SIMPLE RESISTIVE MODELS FOR STEADY FLOW THROUGH UNIFORM AND TAPERED-STIFFNESS COLLAPSIBLE TUBES

An extremely basic model is postulated and examined numerically, to find out which aspects of observed steady-flow collapsible-tube behaviour are predicted and can be explained. The model in simplest form states that the tube has a fixed viscous resistance per unit length when not collapsed, and a higher one when collapsed. Collapse occurs where the falling internal pressure in the streamwise direction causes negative transmural pressure to pass a fixed threshold set by tube wall stiffness. This model suffices to explain (i) the sigmoidal dependence of pressure drop on flow rate when external pressure is fixed, (ii) the weak dependence of pressure-drop on flow rate when downstream transmural pressure is fixed and (iii) the weak dependence of flow rate on pressure drop when upstream transmural pressure is fixed. The effects of incorporating more realistic collapse behaviour (finite compliance once the tube buckles, varying compliance once opposite walls are in contact) on these dependencies are examined. The model is also used to explore the several qualitatively distinct configurations that may be taken up by a tube which varies in stiffness along its length.