Analytical solution for the Hagen-Poiseuille flow of a hard sphere gas with nonlinear shear viscosity

We study the Hagen-Poiseuille flow in cylindrical geometry of a Zwanzig fluid, for which the shear viscosity is a highly nonlinear function of the shear rate. It is shown that the problem has a real solution only if the radial distance from the flow centreline is smaller than a critical value, showing that such a constitutive model is not always compatible with the flow under a constant pressure gradient. This leads to the introduction of scenarios such as shear banding, shear-induced phase transitions, and wall slip, which are generally believed to occur only in complex fluids.