2023/12/18 by Xiaomeng Chen, Chen, Xiaomeng, Shuai Li +5
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Micro and Nano Robotics #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2312.11224
openalex publication_date 2023/12/18 · openalex created_date 2023/12/20 · openalex updated_date 2026/07/28
Suspensions of aerobic bacteria often develop flows from the interplay of chemotaxis and buoyancy, which is so-called the chemotaxis-Navier-Stokes flow. In 2004, Dombrowski et al. observed that Bacterial flow in a sessile drop related to those in the Boycott effect of sedimentation can carry bioconvective plumes, viewed from below through the bottom of a petri dish, and the horizontal "turbulence" white line near the top is the air-water-plastic contact line. In pendant drops such self-concentration occurs at the bottom. On scales much larger than a cell, concentrated regions exhibit transient, reconstituting, high-speed jets straddled by vortex streets. It's interesting to verify these turbulent phenomena mathematically. In this note, we investigate the Hausdorff dimension of these vortices (singular points) by considering partial regularity of weak solutions of the three dimensional chemotaxis-Navier-Stokes equations, and showed that the singular dimension is not larger than 1, which seems to be consistent with the linear singularity in the experiment.