Cilia-induced flow of viscoelastic mucus through an idealized two-dimensional model of the human trachea is presented. The cilia motion is simulated by a metachronal wave pattern which enables the mobilization of highly viscous mucus even at nonzero Reynolds numbers. The viscoelastic mucus is analyzed with the upper convected Maxwell viscoelastic formulation which features a relaxation time and accurately captures normal stress generation in shear flows. The governing equations are transformed from fixed to wave (laboratory) frame with appropriate variables and resulting differential equations are perturbed about wave number. The trachea is treated as an axisymmetric ciliated tube. Radial and axial distributions in axial velocity are calculated via the regular perturbation method and pressure rise is computed with numerical integration using symbolic software MATHEMATICA^‘TM’. The influence of selected parameters which is cilia length, and Maxwell viscoelastic material parameter i.e. relaxation time for prescribed values of wave number are visualized graphically. Pressure rise is observed to increase considerably with elevation in both cilia length and relaxation time whereas the axial velocity is markedly decelerated. The simulations provide some insight into viscous-dominated cilia propulsion of rheological mucus and also serve as a benchmark for more advanced modeling.

纤毛诱导的粘弹性粘液流通过人类气管的理想二维模型。纤毛运动是由异时波模式模拟的，即使在非零雷诺数下，也能动员高粘度粘液。用上部对流的麦克斯韦粘弹性制剂分析粘弹性粘液，该制剂具有松弛时间并准确地捕获剪切流中的正应力。用适当的变量将控制方程从固定框架转换为波动（实验室）框架，并且所产生的微分方程会受到波动数的干扰。气管被视为轴对称的纤毛管。^'TM'。所选参数（纤毛长度）和麦克斯韦粘弹性材料参数（即波数规定值的弛豫时间）的影响以图形方式显示。观察到压力升高随纤毛长度和松弛时间的增加而显着增加，而轴向速度明显减速。这些模拟为流变粘液的粘性主导的纤毛推进提供了一些见识，并且还可以作为更高级建模的基准。