Capillary-elastic Instabilities of Liquid-lined Lung Airways

Abstract

To model the competition between capillary and elastic forces in controlling the shape of a small lung airway and its interior liquid lining, we compute the equilibrium configurations of a liquid-lined, externally pressurized, buckled elastic tube. We impose axial uniformity and assume that the liquid wets the tube wall with zero contact angle. Non-zero surface tension has a profound effect on the tube’s quasi-steady inflation-deflation characteristics. At low liquid volumes, hysteresis arises through two distinct mechanisms, depending on the buckling wavenumber. Sufficient compression always leads to abrupt and irreversible collapse and flooding of the tube; flooding is promoted by increasing liquid volumes or surface tension. The model captures mechanisms whereby capillary-elastic instabilities can lead to airway closure.