### Trapping and displacement of liquid collars and plugs in rough-walled tubes

Authors: Oliver Jensen, Feng Xu

Journal: Physical Review Fluids

Publication Date: 18 September, 2017

Department of: Mathematics

### In Abstract

**Predicting the probability of unblocking a lung airway**

Researchers from the Universities of Manchester and Birmingham have predicted the probability that an imposed force will displace a liquid plug obstructing a narrow rough-walled tube, when the shape of the tube is known only in statistical terms. Surface tension can cause a liquid film lining the interior of a cylindrical tube to form an occlusive plug (as seen in a drinking straw) or an annular collar. Blowing hard into a straw will expel any trapped liquid. Likewise, a deep breath or a cough can displace mucus plugs that form in lung airways. However airways have an irregular shape, and internal roughness can trap liquid plugs and collars, inhibiting their removal and hindering normal respiration. Given the practical difficulty of measuring airway geometry precisely, the outcome of a particular experiment or manoeuvre must be predicted as a probability (for example, that an imposed force is sufficient to displace fluid from a tube with given statistical properties). Now, by identifying the topographic features of rough-walled tubes that promote liquid trapping, the researchers show how techniques of interfacial fluid mechanics and uncertainty quantification can be combined to derive explicit displacement probabilities. This will enhance simulations of lung function and related engineering applications.

- Surface tension influences the distribution of airway liquid as well as the overall compliance of the lung