When performing a shear startup experiment for several values of the shear rate, you measure the shear stress as a function of time; the transient shear viscosity is obtained as the ratio of the shear stress and the (constant) shear rate. In general, the measured curves exhibit an initial development of the transient viscosity that matches the linear behavior , and subsequently departs from the linear response. The departure from the linear response is delayed when a low shear rate is considered.

The Gleissle mirror relationship [6] is empirical and relates the linear transient viscosity, with the nonlinear steady shear viscosity, as follows:

(9–4)

That is, there is a graphical mirror relationship between the transient shear viscosity and the nonlinear steady shear viscosity. This relationship has been observed for oils, as well as polymeric melts such as polyisobutylenes and polyethylenes. It also provides a useful tool for validating measurements obtained via various techniques.

A second Gleissle mirror relationship concerns the first normal stress coefficient, . It is given by:

(9–5)

Here again, there is a graphical mirror relationship between the transient first normal stress coefficient and the corresponding nonlinear steady property.

When necessary, it may be possible to extend the Gleissle mirror relationship for obtaining preliminary information on the transient elongation viscosity.

(9–6)