Mucus Transport in the Larger Airway Due to Prolonged Mild Cough: Effect of Serous Fluid and Cilia Beating

Abstract

Since mucus production and transport is an important defense mechanism of the lower airways, this study focuses on this aspect. In this paper it is assumed that the co-axial flows of mucus and air is taking place in a circular tube representing a larger airway. In the central core, air is assumed to flow under quasi steady state turbulent condition and the mucus layer surrounding this central core is assumed to flow under unsteady laminar condition. The prolonged mild cough is represented by a time dependent pressure gradient function. To consider the effect of serous fluid, it has been assumed that the cilia bed is approximated by a porous matrix within which serous fluid flows following Darcy’s law. Further, the effect of cilia beating has been considered by assuming that a constant mean velocity which is a resultant of effective and recovery stroke is imparted on the serous fluid and this velocity is superimposed on the Darcy flow. For constant porosity of cilia bed and mucus viscosity, it is shown that air and mucus flow rates decrease with increase in serous fluid viscosity. The effect of porosity of cilia bed and cilia beating has been found to increase the air and mucus flow rates.

Keywords Cilia Beating; Porous Matrix; Mucus Transport; Circular Model; Prolonged Mild Cough.

MSC (2010) No.:76Z05