Date of Award

Fall 2007

Project Type


Program or Major

Mechanical Engineering

Degree Name

Master of Science


During last few years several new respiratory diseases including SARS and avian flu have appeared in various parts of the world. With deteriorating environmental conditions and increased air travel, more and more people will suffer breathing disorders, leading to an increased demand for methods to prevent and treat these diseases. To properly address this problem, it is necessary to gain a more complete understanding of the mechanics of respiration. This research constitutes a further step toward this goal by focusing on the coupled solid/liquid micromechanics of an idealized piece of lung tissue.

Gas exchange in mammalian lungs is efficient because 90% of lung volume is partitioned into a labyrinth of small, systematically connected air spaces termed alveoli. Because these air spaces are (at least partially) lined with a thin liquid film, the lung contains an extensive and a highly curved liquid-gas interface. Surface tension forces acting at this interface play a central role in respiratory mechanics, and it is of fundamental as well as practical interest to establish the mechanisms by which surface tension moderates the distribution of the liquid lining. Further research on the fluid dynamics of the alveolar liquid lining is needed to enable a complete understanding of the mechanical force balance, surfactant distribution and particulate transport within the lung parenchyma.

Anatomical studies have shown that the liquid lining accumulates in pools in the corners of polyhedral alveoli. During respiration, the alveolar walls (or septa) are subjected to a periodic strain, and liquid is drawn into and out of these pools by the wall movement. The objective of this research is to investigate how surface tension forces compete with the viscous stresses associated with substrate stretching to control the thin film distribution in the vicinity of an alveolar corner, where septal planes meet. For this purpose, a mathematical model is proposed that couples thin-film fluid dynamics to a stretching substrate; this model extends prior, related investigations by accounting for the corner geometry through a localized (regularized) substrate curvature term.

Key model parameters include the liquid lining volume and the substrate stretching frequency and amplitude. Numerical simulations of this model (a highly nonlinear partial differential equation) are used to characterize the dependence of the film distribution on these system parameters, while asymptotic analysis is used to gain insight into the dominant physical mechanisms. The simulations reveal that the film distribution exhibits qualitatively different behavior with variations in the amplitude and frequency of stretching. At low stretching frequency, new small scale regions are found that control the net fluid flux during stretching. At high frequency, large-amplitude pressure fluctuations are observed near the corner, which may affect capillary blood flow and alveolar stability. At O(1) frequencies, a capillary wave propagates from the corner to the nearest contact point; where it is largely reflected. The analysis developed here provides insight into the physics underlying the bifurcations evident in the computational results.