Surfactant amplifies yield-stress effects in the capillary instability of a film coating a tube

TL;DR

This study investigates how surfactant influences the capillary instability of a mucus-like layer in lung airways, revealing that surfactant amplifies yield-stress effects and delays plug formation, with implications for lung disease understanding.

Contribution

The paper introduces a combined theoretical and numerical analysis of surfactant effects on yield-stress mucus layers, highlighting amplified stabilization and delayed airway plugging.

Findings

Surfactant slows the growth of the Rayleigh-Plateau instability.

Increased surfactant strength raises the critical layer thickness for plug formation.

Surfactant amplifies the yield-stress effects in airway mucus stability.

Abstract

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.