Generic flow profiles induced by a beating cilium

Abstract

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.

12 pages, 6 figures, to appear in EPJ E

References in corpus (13)

• The hydrodynamics of swimming microorganisms
• Direct measurement of the flow field around swimming microorganisms
• Life around the scallop theorem
• Enhanced diffusion due to active swimmers at a solid surface
• Hydrodynamic flow patterns and synchronization of beating cilia
• Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia
• Finding the ciliary beating pattern with optimal efficiency
• Generic Conditions for Hydrodynamic Synchronization
• Generic theory of colloidal transport
• Fluid transport at low Reynolds number with magnetically actuated artificial cilia
• A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
• Collective beating of artificial microcilia
• Synchronization in A Carpet of Hydrodynamically Coupled Rotors with Random Intrinsic Frequency

Cited by in corpus (4)

• Nonreciprocal interactions give rise to fast cilium synchronisation in finite systems
• Magnetically powered metachronal waves induce locomotion in self-assemblies
• Metachronal waves in the flagellar beating of $Volvox$ and their hydrodynamic origin
• Asymptotic limits of the axisymmetric solution of the Brinkman equation for a point force near a no-slip wall