Propulsion by beating cilia is an universal phenomenon developed by nature as a way to propel fluids. For the particular case of the human body, cilia are responsible for the left-right asymmetry of the heart in the early embryonic development, for the transport of nutrients in the brain, and for the transport of bronchial mucus in the mucociliary clearance process, which motivates the present work.

During the breathing process, a large number of foreign particles (bacteria, dusts, pollutants or alergens) penetrate inside the organism. Mucociliary clearance is one of the defence mechanisms developed by the human body for eliminating these particles. Defects in this process usually lead to infections, difficulty to breath, and in some cases to death. Severe asthma and cystic fibrosis are examples of disease directly connected to mucociliary clearance. For patients suffering from severe asthma, less vibratile cilia are present on the epithelial surface, and some of these remaining cilia are also not fully functional, reducing the transport of mucus in the airways.

The objective of the present work is to find out how mucociliary clearance is achieved, and especially, to understand the underlying mechanism that allows millions of cilia to act as a whole for the transport of mucus. Here, one focuses on the metachronal waves, which form at the ciliary tips and are known to enhance the fluid transport.

The present work reports the formation and the characterization of antiplectic and symplectic metachronal waves in 3D cilia arrays immersed in a two-fluid environment, with viscosity ratios up to 25. A coupled lattice-Boltzmann - Immersed-Boundary solver is used, and the code is fully parallelized using MPI libraries. Hence, the simulation of a large number of cilia is possible. The periciliary layer is confined between the epithelial surface and the mucus. Its thickness is fixed such that the tips of the cilia can penetrate the mucus. A purely hydrodynamical feedback of the fluids is taken into account and a coupling parameter α 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 antiplectic and symplectic waves, mapping a cilia inter-spacing ranging from 1.67 up to 5 cilia length and Reynolds numbers from 0.03 to 20, is performed by imposing the metachrony. Antiplectic 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 synchronised motion. These results are relevant in the context of medical investigations on respiratory diseases and give new insights regarding the methods for drug transportation in the human body.