Strong Alignment of Micro-rotation and Vorticity in 3D Micropolar Flows

TL;DR

This paper proves that in 3D micropolar flows, rigid particles' angular velocity and fluid vorticity become strongly aligned over time, with estimates on how quickly this alignment occurs.

Contribution

The work provides the first rigorous proof of the strong alignment between particle angular velocity and vorticity in micropolar fluids, including decay rate estimates.

Findings

Particles' angular velocity and vorticity align over time.

Decay estimates for the difference between angular velocity and vorticity.

Quantitative measures of the alignment rate.

Abstract

Rigid particles suspended on a micropolar fluid provide microstructure that coexists and interacts with the local rotation of the fluid given by the vorticity. In this work we prove that the particles' angular velocity and the vorticity strongly align for large times. We provide average and supnorm estimates for the decay rate of the difference between these two vectors, which measures the alignment.