A planar model for mucociliary transport: effect of mucus viscoelasticity

A planar two-layer fluid model is proposed to study the transport of mucus in the respiratory tracts due to cilia beating and air motion by considering mucus as a viscoelastic fluid. The effect of air motion due to forced expiration and other processes is considered by prescribing shear stress at the mucus-air interface. It is shown that the transport of mucus increases as the pressure drop, shear stress due to air motion and the velocity generated by cilia tips and the serous sublayer increase. Mucus transport also increases as the shear modulus of elasticity decreases. This property is effective only in the presence of pressure drop or air motion. It is noted that the effect of gravity is similar to pressure drop. It is observed that mucus transport decreases as the viscosity of serous layer fluid increases, but any increase at high values of mucus viscosity does not seem to affect the mucus transport. It is also found that for a given total depth of serous and mucus layers, there exists a serous fluid layer thickness for which the mucus transport is maximum. The functional dependence of mucus transport predicted by the model is discussed in relation to experimental observations.