Thin layer flows due to surface tension gradients over a membrane undergoing nonuniform, periodic strain

Measurements of surface tension in the lung have shown that a time-mean gradient exists with the potential to generate clearance flows toward the mouth in the thin liquid layer that lines the airways. A model is developed to explore this phenomenon in the simple case of a membrane with linear variation in strain along its length, coupled with the unique properties of pulmonary surfactant. The evolution equations are solved numerically for liquid layer thickness and surfactant concentration during a single oscillatory cycle, and the net volume exchanged is computed. The parameters governing the flow are shown to be time scales for viscous effects, tau(v), surface diffusion, tau(DS), surfactant adsorption, tau(A), surfactant desorption, tau(D), oscillation, tau(o), and the average membrane strain epsilon. The volume pumped toward the less compliant end on the initial cycle is maximized when tau(o)/tau(v) approximately O(1) and is relatively insensitive to tau(DS). Rapid adsorption generally augments liquid transport for tau(o)/tau(D) < O(1). Pumping drops precipitously if tau(o)/tau(D) > O(1). Effects of strain amplitude are reported as well. For parameter values approximating those in the lung, pumping rates are near optimal; the mean surface velocity is approximately 0.05 mm/sec, compared with 0.2 mm/sec produced by the action of cilia on the mucus layer. This mechanism might therefore be important in assisting clearance from the lung or maintaining a liquid layer over alveolar facets.