Flow of a Bingham fluid in a concentric cylinder viscometer

We propose an evolution model for Bingham flows, starting from the constitutive law expressing the shear stress as a linear function of the shear rate. The governing equations are the equation of motion for the fluids in the viscous region and the equation of motion for the rigid part, which reduces to a boundary condition on the free boundary, that is, the surface dividing the fluid and rigid zones, where we assume that the strain rate is zero. Our model includes an approach to the study of the physical problem that takes into account the possible formation of rigid zones inside the fluid at the points where the shear rate becomes zero and possibly changes its sign.