| This study is composed of two parts: In part I, the stability behavior of a finite length uniform planar channel conveying fluid is examined for application as a model of forced expiration and wheezing observed in obstructive airway diseases. Using the Galerkin finite element method, it is shown that subcritical flutter occurs due to the presence of fluid dissipation; this is followed by buckling (onset of flow limitation) as the flow speed exceeds the wave speed. However, the results show that the flutter predicted has a weak growth rate and that a uniform channel assumption may be inappropriate for a model of wheezing.; Therefore, in part II, we have modeled a nonuniform planar channel that is a two-step procedure: In the first step, a nonlinear analysis is carried out to obtain equilibrium solutions for a collapsible airway conveying sub- or supercritical flow. In the second step, a linear stability analysis of the nonuniform channel is performed that predicts two distinct modes of flutter: a weak growth high frequency flutter due to energy loss downstream and a sudden strong growth low frequency flutter that appears to have a causal link to the onset of flow limitation. |
