Flow in collapsible tubes: Computations, experiments and (at last!) a rational mathematical model for the onset of self-excited oscillations

Lead Research Organisation: University of Manchester
Department Name: Mathematics


Many physiological flows (e.g. blood flow in the veins and arteriesor the flow of air in the pulmonary airways)are strongly affected by the interaction between the fluid flowand the vessel wall elasticity. The problem of flow in collapsible tubes has therefore received much interest in the biofluids researchcommunity. Experimentally, the problem is typically studied with a `Starling resistor', a device in which fluid isdriven through a finite-length, thin-walled, elastic tube whichis mounted on two rigid tubes and enclosed in a pressure chamber.One of the most striking features of this system is its propensity to develop large-amplitude self-excited oscillations. Our understanding of the mechanism(s) that initiate and maintain these oscillations is still very limited. It is the aim of this research proposal to undertake the firsttruly comprehensive study of flow in 3D collapsible tubes, employinga combination of theoretical (asymptotic), numerical and experimental methods.


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Whittaker R (2010) A Rational Derivation of a Tube Law from Shell Theory in The Quarterly Journal of Mechanics and Applied Mathematics