Delivery of aerosols to the lung can treat various lung diseases. However, the conducting airways are coated by a protective mucus layer with complex properties that make this form of delivery difficult. Mucus is a non-Newtonian fluid and is cleared from the lungs over time by ciliated cells. Further, its gel-like structure hinders the diffusion of particles through it. Any aerosolized treatment of lung diseases must penetrate the mucosal barrier. Using computational fluid dynamics, a model of the airway mucus and periciliary layer was constructed to simulate the transport of impacted aerosol particles. The model predicts the dosage fraction of particles of a certain size that penetrate the mucus and reach the underlying tissue, as well as the distance downstream of the dosage site where tissue concentration is maximized. Reactions that may occur in the mucus are also considered, with simulated data for the interaction of a model virus and an antibody.