Surfactant spreading on thin viscous films: film thickness evolution and periodic wall stretch

Surfactant spreading on thin viscous films is of interest in the context of surfactant and liquid transport in the lungs, for both normal lung function and treatment of disease, as well as for many industrial processes. This paper presents experimental techniques for the measurement of film deformations due to spreading surfactant and for the investigation of the effects of periodic stretching of the wall supporting the thin film to mimic airway wall motion in the lung due to breathing. Additionally, we present results from both types of experiments, which agree favorably with our theoretical work. List of symbols Bo Bond number Ds surface diffusivity g acceleration due to gravity h film thickness h0 initial film thickness Ld radial position of surface compression disturbance L0 initial radial position of leading edge of new surfactant front Lnew radial position of new surfactant front p pressure Pe Péclet number R membrane well radius R0 initial membrane well radius R̂ R0/L0, non-dimensional initial membrane well radius (same as cycle average well radius) Re Reynolds number t time TC stretching cycle period TC/V ratio of stretch time scale to viscous-surface-tension time scale TV viscous-surface-tension time scale u radial velocity U viscous-surface-tension velocity scale w vertical velocity x radial coordinate z vertical coordinate a shape parameter for initial surfactant distribution Dh film thickness deformation Dx horizontal shift in grid position aspect ratio G surfactant surface concentration Gref reference surfactant surface concentration G0 pre-existing surfactant initial surface concentration G1 new surfactant initial surface concentration g refractive index of fluid l viscosity h angle of incidence q density r surface tension rmax maximum surface tension n membrane wall coordinate