Mathematical modelling of mucus transport in diseased airways with effects of constriction of airway diameter and Mucus viscosity

In this paper, a coaxial flow of air and mucus in a circular tube under time dependent pressure gradient function is modelled and have been considered to study mucus transport in the diseased airway (Bronchial constriction). It is assumed that moist air (assumed to be an incompressible Newtonian fluid) and mucus flow under the quasi-steady state laminar condition caused by prolonged cough. The mucus layer is considered to be divided into two sub-layers, the one in contact with the air flow and the other sub-layer adjacent to the cilia bed, the effect of constriction of the airway diameter on mucus transport and mucus viscosity. The analysis and approximate result shows that mucus transport in constricted airway decreases as diameter changes. It is also shown that air flow rate affected by mucus transport and mucus viscosity in the constricted airway.