The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N1 and N2, especially N1, and the extensional viscosity η(E). In this paper, we shall be mainly interested in 'constant-viscosity' Boger fluids, and, accordingly, we shall limit attention to N1 and η(E). We shall concentrate on two important flows - axisymmetric contraction flow and "splashin" (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high η(E) can retard the flow, whereas high N1 can have the opposite effect. In the splashing experiment, high η(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.