Flow of a magnetic fluid between eccentric rotating disks

We discuss the flow of a magnetic fluid between two parallel disks rotating about non-coincident axes, normal to the disks, but with same angular velocity. This device is known as an orthogonal rheometer and has been used to measure the rheological properties of polymer melts and viscoelastic fluids. For a certain range of effective relaxation times, we obtain an exact solution of this three-dimensional problem in a magnetic fluid and determine the forces exerted by the fluid on one of the rotating disks.