Steady State Creeping Displacement of a Semi-Infinite Gas Bubble in a 2D Channel Filled by a Bingham Liquid

The mucus layer which covers the respiratory tract is a non-Newtonian fluid with a yield stress. The amount of shear stress must exceed a certain value before significant deformation (i.e. flow) can occur. Therefore, for better understanding of some interesting phenomena in the airways, such as the propagation or rupture of a mucus plug, as may occur in asthma, cystic fibrosis, or emphysema, the yield stress behavior of the fluid needs to be considered as well.