2010/07/31 by Zhi Lin, Jean‐Luc Thiffeault, Jean-Luc Thiffeault +1 · 3 citations
Engineering · Physics and Astronomy · #Lattice Boltzmann Simulation Studies #Micro and Nano Robotics #Particle Dynamics in Fluid Flows #cond-mat.soft #physics.bio-ph #physics.flu-dyn
paper · pdf · doi:10.1017/s002211201000563x
published as Journal of Fluid Mechanics 669, 167-177, 2011 · 10 pages, 12 figures. PDFLaTeX with JFM style (included). Accepted for publication in Journal of Fluid Mechanics
arxiv created 2010/10/20 · openalex publication_date 2011/02/01 · arxiv updated 2013/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse a simple ‘Stokesian squirmer’ model for the enhanced mixing due to swimming micro-organisms. The model is based on a calculation of Thiffeault & Childress ( Phys. Lett. A, vol. 374, 2010, p. 3487), where fluid particle displacements due to inviscid swimmers are added to produce an effective diffusivity. Here we show that, for the viscous case, the swimmers cannot be assumed to swim an infinite distance, even though their total mass displacement is finite. Instead, the largest contributions to particle displacement, and hence to mixing, arise from random changes of direction of swimming and are dominated by the far-field stresslet term in our simple model. We validate the results by numerical simulation. We also calculate non-zero Reynolds number corrections to the effective diffusivity. Finally, we show that displacements due to randomly swimming squirmers exhibit probability distribution functions with exponential tails and a short-time superdiffusive regime, as found previously by several authors. In our case, the exponential tails are due to ‘sticking’ near the stagnation points on the squirmer's surface.