Viscous Dissipation in the Flow Between Eccentric Rotating Disks (Orthogonal Rheometer)

The orthogonal rheometer has become increasingly popular for determination of the viscoelastic properties of fluids. Here we present an analytical solution for the steady-state temperature distribution arising from the dissipation due to flow between infinite, isothermal eccentric rotating disks. This information is necessary to experimentalists concerned with obtaining accurate rheological characterizations for materials whose properties are temperature dependent, e.g., polymer melts. The results, temperature profiles and the maximum temperature rise, are presented using two dimensionless parameters which indicate the effects of inertia and fluid elasticity. Thus, the results can be easily used by practitioners to estimate the importance of dissipation in their experiments. For conditions of practical interest, temperature rises large enough to be of concern may be encountered.