Aerosol deposition in mucus-lined ciliated airways

We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall – an outcome that is harmful in case of allergens and pathogens, but beneficial in case of aerosolised drugs. We adopt the weighted-residual integral boundary-layer model of Dietze and Ruyer-Quil ( J. Fluid Mech. 762, 2015, 68–109, to describe the dynamics of the mucus–air interface, as well as the flow in both phases. The transport of mucus induced by wall-attached cilia is also considered, via a coarse-grained boundary condition at the base of the mucus. We show that the capillary-driven Rayleigh–Plateau instability plays an important role in particle deposition by drawing the mucus into large annular humps and leaving substantial areas of the wall exposed to particles. We find, counter-intuitively, that these mucus-depleted zones enlarge on increasing the mucus volume fraction. Our simulations are eased by the fact that the effects of cilia and air turn out to be rather simple: the long-term interface profile is slowly translated by cilia and is unaffected by the laminar airflow. The streamlines of the airflow, though, are strongly modified by the non-uniform mucus film, and this has important implications for aerosol entrapment. Particles spanning a range of sizes (0.1–50 microns) are modelled using the Maxey–Riley equation, augmented with Brownian forces. We find a non-monotonic dependence of deposition on size. Small particles diffuse across streamlines due to Brownian motion, while large particles are thrown off streamlines by inertial forces – particularly when air flows past mucus humps. Intermediate-sized particles are tracer-like and deposit the least. Remarkably, increasing the mucus volume need not increase entrapment: the effect depends on particle size, because more mucus produces not only deeper humps that intercept inertial particles, but also larger depleted zones that enable diffusive particles to deposit on the wall.