Certain polymers exhibit two distinct branches in their capillary flow curves (wall shear stress
versus apparent wall shear rate). This gives rise to oscillatory flow in constant‐piston‐speed
rheometers and to flow curve hysteresis in controlled‐pressure rheometers. These curious
phenomena have attracted considerable interest over a period of many years, but their basic
mechanisms are still the subject of debate. Building on previous work we have developed a
model that predicts all the essential features of the curves of pressure and flow rate versus …