Extensional rheometry of polymeric fluids and the uniaxial elongation of viscoelastic filaments

For viscoelastic fluids such as polymer melts and solutions, the transient uniaxial extensional viscosity is a function of both the rate of stretching and the total deformation or strain imposed. Knowledge of the resulting material function is of great importance in governing the dynamics and stability of polymer processing operations such as fiber-spinning, film-blowing and blow molding. Filament stretching rheometers provide one of the few ways of unambiguously measuring the transient elongational response of ‘mobile’ polymeric fluids that are viscous (1 ≤ η ≤ 1000 Pa.s) but not rigid enough to test in the extensiometers commonly employed for extremely viscous melts such as polyethylene and polypropylene (Hosstetler & Meissner, 1994). However, even in these filament stretching devices the deformable nature of the free-surface of the test fluid and the no-slip boundary conditions pinning the liquid bridge to the endplates preclude truly homogeneous kinematics and it is essential to combine experimental measurements with computational rheometry in order to understand the dynamical characteristics of the device. In the present work, we combine experimental measurements on polymer solutions and polymer melts in a temperature-controlled Filament Stretching Rheometer (F ISER) with time-dependent finiteelement numerical simulations using single and multi-mode formulations of the Giesekus model. During the imposed uniaxial elongation, numerical calculations are able to quantitatively simulate the measured stress growth in the materials. However, experiments and calculations show that the dynamical response of the fluid filament is strongly dependent on the exact form of the transient extensional viscosity. We show that even if a non-Newtonian fluid exhibits some strain-hardening, this can be insufficient to stabilize the contraction in the filament radius as the sample is exponentially elongated. Effects such as elastic recoil in parts of the filament result in a localized rate of thinning or ‘necking’ that is enhanced beyond that of a strain-independent Newtonian filament, and the elongating fluid thread can ‘neck down’ and break in a finite time. This qualitative difference compared with strongly strain-hardening elastic fluids can be understood in terms of a modified Considere analysis commonly employed for describing necking in tensile tests of solid polymer samples. Finally, following cessation of stretching at a finite strain, the tensile stresses in the elongated column rapidly relax and experiments and simulations show