The dynamics of collapsible tubes.

The importance of collapsible-tube phenomena derives primarily from blood, air and urine flows in mammals, although similar principles underlie invertebrate jetting and the avian syrinx. Biological fluid conduits have flexible walls and many experience higher external than internal pressures during physiological manoeuvres. The tube typically becomes noncircular, and large shape and cross-sectional area changes occur for small transmural pressure change. Two consequences ensue: a highly nonlinear constitutive relationship, and strong coupling between the fluid and solid mechanics. Depending on how flow is controlled, the tube can exhibit flow-rate-independent pressure-drop, or pressure-drop-independent flow-rate, or a locally negative slope to the pressure-drop to flow-rate relationship. At sufficiently large Reynolds number, these behaviours are accompanied by self-excited oscillation in a surprising variety of modes, including aperiodic ones. Chaotic behaviour has been predicted numerically, but not unequivocally demonstrated. Intrinsic chaotic oscillation must be distinguished from sensitivity to turbulent through-flow. To this end, the response to periodic upstream forcing is currently being investigated.