Instabilities of liquid-lined flexible tubes with interfacial surfactant

Abstract eng:
The linear instability and dynamic behaviours of a liquid-lined flexible tube are studied as a simplified model of pulmonary airway. The liquid-air interface is occupied with an insoluble surfactant. The primary flow can be driven by an external force (e.g. gravity), an interfacial shearing stress, or their combination. A modified lubrication approximation is proposed with the pressure being assumed to vary linearly with the radial position. The linear instability property of the system is examined using normal-mode analysis. For the extremely thin liquid film (ε →0), the approximate dispersion relations are derived. For liquid film with relative small thickness (e.g. ε = 0.1), though either the interfacial shearing stress or the external force destabilizes the interface, the combination can cause stabilization in the presence of surfactant. Island of stability, which is caused by the dual role of primary flow in affecting the instability, is detected in the σs − Bo plane.

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