  To assess how the presence of surfactant in lung airways alters the flow of
mucus that leads to plug formation and airway closure, we investigate the
effect of insoluble surfactant on the instability of a viscoplastic liquid
coating the interior of a cylindrical tube. Evolution equations for the layer
thickness using thin-film and long-wave approximations are derived that
incorporate yield-stress effects and capillary and Marangoni forces. Using
numerical simulations and asymptotic analysis of the thin-film system, we
quantify how the presence of surfactant slows growth of the Rayleigh-Plateau
instability, increases the size of initial perturbation required to trigger
instability and decreases the final peak height of the layer. When the
surfactant strength is large, the thin-film dynamics coincide with the dynamics
of a surfactant-free layer but with time slowed by a factor of four and the
capillary Bingham number, a parameter proportional to the yield stress, exactly
doubled. By solving the long-wave equations numerically, we quantify how
increasing surfactant strength can increase the critical layer thickness for
plug formation to occur and delay plugging. The previously established effect
of the yield stress in suppressing plug formation [Shemilt et al., J. Fluid
Mech., 2022, vol. 944, A22] is shown to be amplified by introducing surfactant.
We discuss the implications of these results for understanding the impact of
surfactant deficiency and increased mucus yield stress in obstructive lung
diseases.
