A preliminary model of pulmonary airway reopening is developed that includes the physicochemical influence of surfactant under bulk-equilibrium conditions. The airway is modeled following Gaver et al. [J. Fluid. Mech. 319, 25-65 (1996)] as a flexible-walled channel, where walls are membranes under longitudinal tension T, and supported with elasticity E with a stress-free separation distance 2H. The lining fluid has viscosity mu and surface tension gamma*. Airway reopening occurs when a semi-infinite bubble of air with pressure P-b* progresses steadily at velocity U and separates the walls. Surfactant exists in the lining fluid (C*) and at the air-liquid interface (Gamma*). Bulk equilibrium is assumed (C* = C-0) and the kinetic transfer of surfactant between the bulk and interface occurs with a rate k. The equilibrium relationship between Gamma* and C* is based upon Henry's isotherm (Gamma(eq)=KC0) The surface tension equation of state, a relationship between gamma* and Gamma*, is assumed to be linear near Gamma(eq). Marangoni stresses develop from the transport of surfactant at the interface, leading to interfacial rigidification and changes in the airway reopening behavior. The behavior is governed by the following dimensionless parameters: the capillary number Ca = mu U/gamma(eq), the surface elasticity number El= - (d gamma*/d Gamma*)(Gamma(eq)/gamma(eq)), the modified Stanton number St(lambda)=(k/K)/(U/H), the wall elastance parameter beta=EH2/gamma(eq), the wall tension ratio eta = T/gamma(eq), and the surface Peclet number Pe(int)= UH/D-int. The results indicate that El can have a dual, contrasting influence on the airway reopening behavior. By increasing El through an increase in re d gamma*/d Gamma* (method 1), larger P-b* predicted from the resulting interfacial surfactant gradients and interfacial rigidification. In contrast, increasing Gamma(eq) (method 2) increases El but reduces P-b* dueto the global reduction of gamma*; however, the reduction in P-b* is augmented by the increasing importance of viscous, elastic, tension and Marangoni stresses. Furthermore, for St(lambda)>10 the interface remains mobile due to rapid surfactant adsorption and the elimination of Marangoni stresses, which minimizes P-b*. This behavior may be important in the development of improved exogenous surfactants for the treatment of a variety of pulmonary diseases. (C) 1998 American Institute of Physics.
