UNIAXIAL AND BIAXIAL UNSTEADY INFLATIONS OF A VISCOELASTIC MATERIAL

Two cases of unsteady viscoelastic elongational flow configurations are considered theoretically, namely the inflation of an infinite cylinder (uniaxial elongation) and that of a sphere (biaxial elongation) subject to a constant pressure difference. The evolution of the viscoelastic material is modelled using the modified ZFD (MZFD) constitutive equation. The various adjustable parameters are established on the basis of shear flow measurements. In this work we examine the influence of the Deborah number, De, and the initial thickness-to-radius ratio, R(r). It is found that in the spherical configuration the volume growth is not always monotonic with time for all De values and is oscillatory for large De and large material thickness. The oscillations eventually die out in the long time limit as the thickness becomes small and the influence of normal stresses is no longer significant. In the small De range the growth is monotonic. In the limit of small R(r) values, viscous effects become negligible and the flow approaches an ideal behaviour. In the present geometries the fluid pressure is decoupled from normal stresses and (radial) velocity so that the pressure has no influence on material growth. However, when the fluid pressure itself is determined from the radial momentum equation it is found to decrease as the material expands and eventually reaches a zero value at a critical time which depends on De, R(r), the outer-to-inner pressure ratio and the capillary number. This indicates that the material, not withstanding any internal pressure, has reached the growth limit or rupture.