Fluid-dynamic flapping of a collapsible channel: Sound generation and flow limitation

A flattened airway is mathematically modelled by an inviscid, incompressible fluid flowing through an infinite, two-dimensional, flexible channel. The allowed flapping frequencies of stable oscillations are determined for infinitesimal disturbances to a steady flow. Furthermore, the onset of flutter is determined. The occurrence of a type of flow limitation in collapsible conduits is found to be associated with zero-velocity upstream waves and energy fluxes. Conditions of flow limitation and stability are compared with and contrasted to previous steady models of one-dimensional, massless tubes. The vibrations are implicated with the occurrence of wheezing and physiological correlations in the lung are discussed in terms of parameter changes, both normal and pathological, that influence stable and unstable oscillations.