Flow of Bingham fluids in an orthogonal rheometer

We consider the flow of a viscoplastic fluid between two parallel discs that rotate at the same angular velocity about axes perpendicular to the discs, but not coincident. This device is known as the orthogonal rheometer, and it is also referred to as an eccentric rotating disc device. The Biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest. The equations of motion are solved numerically to determine the velocity field and the stress components. The location of the yield surface is also determined numerically. An asymptotic solution of the equations of motion in the Bingham limit has also been constructed. A comparison between the numerical and asymptotic solutions for the location of the yield surface is given.