COLLAPSIBLE TUBE FLOW: A MATHEMATICAL MODEL

摘要

In human body, all the conduits are flexible and also collapsible. That is, when the external pressure exceeds the internal pressure, the tube cross-sectional area can be significantly reduced, if not fully diminished. In this paper, a mathematical model describing the fluid dynamics of collapsible tube is presented. Analytical solutions are constructed for the problem using perturbation technique. The computer extension of the resulting power series solutions, its analysis and analytic continuation, including bifurcation study is performed with a special type of Hermite-Pade approximants. We obtained accurately a turning point R_c (R the flow Reynolds number), as well as the asymptotic behaviour of the skin friction and fluid pressure gradient as R → 0 on the secondary solution branch. The model is most appropriate to simulate wind tunnel tests on rheological phenomenon in physiological systems.