2012/07/06 by Andrej Vilfan
Engineering · Mathematics · Physics and Astronomy · #Biology #Cilium #Classical mechanics #Flow (mathematics) #Inclined plane #Mathematical analysis #Mathematics #Mechanics #Micro and Nano Robotics #Microfluidic and Bio-sensing Technologies #Multipole expansion #Physics #Planetary Science and Exploration #Quadratic growth #Reynolds number #Turbulence #physics.bio-ph #physics.flu-dyn
paper · pdf · doi:10.1140/epje/i2012-12072-3
published as Eur. Phys. J. E 35 (2012) 72 · 12 pages, 6 figures, to appear in EPJ E
arxiv created 2012/07/06 · openalex publication_date 2012/08/01 · arxiv updated 2012/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.