STEADY OSTWALD FLOW BETWEEN 2 DIFFERENTIALLY ROTATING COAXIAL DISCS

The steady flow of a power-law (Ostwald) fluid between two differentia lly rotating, parallel, co-axial discs has been considered for both la rge and small Reynolds number. All edge effects of the discs are negle cted, the discs rotate in the same sense and the distance between the two discs is much smaller than their radius. In the large Reynolds num ber case a similarity solution is sought. It is assumed that the flow consists of boundary layers on the discs, while the core rotates as a rigid body with speed intermediate of those of the discs. The boundary layer is thinner than in the equivalent Newtonian problem, and the de cay of the boundary layers is found to be algebraic. This slow decay c ontrasts with the faster exponential decay in the Newtonian case. For the low Reynolds number problem, the ratio of the disc separation to r adius was taken to be much smaller than the Reynolds number. This is, in effect, a lubrication-type problem. The velocity components are exp ressed as expansions in ascending powers of the Reynolds number. For b oth the large and small Reynolds number flow, the torque is calculated as a function of the disc speeds, for various values of the power-law index n.