Minimal model of the hydrodynamical coupling of flagella on a spherical body with application to Volvox

Flagella are hairlike 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 modeled 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.