A Minimal Model of the Hydrodynamical Coupling of Flagella on a Spherical Body with application to Volvox

Abstract

Flagella are hair-like appendages attached to microorganisms that allow the organisms to traverse their fluid environment. The algae Volvox are spherical swimmers with thousands of individual flagella on their surface and their coordination is not fully understood. In this work, a previously developed minimal model of flagella synchronization is extended to the outer surface of a sphere submerged in a fluid. Each beating flagellum tip is modelled as a small sphere, elastically bound to a circular orbit just above the spherical surface and a regularized image system for Stokes flow outside of a sphere is used to enforce the no-slip condition. Biologically relevant distributions of rotors results in a rapidly developing and robust symplectic metachronal wave traveling from the anterior to the posterior of the spherical Volvox body.

arXiv comment7 pages, 4 figures

References in corpus (7)

• Green Algae as Model Organisms for Biological Fluid Dynamics
• Hydrodynamic flow patterns and synchronization of beating cilia
• Squirmers with swirl -- a model for $Volvox$ swimming
• Bistability in the synchronization of actuated microfilaments
• Nonlinear amplitude dynamics in flagellar beating
• Hydrodynamic synchronization of spontaneously beating filaments
• Hydrodynamic interactions of cilia on a spherical body

Cited by in corpus (3)

• A multiscale biophysical model gives quantized metachronal waves in a lattice of cilia
• Nonreciprocal interactions give rise to fast cilium synchronisation in finite systems
• Role of activity and dissipation in achieving precise beating in cilia: Insights from the rower model