On the effect of boundary vibration on mucus mobilization

Abstract

In this study, we investigate the mobilization of mucus in a cylindrical tube of constant cross-section subjected to a Small Amplitude Oscillatory Shear (SAOS) assuming the viscoelastic behavior of mucus is governed by the Oldroyd-B constitutive equation. The Laplace transform method was adopted to derive expressions for the velocity profile, average velocity, instantaneous flowrate and mean flowrate (i.e., mobilization) of the mucus within the tube. Additionally, a 2D finite element model (FEM) was developed using COMSOL Multiphysics software to verify the accuracy of the derived analytical solution considering both a Newtonian and an Oldroyd-B fluid. Furthermore, sensitivity studies were performed to evaluate the influence of the vibration frequency, vibration amplitude, mean relaxation time, and zero-shear viscosity on mucus mobilization. Results prove that the analytical and numerical results are within acceptable error tolerance and thus in excellent agreement. Besides, the parametric studies indicate a 48%, 57%, and 343% improvement in mucus mobilization when the mean relaxation time, vibration amplitude, and vibration frequency, respectively were each increased by a factor of 6 from the assumed nominal values. Conversely, the mucus mobilization decreased by 25% when the zero-shear viscosity was increased by a factor of 6 from the assumed reference value. In general, this study confirms that mucus mobilization in a tube can be improved by increasing the magnitude of vibration amplitude and vibration frequency. Similarly, the larger the magnitude of mucus mean relaxation time the better the mucus mobilization when the tube is subjected to boundary vibrations. Finally, mucus mobilization decreases as the magnitude of mucus viscosity increases.