Mucociliary clearance is the first line of defense of the mammalian respiratory system. The mucociliary system consists of two major parts: mucus and cilia. Mucus is a thin fluid layer that coats the lung airway; cilia are hair-like organelles protruding from the cell surface and bathed in the mucus. With breathing, the mammalian respiratory tract is constantly in contact with particles in the air that could contain potentially infectious microorganisms or toxic substances. Foreign particles that land in the lung airway through airflow will be trapped in the mucous layer. The cyclic beatings of the cilia drive a unidirectional flow of mucus, which eventually move these particles out of the airway.

Source : Cells. 2019 Jul; 8(7): 736.

The co-ordinated beating of the cilia, which leads to an upward, wave-like motion in the trachea, moving at a speed of between 6 and 20 mm per minute, has been investigated for many decades, and is still not fully explained.

Mathematical models (see paper above) have attempted to replicate the movements

In this mini-review, we have presented a brief survey of classical mathematical models of the mucociliary system over the last six decades, with particular attention to the cilia–fluid coupling and force generation machinery. These mathematical models were somewhat useful in helping to test hypotheses and facilitated our understanding of the fundamental mechanisms of the mucociliary system.

[Source as above]

Note : In addition to the as-yet-unexplained wave-like co-ordination, the mechanism(s) behind the movement of the individual cilia is also not yet fully understood - see Flagellaplugin-autotooltip__plain plugin-autotooltip_bigFlagella

A flagellum is a lash-like movable appendage - often used as a means of propulsion - which is attached to the cell body of many bacteria and some eukaryotic cells. There are some notable examples in plants (e.g. fern spores) and even mammals (e.g. sperm cells).