Roles of Airflow Velocity and Porosity Parameter on Mucus Transport in the Human Lung Airways under the Influence of Time Varying Pressure Gradient

Abstract

This paper presents a two-layer circular unsteady state mathematical model and its analysis on mucus transport in the human lung airways. The model incorporates the roles of airflow velocity and porosity parameter on mucus transport under the influence of time varying pressure gradient generated due to coughing. The porosity parameter is incorporated because of immotile cilia forming a porous matrix bed in the serous sub-layer in contact with the epithelium in unhealthy state of human lung airways. The mod-el also incorporates the effect of airflow velocity caused by high shear stress that shears secretions and unwanted foreign particles off the bronchial wall and propels them towards the larger airways and trachea under a normal cough mechanism. In the model, the mucus layer is taken as a visco-elastic fluid and the serous layer as an incompressible Newtonian fluid. The analysis of the model reveals that mucus transport rate increases with increase in airflow velocity, porosity parameter, acceleration due to gravity, mucus layer thickness and pressure gradient. It is also noted that the mucus transport rate decreases with the in-crease in coughing duration, mucus viscosity and its elastic modulus and viscosity of serous layer fluid.