Airway Closure: Static Liquid Bridges in Non-Axisymmetrically Buckled Elastic Tubes


The lung's airways are coated with a thin liquid film which affects many aspects of its mechanical behaviour. In the smaller airways where the wall curvature is large, the surface tension of the liquid film is important and is generally believed to be the cause of `airway closure' which has been observed directly and indirectly in the excised lungs of laboratory animals.

Airway closure occurs through the formation of occluding liquid bridges across the airway lumen. The formation of these liquid bridges is assumed to follow the growth of a Rayleigh instability of the liquid lining which is commonly referred to as `film collapse'. The formation of the liquid bridge can be accompanied (and indeed dominated) by large elastic deformations of the airway walls, leading to a so-called `compliant collapse'.

The physiological problems associated with airway closure are greatly enhanced in prematurely born babies whose lungs cannot produce sufficient quantities of the surfactant which reduces the liquid film's surface tension. This manifests itself in the potentially life-threatening `Respiratory Distress Syndrome'.

The Problem

Previous theoretical investigations of this problem were restricted to axisymmetric geometries. In the study presented here, we examine if the compressive force that the liquid bridge exerts on the airway wall is strong enough to make the airway buckle non-axisymmetrically. This would have important implications since much smaller volumes of fluid are required to form an occluding liquid bridge in a non-axisymmetrically collapsed airway than in an axisymmetric one. The volume of fluid required to form a `minimal liquid bridge' in a non-axisymmetrically buckled tube is therefore an important parameter to be determined in this study.

I. The model problem.

II. Minimal liquid bridges for zero surface tension.

III. Minimal liquid bridges for finite surface tension.

IV. Opposite wall contact and higher buckling modes.

V. Conclusions.

Page last modified: September 29, 2000

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