Torque reversal of a linear Oldroyd fluid ($\Omega (t)=-{\Omega }_{+}\left[1+\frac{2G_0\tau }{{\mu }_0}{e}^{-t/{\lambda }_2}\right]$)

In an inertialess cone-and-plate rheometer, reverse a steady torque from T to -T at time zero. The polymer shear stress remains continuous while the positive solvent viscosity allows the rate to jump. The linear stress equation gives ${\lambda }_2={\mu }_0\tau /({\mu }_0+G_0\tau )$ and the displayed velocity for t>0, where ${\Omega }_{+}=3\alpha T/[2\pi a^3({\mu }_0+G_0\tau )]$. The transient backward speed exceeds the final backward speed because stored polymer stress initially retains its former sign.