The onset of flow-rate limitation and flow-induced oscillations in collapsible tubes

Experiments were mounted to investigate the onset in a ‘Starling resistor’ of collapsible-tube oscillation, at the lowest possible Reynolds number so as to facilitate matched numerical simulations. The protocol adopted was to set pressure outside the tube and inside the tube at the upstream end, constant and equal to each other, then to progressively lower the downstream pressure past the point of tube collapse and, when this occurred, of oscillation onset. The working fluid was a glycerine/water mixture, and the silicone-rubber tube was suspended horizontally in air. Measurements were made of pressures and flow-rates and of the cross-sectional area at the approximate location of maximum oscillation; separately, the cross-sectional area of the tube in relation to transmural pressure was measured. Parameters varied in the flow experiments were the length of rigid pipe downstream of the collapsing tube, and the fluid viscosity. The pressure/flow-rate coordinates of both the point of peak flow-rate achieved before flow-rate limitation, and the point of oscillation onset, were satisfactorily independent of the pipe length downstream. Both points occurred at flow-rates that decreased with increasing fluid viscosity, so that the corresponding Reynolds numbers decreased more so. Oscillation did not break out below a Reynolds number of about 290 unless there was external mechanical agitation of the apparatus. The amplitude of oscillation decreased progressively towards zero at this point as viscosity was raised. After the flow-rate peak, flow limitation causes a local flow-rate minimum. When oscillation occurred, it started just before this minimum, and died away at the minimum.