Polymeric liquid bridges are known to fail during extension. This phenomenon of failure seemingly calls into question the operating principle of filament stretching rheometers. In these devices, a polymeric sample is initially placed between two plates. The sample is then stretched into a liquid bridge by moving the plates apart in a specified way. We here show that a steady extensional viscosity can be measured if the plates are separated in such a way that the stretch rate in the filament symmetry plane is kept constant, even for liquids highly prone to instability. Moreover, reliable measurements of the stress during a relaxation phase can be obtained as well. The conclusions are based on simulations for a number of constitutive equations, including the Newtonian liquid, the Oldroyd-B model, the differential non-stretch Rolie–Poly model, and the integral Doi–Edwards model with and without associated stretch relaxation dynamics.

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