Effects of continuous and discrete boundary conditions on the movement of upper-convected maxwell and Newtonian mucus layers in coughing and sneezing

Mucociliary clearance is an important phenomenon inside the respiratory system as a first defensive mechanism against pathogens. Therefore, any assumption considered for the mucociliary clearance and affects its functionality must be validated. The present research deals with the effects of boundary conditions on the movement of upper-convected Maxwell and high viscosity Newtonian mucus layers, numerically. Furthermore, the validity of replacing the viscoelastic mucus layer with a high viscosity Newtonian layer is evaluated. The airway surface liquid layer is considered a two-layer model including non-Newtonian mucus and Newtonian periciliary layers. Four cyclic boundary conditions are imposed at the mucus-periciliary interface as the cilia movement to obtain variations of mucociliary clearance. The upper boundary of the mucus layer is also exposed to different shear stress levels including free slip, cough, and sneeze conditions. By investigation of velocity variations inside mucus and periciliary layers, it is concluded the differences between viscoelastic and Newtonian mucus are not negligible. The maximum velocity differences between the two fluids are more than 52% and 215% during cough and sneeze, respectively. The results show there is a high order of dependency between the relaxation time and the imposed boundary conditions at the mucus-periciliary interface that leads to the invalidation of replacing two fluids with each other. Moreover, the results show substituting the viscoelastic mucus with a high viscosity Newtonian one depends on the mucus-periciliary interface boundary condition. If an independent time-varying boundary condition is used, the substitution leads to an error less than 7% under different shear stress levels. However, time-varying boundary condition shows 38% and 88% differences between high viscosity Newtonian and viscoelastic mucus layers. Furthermore, neglecting the recovery stroke leads to a velocity underestimation up to 50% by substituting viscoelastic mucus with a high viscosity Newtonian one. Therefore, replacing the viscoelastic mucus with a high viscosity Newtonian one is not acceptable for numerical simulations.