Instability of collapsible tubes is studied theoretically and experimentally in many papers in the context of biological applications. Up to the present day, only Newtonian fluid flows in elastic tubes have been studied. However, there are circumstances when blood, bile and other biological fluids show essentially non-Newtonian behaviour. In this paper, we re-investigate theoretically axisymmetric stability of elastic tubes conveying power-law fluids. It is shown that for the power-law index $n=1$ , i.e. for the Newtonian case, axisymmetric disturbances in infinite-length tubes are damped, which is in accordance with experimental and theoretical observations, where the oscillations always involve non-axisymmetric motion of the tube walls. However, for $n<0.611$ , the axisymmetric disturbances can be growing, which predicts a new type of instability of elastic tubes conveying pseudoplastic (shear-thinning) fluids. For $n<1/3$ , local instability of axisymmetric perturbations becomes absolute in infinite tubes, while finite-length tubes become globally unstable. The effects of the axial tension, elastic tube length and, if present, lengths of inlet and outlet rigid tubes on the stability of finite-length tubes are analysed.
Experimental studies of the stability of the collapsible tubes conveying fluid have been previously conducted in the context of cardiovascular mechanics mostly for turbulent flows, although blood flows are laminar under normal conditions. In this paper, the turbulent and laminar regimes with equal flow rates and pressure drops are investigated experimentally to identify the stability boundary and self-exciting oscillation modes of Penrose tubes conveying fluid in the Starling resistor. Four oscillation modes for laminar and for turbulent regimes were observed visually and by measuring the pressure drop and the output pressure. Comparison of amplitudes, frequencies, and boundaries between different oscillation modes for equivalent laminar and turbulent flow regimes is performed.
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