IV-6

David Halpern

University of alabama, Tuscaloosa

James B. Grotberg

Unviersity of Michigan

Abstract

The lung consists of a branching network of airways coated with a thin viscous film. If the surface tension of the liquid lining is not sufficiently low, a surface tension driven instability at the air-liquid interface may induce the break up of the air-core fluid into disconnected inclusions, thus blocking airflow. Because of the negative pressures generated within the non-uniform film, the airway wall may also collapse if the elastic forces of the tube are not large enough. Premature neonates, whose lungs have not developed sufficient surfactant to maintain the surface tension of the lung at a sufficiently low level for healthy functioning, are vulnerable to problems caused by airway closure. Often they are placed in ventilators to diminish the risk of airway closure. Two key parameters are the frequency of the breathing cycle and the tidal volume. If airways can be kept open by setting a ventilator at some given frequency, then this would be important in the treatment of such patients. The present work examines the quantifies these particular issues. We will consider an individual compliant airway coated with a thin film of Newtonian fluid, and examine this simplified system for instabilities. To simulate breathing and other imposed oscillations, the airway mean radius is forced to oscillate, and an oscillatory shear-stress is imposed at the air-liquid interface. A system of weakly nonlinear evolution equations is derived for the film thickness and wall position assuming small deflections. The equation for the film thickness has some features of the Kuramoto-Sivashinsky equation but with a modified time-dependent term multiplying the nonlinear term representing the shear stress. During part of the oscillatory cycle when the shear stress is small, the film thickness grows due to the destabilizing transverse component of curvature. At some point during the cycle, the nonlinear shear-stress is small, the film thickness grows due to the destabilizing transverse component of curvature. At some point during the cycle, the nonlinear shear-stress term becomes dominant, stopping further growth. Wave steepening and distortion also occur. A model suitable for thicker films has also been developed which shows that there is a critical film thickness dependent on wall properties and the frequency of the oscillatory shear stress above which stable collars breakup to form lenses. This critical film thickness decreases with increasing wall compliance and decreasing the shear-stress frequency.