Rapid conical flows of viscoelastic solutions

Several examples of conical, stretching flows of viscoelastic solutions are described. Two cases are then examined in more detail, the rapidly stretching free jet and an internally pressurised sheet of liquid in which extension takes place in a circumferential direction.It is shown that both the stress and strain rate may readily be calculated at different positions, provided certain assumptions are made. The changes of extensional viscosity necessary to produce the specified flow geometries are then shown to be anomalous and inconsistent. If, however, a solid-like model based on the Green measure of strain is used, a more satisfactory interpretation of the behaviour is achieved.It is emphasised that these are high-speed, high Deborah number flows and that such a flow pattern is not a general one.An example is also given in which the stretching of rubber is shown to be consistent with the same solid-like model, and values of the extensional moduli of elasticity are quoted for both liquids and rubber.