The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube

Abstract

We have utilized a computational model of semi-infinite air bubble progression in a surfactant-doped, fluid-filled rigid capillary to investigate the continual interfacial expansion dynamics that occur during the opening of collapsed pulmonary airways. This model simulates mixed-kinetic conditions with nonlinear surfactant equations of state similar to those of pulmonary surfactant. Several dimensionless parameters govern the system responses: the capillary number (Ca) that relates viscous to surface tension forces; the elasticity number (El), a measure of the ability of surfactant to modify the surface tension; the bulk Péclet number (Pe), relating bulk convection rates to diffusion rates; the adsorption and desorption Stanton numbers (St_a and St_d) that relate the adsorption/desorption rates to surface convective rates; and finally the adsorption depth (λ), a dimensionless bulk surfactant concentration parameter. We investigated this model by performing detailed parameter variation studies at fixed and variable equilibrium concentrations. We find that the surfactant properties can strongly influence the interfacial pressure drop through modification of the surface tension and the creation of Marangoni stresses that influence the viscous stresses along the interface. In addition, these studies demonstrate that, depending upon the range of parameters, either film thickening or film thinning responses are possible. In particular, we find that when Pe[Gt ]1 (as with pulmonary surfactant) or when sorption rates are low, concentration profiles can substantially differ from near-equilibrium approximations and can result in film thinning. These responses may influence stresses on epithelial cells that line pulmonary airways and the stability of these airways, and may be important to the delivery of exogenous surfactant to deep regions of the lung.