Direct interception or inertial impaction? A theoretical derivation of the efficiency power law for a simple and practical definition of capture modes

TL;DR

This paper derives a theoretical power law for particle capture efficiency around a cylinder, distinguishing between direct interception and inertial impaction based on particle size and boundary layer thickness.

Contribution

It provides a simple, practical criterion to identify dominant capture modes, resolving existing controversies in capture efficiency scaling.

Findings

Captured particles follow the power law and are smaller than the boundary layer, undergoing direct interception.

Particles diverging from the power law are larger and experience inertial impaction.

A size-boundary layer comparison accurately predicts the dominant capture mode.

Abstract

We study the capture of particles advected by flows around a fixed cylinder. We derive theoretically the power law of the capture efficiency, usually obtained from data fitting only. Simulations of particle trajectories reveal that captured particles following the power law are smaller than the boundary layer of the cylinder and experience direct interception, whereas the ones diverging from it are larger and observe inertial impaction. We show that a simple comparison between the particle size and boundary layer thickness splits accurately numerical results into their dominant capture mode. This criterion is practical in experiments and simulations, and would lift the controversy on the scaling of the capture efficiency.