Transport efficiency of metachronal waves in 3D cilium arrays immersed in a two-phase flow

` This work reports the formation and characterization of antipleptic and symplectic metachronal waves in 3D cilium arrays immersed in a two-fluid environment, with a viscosity ratio of 20. A coupled lattice Boltzmann-immersed-boundary solver is used. The periciliary layer is confined between the epithelial surface and the mucus. Its thickness is chosen such that the tips of the cilia can penetrate the mucus. A purely hydrodynamical feedback of the fluid is taken into account and a coupling parameter alpha is introduced, which allows tuning of both the direction of the wave propagation and the strength of the fluid feedback. A comparative study of both antipleptic and symplectic waves, mapping a cilium interspacing ranging from 1.67 up to 5 cilium lengths, is performed by imposing metachrony. Antipleptic waves are found to systematically outperform symplectic waves. They are shown to be more efficient for transporting and mixing the fluids, while spending less energy than symplectic, random or synchronized motions.