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Absolute instability in the higher-generation airways: a pathway for airway closure

Published online by Cambridge University Press:  04 March 2025

Ramkarn Patne Open the ORCID record for Ramkarn Patne [Opens in a new window]
Ramkarn Patne*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana 502285, India
*
†Email address for correspondence: [email protected]
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Abstract

Experiments on microfluidic core–annular flows demonstrated a transition from a continuous core jet to core-fluid drops and slugs separated by the annular fluid films/slugs due to absolute instability. The flows in the higher-generation airways could be modelled as core–annular flow with the laminar core airflow and annular airway surface liquid (ASL). Thus, if an absolute instability exists in the higher-generation airways, then it could lead to ASL film/slug-induced airway closure, necessitating the present study. Taking cues from previous studies, we derive an evolution equation using the lubrication approximation. The analysis, using the dispersion relation obtained from the evolution equation, predicts the existence of the critical capillary number $Ca_c$ such that, for $Ca < Ca_c$, the flow will be absolutely unstable for vanishing Reynolds number $Re$. The parameter $Ca_c$ exhibits the scaling as $Ca_c \sim (1-H)^2/\mu _r$, where $1-H$ is the dimensionless thickness of the ASL, and $\mu _r$ is the ratio of the air viscosity to the ASL viscosity. In agreement with the experimental observations, for a healthy lung, the analysis predicts absolute instability triggered airway closure only at the end of expiration during a breathing cycle. For a diseased lung, the ASL thickness and viscosity drastically increase the possibility of absolutely unstable flow and, thus, airway closure. Increasing inertial effect (i.e. $Re$) exacerbates airway closure by curtailing the convectively unstable region. Similarly, the ASL shear thinning widens the absolute instability parametric region. Thus, the present analysis demonstrates a pathway for airway closure in the higher-generation airways due to absolute instability.

JFM classification

Biological Fluid Dynamics: Pulmonary fluid mechanics Instability: Absolute/convective instability Multiphase and Particle-laden Flows: Core-annular flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1005 , 25 February 2025 , A15
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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