Model of Fluid Draining in Lung Airways
Just as surface tension causes a narrow stream from a faucet to break up into drops, it can also cause the mucus coating the tubes in our lungs to form regions of increased thickness called collars. As they flow downward, collars can thicken to become plugs that block airways. Few theoretical studies of collars have accounted for the mucus’s viscoplasticity—it’s spring-like when pushed gently but permanently deformable when pushed beyond its so-called yield stress. James Shemilt, now at the University of British Columbia in Canada, and his colleagues used analytical and numerical techniques to model the effects of viscoplasticity on collar flow [1]. They determined the conditions that lead to a stable collar that doesn’t enlarge as it drains downward, results that may eventually be useful for the development of drugs for lung diseases like cystic fibrosis.
The team derived an equation that describes a falling viscoplastic collar and solved it under the assumption of a thin liquid coating and strong surface tension. One key result was that if the film thickness ahead of the collar is less than a critical value, the collar can remain stable and not grow into an airway-blocking plug. By contrast, in the well-studied case of a classic Newtonian (nonviscoplastic) fluid, there is only one thickness that supports this stable state, so any slight thickness variation would cause the collar to grow or shrink.
Shemilt says that a model incorporating more of the properties of airway mucus is needed to fully understand the fluid-mechanical effects on the lungs. But he says that the work may be relevant for efforts to improve cystic fibrosis drugs that target the mucus’s mechanical properties.
–David Ehrenstein
David Ehrenstein is a Senior Editor for Physics Magazine.
References
- J. D. Shemilt et al., “Viscoplasticity can stabilize liquid collar motion on vertical cylinders,” Phys. Rev. Fluids 10, 103301 (2025).