Molten polymers often flow very differently from simple Newtonian liquids.

For a Newtonian fluid, shear stress $\tau$ is proportional to shear rate $\dot\gamma$:

$$\tau=\mu\dot\gamma,$$

with constant viscosity $\mu$.

Many polymer melts are shear thinning: their apparent viscosity decreases as shear rate increases. A simple power-law model is

$$\tau=K\dot\gamma^n,$$

with $n<1$ for shear-thinning behavior. The apparent viscosity is then

$$\mu_{app}=\frac{\tau}{\dot\gamma}=K\dot\gamma^{n-1}.$$

If $n=0.5$, increasing shear rate by a factor of 100 reduces apparent viscosity by a factor of $100^{-0.5}=10$ in this idealized model.

Temperature also strongly affects polymer viscosity. Heating generally makes flow easier, but excessive temperature or residence time can degrade the polymer.

These effects matter because polymer processing drives melt through gates, dies and channels with very different local shear rates. A narrow gate can create high shear and low apparent viscosity while a large reservoir flows more slowly and remains more viscous.

Polymer process design therefore needs a processing window: temperature and flow conditions must permit filling or extrusion without excessive pressure, degradation or unstable flow.