A Mathematical Model for Mucus Transport in Human Lungs Airways under an Oscillatory Pressure Gradient due to Coughing

Abstract

This paper presents a two layers circular unsteady state mathematical model for mucus transport in the human lung airways by considering the time dependent pressure gradient induced mucus transport in the respiratory system caused by coughing. It is also assumed that the mucus is a visco-elastic fluid. A comprehensive discussion is given to the pressure gradient, which is particular case of a sinusoidal function of time. The effects of various parameters on mucus transport are examined and found that mucus transport rate increase when the viscosities of mucus and serous layer fluid and shear modulus of elasticity decreases. It is also found that mucus transport rate increase when oscillating pressure gradient, air velocity and thickness of mucus increase but mucus transport rate decrease when duration of cough increase.