Analytical model of magnetically actuated mucociliary pumping in a bronchial tube

In this study we investigate the concept of magnetically actuated mucociliary pumping in a bronchial tube. To analyze the muco ciliary clearance in bronchial tube different techniques have been used to observe the ciliary beat frequency. CT-scan and MRI-scan are very effective to detect the ciliary motions which are possible due to the presence of magnetic field. In this study velocity, pressure difference and flow rate are analyzed with the help of continuity equation, Darcy's law and non-linear momentum equation. The mucus layer is considered as a viscoelastic fluid, therefore stress components are simplified for the Maxwell fluid (viscoelastic model). The transportation of mucus layer in the bronchial tube with the help of ciliary movement is modeled in the wave and fixed frame. The resulting PDE's are solved by the perturbation and Adomian decomposition method. Effects of magnetic field, Darcy's resistance and viscoelastic parameter are discussed at length in the graphical results section.