8.3.3 Shear Thinning

Early NEMD simulations yielded an unexpected result: at high shear rates ( $\gamma^{*} \approx 1$) the viscosity decreased strongly, to increase again at even higher $\gamma$. (See, e.g. [Heyes et al., Mol. Phys. 57(1986)1265].)

This ``Non-Newtonian'' behaviour may indeed be observed experimentally. While a value of $\gamma^{*}=1$ is unrealistically high for gases, it is in an accessible range for liquids composed of large molecules, i.e. polymer melts:

$$\gamma^{*}= 1 \;\;\; \rightarrow \;\;\; \gamma \equiv \frac{... ...ta z} = \frac{1}{t_{0}} = \sqrt{\frac{\epsilon}{m \sigma^{2}}}$$ (8.42)

Argon: $\gamma =1/t_{0}=0.3 \cdot 10^{12} s^{-1}$; with $\Delta z=10^{-4} m$ this would mean $\Delta u_{x}=0.3 \cdot 10^{8} ms^{-1}$

Colloid: Let $\sigma=10^{-6} m$ and $m=10^{-15} kg$; then $t_{0}=1 s$ and with $\Delta z=10^{-3}\, m$ we have $\Delta u_{x}=10^{-3} ms^{-1}$.

Explanation: When $u_{x}$ becomes comparable to the thermal speed, the molecules spontaneously arrange in flow lines that glide along each other without interdiffusion. A plane perpendicular to the lines will be crossed at points that form a hexagonal lattice.

At even higher shear the formation of vortices destroys the flow line pattern, and the viscosity increaes again.

Heyes' results were later challenged and suspected of being computational artefacts after all, the argument being that the specific method of thermostating the sample was the source of trouble. As with Spring 2002 the issue seems unsettled.

[Lit.??]