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

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.