Co-Axial Cylindrical Model for Turbulent Airflow and Laminar Mucus Flow in Constricted Lung Airways

Abstract

This paper presents a two-layer cylindrical quasi-steady co-axial flow model of air and mucus in constricted airways that is affected by a time-varying pressure gradient. In this model both air and mucus are treated as incompressible Newtonian fluids. The air is considered to flow under quasi-steady state turbulent conditions whereas the mucus is assumed to flow under quasi steady-state laminar conditions. The model includes the effect of the immotile cilia layer by considering a slip condition at the airway wall. This makes the model more realistic and helps to better describe the interaction between airflow and mucus in narrowed airways than conventional no-slip models. The analysis indicates that both air and mucus flow rates decrease as the viscosity of mucus and constriction thickness increases. The analysis also indicates that both air and mucus flow rates increase with a higher pressure gradient and slip parameter. These findings provide insight into mucus clearance mechanisms in obstructive respiratory diseases such as asthma, chronic bronchitis, COPD and tracheal stenosis.