The isochoric and isothermal flow of a viscoelastic fluid in the annular region between two confocal ellipsoids is investigated . This study is carried out in terms of the elliptic (prolate spheroidal) coordinates , where the inner and the outer ellipsoids are uniformly rotating; respectively, with angular velocities about the axis connecting their foci.
The equations of motion of first and second orders are formulated and solved for the first order only . However, the equation of second order indicates the presence of secondary flow superimposed onto the primary one. The stress distributions are computed and used to determine the resultant forces and torques acting on the outer elllipsoid when it is being at rest. An important result for rheometry is that the resultant torques can be used to determine the coefficient of viscosity .