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The reopening of a collapsed fluid-filled elastic tube

Published online by Cambridge University Press:  23 January 2007

ANNE JUEL  and
ALEXANDRA HEAP
ANNE JUEL
Affiliation:
School of Mathematics, The University of Manchester, Manchester M13 9PL, [email protected]
ALEXANDRA HEAP
Affiliation:
School of Mathematics, The University of Manchester, Manchester M13 9PL, [email protected]
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Abstract

We present an experimental study of the reopening mechanics of a collapsed liquid-filled elastic tube. The experiment is a simple mechanical model of pulmonary airway reopening and aims to assess the robustness of existing theoretical models. A metre-long horizontal elastic tube of inner radius Ri=4.88 ± 0.14mm is filled with silicone oil and is carefully collapsed mechanically. The injection of nitrogen at a constant flow rate results in the steady propagation of an air finger, after the decay of initial transients. This behaviour is observed over the realizable range of the capillary numbers Ca, which measures the ratio of viscous and capillary forces. With increasing Ca, the transition region between the collapsed and reopened sections of the tube shortens, and the height of the tube behind the bubble tip increases. We also find that air fingers can propagate in partially reopened tubes, in which the transmural pressure is negative far behind the finger tip.

The effect of viscosity on the reopening dynamics was explored by performing experiments using three different grades of silicone oil, with kinematic viscosities of 1000cS, 200cS and 100cS. A direct comparison between the experimental pressure dependence on Ca and numerical simulations of the zero-gravity three-dimensional airway-reopening model of Hazel & Heil (Trans. ASME: J. Biomech. Engng, vol. 128, 2006, p. 473) highlights some significant differences. Within the experimental parameter range, gravity profoundly influences the reopening mechanics in several ways. The reopening tube is supported by a rigid base, which induces an asymmetry about the horizontal mid-plane of the collapsed tube, resulting in distinct phases of reopening as Ca increases. In addition, buoyancy forces act on the air finger, which is observed to propagate near the top of the cross-section of the tube, leaving a thicker fluid-lining below. In the limit of small Ca, the height of the reopened tube increases significantly with viscosity. Experimental evidence suggests that this increase in viscosity leads to significant changes in the film configuration behind the propagating finger, caused by the increased contribution of buoyancy forces. The altered film configuration changes the mechanical load on the tube walls and, hence, the shape of the reopened tube.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 287 - 310
Copyright
Copyright © Cambridge University Press 2007

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References

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