  The present work reports the formation and the characterization of
antipleptic and symplectic metachronal waves in 3D cilia 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 allowing the 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 cilia inter-spacing
ranging from 1.67 up to 5 cilia length, is performed by imposing the
metachrony. Antipleptic waves are found to systematically outperform sympletic
waves. They are shown to be more efficient for transporting and mixing the
fluids, while spending less energy than symplectic, random, or synchronized
motions.
