding unity.

Abstract

The rate at which small inertial particles collide with a moderate-Reynolds-number spherical body is found to be strongly affected when the formers are also settling under the effect of gravity. The sedimentation of small particles indeed changes the critical Stokes number above which collisions occur. This is explained by the presence of a shielding effect caused by the unstable manifolds of a stagnation-saddle point of an effective velocity field perceived by the small particles. It is also found that there exists a secondary critical Stokes number above which no collisions occur. This is due to the fact that large-Stokes number particles settle faster, making it more difficult for the larger one to catch them up. Still, in this regime, the flow disturbances create a complicated particle distribution in the wake of the collector, sometimes allowing for collisions from the back. This can lead to collision efficiencies higher than unity at large values of the Froude number.