Abstract
Background: In this paper, a four layer model of the simultaneous and coaxial flow of moist air, mucus, mixture of mucin and periciliary liquid and serous fluid (assumed to be incompressible and Newtonian fluids) in a circular tube under time dependent pressure gradient representing prolonged cough is analyzed to study the mucus transport in an airway in the presence of prolonged cough. It is assumed that air and mucus flow under quasi steady state turbulent conditions while the mixture of mucin and periciliary liquid and serous layer surrounding mixture layer flows under unsteady laminar condition in presence of immotile cilia carpet.
 Result: It is shown that the mucus transport increases as the viscosity of serous fluid decreases. Also the mixture and serous fluid flow rates increase as the viscosity of serous fluid decreases. It is also observed that the effect of resistance to flow by serous fluid in the cilia bed is to decrease flow rates. The flow rates of mucus and mixture of mucin and periciliary fluid increase as the viscosity of mixture decreases also air and mixture of mucus and periciliary fluid flow rates increase as the thickness of mixture increases.
 Conclusion: As the thickness of mucus increases its flow rate increases on the other hand the mixture flow rate, mucus and serous fluid flow rate decreases with the increase of the mixture thickness.
 Bangladesh Journal of Medical Science Vol.19(1) 2020 p.53-63
Highlights
Under pathological conditions of the lung, various diseases such as chronic bronchitis, cystic fibrosis, etc. excessive mucus is formed and is transported by forced expiration or cough[1,2,3]
In other way around, when airways are affected by immotile cilia syndrome, cough is the main mechanism by which mucus is transported
Several experiments related to two phase flow in tubes under externally applied pressure have been studied to simulate mucus transport in airways due to cough 4-6, 7, 8, 9
Summary
Under pathological conditions of the lung, various diseases such as chronic bronchitis, cystic fibrosis, etc. excessive mucus is formed and is transported by forced expiration or cough[1,2,3]. This result is expected to be high, as viscous fluid occupies the corresponding air-space They have pointed out that, after the onset of turbulence there is a considerable increase in flow resistance which occurs simultaneously with wave formation on the surface of liquid film. Agarwal[11] have studied the In equation (2.1) - (2.7), the notations are as: mucus gel transport in a constricted simulated cough where, t : time; machine and found that mucus transport increases in z : coordinate along the flow direction the axis presence of serous fluid. Agarwal[23] have studied of the tube; by means of experiment, the transport of mucus gel r : coordinate perpendicular to fluid flow in the in a simulated cough machine where the bottom radial direction; plate was grooved and, flooded with serous fluid and found that the mucus transport increases as the cross-.
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