Two-Dimensional Fluid Flow Due to Blade-Shaped Waving of Cilia in Human Lungs

The mucociliary clearance system is an innate defense mechanism in the human respiratory tract, which plays a crucial role in protecting the airways from infections. The clearance system secretes mucus from the goblet cells, which scatters in the respiratory epithelium to trap foreign particles entering the airway, and then the mucus is removed from the body via the movement of cilia residing under the mucus and above the epithelium cells. The layer containing cilia is called the periciliary layer (PCL). This layer also contains an incompressible Newtonian fluid called PCL fluid. This study aims to determine the velocity of the PCL fluid driven by the cilia movement instead of a pressure gradient. We consider bundles of cilia, rather than an individual cilium. So, the generalized Brinkman equation in a macroscopic scale is used to predict the fluid velocity in the PCL. We apply a mixed finite element method to the governing equation and calculate the numerical solutions in a two-dimensional domain. The numerical domain is set up to be the shape of a fan blade, which is similar to the motion of the cilia. This problem can be applied to problems of fluid flow propelled via moving solid phases.