Stability and deformation of a wet elastic substrate

Motivated by an application to pulmonary alveolar micro-mechanics, the stability and deformation of an elastic septum lined with liquid films is investigated. The normal force balance on the septum, which is modeled as an inertia-less, kinematically nonlinear Euler-Bernoulli beam, yields an equation for the septal curvature that is coupled to time dependent lubrication equations for the adjacent liquid films. Linear stability analysis of the (compressed) flat configuration reveals that the presence of the films simultaneously stabilizes the buckling instability of the dry septum while introducing a new mode of flexural instability. Numerical simulations complemented by asymptotic analysis of the coupled system are used to explore the nonlinear development of the instabilities.