Following , we solve for the 2D creeping flow between two coaxial cylinders. The inner cylinder rotates at a constant speed. The outer cylinder is fixed. The viscosity is a function of the second principal invariant of the shear strain rate tensor:
We use a general Herschel-Bulkley formulation of the form:
where τy is the yield stress. The solutions obtained for the stationary tangential velocity profiles for Newtonian, Power law (N=0.5), Herschel-Bulkley (µ=0.0672, τy=0.12, N=0.5) and Bingham (µ=1, τy=10, N=1) fluids are illustrated on Figure 67, together with the analytical solutions given by .
The Bingham fluid case is a particularly severe test of the diffusion solver, as the outer part of the fluid ring (r>0.35) behaves likes a rigid body attached to the outer boundary.