Particle dynamics in liquid-lined lung airways - Weekley, Susan Jill (2004)
Every time we breathe in we inhale thousands of particles, some of which may become trapped in the liquid lining of the airway wall. In this thesis we use theoretical fluid dynamics to model various aspects of the dynamics of these particles after their initial deposition on the airway wall. In Chapter 2 we consider the behaviour of an inhaled particle trapped in an alveolar corner, modelled as a two-dimensional cylinder partially immersed in a liquid pool in the corner of a rigid-walled wedge. We balance quasistatic capillary forces acting on the particle with viscous forces, modelled using lubrication theory, acting in a small gap between the particle and the wall. The direction of particle motion is non-intuitive and we obtain predictions for the fate of a particle dependent on the wedge angle, liquid volume and the size and deposition site of the particle. In practice, surface forces have been shown to pull particles into the airway liquid lining with sufficient force to depress underlying epithelial cells. In Chapters 3 and 4, using elastohydrodynamics, we consider the unsteady motion of a particle close to a deformable surface and the effect of wall deformation on the particle's behaviour. We model this initially as a two-dimensional cylinder moving in fluid perpendicularly and transversely close to a spring-backed plate, using simulations and asymptotic analysis based on lubrication theory. Viscous forces cause a transient overshoot of the force acting on the particle following a prescribed perpendicular displacement. Transverse motion of the particle causes the formation of a `corner' in the wall, which is particularly sharp immediately following the particle's initial displacement. In addition we consider the extension of the model into three dimensions and examine a sphere moving close to a deformable plane in a fluid environment. In Chapter 5 we consider the motion of a particle trapped in a mucus layer which is propelled by cilia acting within an underlying serous layer. We model this as a cylindrical disk moving within a viscous sheet, with a uniformly distributed body force in the lower layer representing the cilia. We predict the speed of the particle as a function of disk shape, ciliary activity and other material parameters.