Stokes flow in collapsible tubes: computation and experiment

We are concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics. In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically nonlinear shell theory. Finite element methods are used to solve the large-displacement fluid-structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups