Complex fluids that contain, for example, flexible long-chain polymers can undergo orders-of-magnitude increases in apparent extensional viscosity when they are stretched as compared to when they undergo shearing deformations. This is due to the ability of stretching flows to generate significant alignment and orientation of the macromolecules along the flow direction, which results in increased segment-solvent frictional interactions. Extensional viscosity is widely recognized as a fundamental material function that is necessary for the complete characterization of complex fluid samples. However, the measurement of extensional viscosity, particularly for dilute or low viscosity fluids, is one of the most challenging aspects of rheometry due to the dependence on both the extensional strain rate and the Hencky strain accumulated in the fluid. Some of the most successful devices developed for measuring extensional viscosity are the filament stretching extensional rheometers or (FiSER’s). In these instruments a quantity of test fluid is loaded between two circular parallel plates to form a cylindrical liquid bridge of diameter  and initial separation . The plates are then separated at an exponentially increasing rate such that , thus imposing a constant nominal extensional strain rate () on the fluid. As the fluid filament is stretched measurements are made of the tensile force, , on one of the endplates and the diameter of the fluid filament at its mid-point, . The instantaneous Hencky strain () is found from:

,                                                                                                                                                                    (1)

which can be differentiated to obtain the true strain rate at the midpoint of the filament:

.                                                                                                                                                                (2)

The transient extensional viscosity can be computed according to the expression:

,                                                                                                                                   (3)

where a small correction should be made to  to account for surface tension and gravitational body forces.

Figure 1. Sketch of a filament stretching experiment. (a) Initial configuration of endplates and fluid at time t = 0 s.        (b) Configuration at an arbitrary time t during the stretch.