Surface-tension-driven evolution of a viscoplastic liquid coating the interior of a cylindrical tube

One mechanism for airway closure in the lung is surface-tension-driven instability of mucus layer which lines wall. We study an axisymmetric viscoplastic Bingham liquid coating interior a rigid tube, simple model that takes into account yield stress mucus. An evolution equation thickness derived using long-wave theory, from we also derive simpler thin-film equation. In case show two branches marginally yielded static solutions can be used to both predict size initial perturbation required trigger and quantify how increasing capillary number (a parameter measuring relative surface tension) reduces final deformation layer. Using numerical equation, critical form plug tube increases as increased. discuss significance these findings modelling obstructive conditions such cystic fibrosis, where often thicker has higher stress.