FLOW LIMITATION IN UNIFORM THICK-WALLED COLLAPSIBLE TUBES

To investigate the flow-rate limitation behaviour of the same thick-walled silicone-rubber tubes with aqueous flow as have previously been characterized by this laboratory in terms of their pressure-drop limitation behaviour, we measured how the pressure drop along the tube varied with flow rate, when both the upstream head and the external pressure were varied in such a way as to keep the transmural pressure at the upstream end to the tube at a series of constant values. Flow limitation with ‘negative effort dependence’ occurred, and it was found that the flow rate depended not just on the upstream transmural pressure but also on its history, in a hysteretic manner. Furthermore, when external pressure was being reduced to the required point, either flow limitation or absence of collapse could be obtained for the same values of upstream transmural pressure. The reductions in flow rate when flow limitation came into effect were typically much greater, relative to the flow-limited flow rates themselves, than has been reported by others using thinner tubes and lower flow rates. Large-amplitude self-excited oscillation was confined to this reducing-flow-rate transition when external pressure was being increased to set the required point, and largely confined to this transition when it was being reduced. Flow limitation was mostly associated with only small-amplitude noise-like fluctuations of the downstream pressure. The transition was analysed and explained by reference to modified control-space diagrams, which show explicitly all oscillatory and divergent instabilities as closed regions. The prominence of the transition in these results forced consideration of whether flow limitation occurs when the flow rate ceases to increase or when it becomes substantially independent of the pressure drop. In adopting the latter definition, we were led to hypothesize that the initial collapse-inducing instability is not the result of choking.