A brief lesson in viscosity

Johnson and Steinberg reply: In particle physics, viscosity is rarely discussed at the microscopic level, and many in the field are similarly surprised by the counterintuitive relationship between shear viscosity and interaction strength. In kinetic theory, shear viscosity typically scales in inverse proportion to the cross section; that is, the larger the cross section, the smaller the shear viscosity. Furthermore, the quantity of direct interest, the ratio of shear viscosity to entropy density, turns out to be proportional to the mean free path of the system constituents. Thus it is the smallest for systems with the strongest interaction. In such systems, disturbances—imagine putting an oar in water—are propagated nearly perfectly without dissipation. As the interactions between constituents become weaker, dissipative effects become more dominant, damping out local disturbances. As a system with noninteracting particles, an ideal gas has essentially an infinite viscosity, since there are no interactions to propagate disturbances.

We emphasize the ratio of shear viscosity to entropy density, which typically scales with the density of particles in the system, since the absolute scale of shear viscosity itself does not lead to meaningful comparisons between different materials. The absolute shear viscosity of the quark—gluon plasma is estimated at 5 × 10¹¹ Pa · s, while pitch has a shear viscosity of 2.3 × 10⁸ Pa · s (both numbers are from http://en.wikipedia.org/wiki/Viscosity ). The difference in how the two systems flow is not just about the interaction strength but about the densities and temperatures involved.