# Particle flows around an intruder

## TL;DR

This study numerically investigates particle flows around an intruder, revealing a transition in drag force laws from Epstein's to Newton's and Stokes' laws, and identifies turbulent-like behavior at high speeds and large intruder sizes.

## Contribution

It demonstrates the crossover of drag laws depending on flow speed and intruder size, and analyzes turbulent-like flow behavior behind the intruder.

## Key findings

- Crossover from Epstein's to Newton's law based on speed ratio.
- Transition from Epstein's to Stokes' law in low-speed regime.
- Detection of turbulent-like flow behind the intruder at high speeds.

## Abstract

Particle flows injected as beams and scattered by an intruder are numerically studied. We find a crossover of the drag force from Epstein's law to Newton's law, depending on the ratio of the speed to the thermal speed. These laws can be reproduced by a simple analysis of a collision model between the intruder and particle flows. The crossover from Epstein's law to Stokes' law is also found for the low-speed regime as the time evolution of the drag force caused by beam particles. We also show the existence of turbulent-like behavior of the particle flows behind the intruder with the aid of the second invariant of the velocity gradient tensor and the relative mean square displacement for the high-speed regime and a large intruder.