A DOMAIN PERTURBATION STUDY OF STEADY FLOW IN A CONE-AND-PLATE RHEOMETER OF NONIDEAL GEOMETRY

The method of domain perturbation developed by Joseph is used to calcu late velocity and stress profiles in a slightly misaligned cone-and-pl ate rheometer where the cone is spinning and the plate is stationary. Results for a Newtonian fluid, a Criminale-Ericksen-Filbey fluid, an u pper-convected Maxwell fluid, and a White-Metzner fluid are presented and compared with earlier results in which the cone is stationary and the plate is spinning (Dudgeon and Wedgewood, 1993). Streamlines calcu lated for the Newtonian fluid show a very small recirculationl region near the stationary plate. Velocity and stress contours are symmetric around the plane of largest gap width. For the elastic fluids studied, streamlines are asymmetric. The fluid response lags where the fluid i s dominated by memory effects. Much larger recirculation regions are c alculated for fluids dominated by shear thinning. These recirculation regions contain a large fraction of the fluid in the apparatus and hav e the effect of changing the shape of the flow domain for the remainin g fluid that rotates around the cone's axis. Elasticity also has a pro nounced effect on the stress profile, indicating that the accuracy of the cone and plate may be compromised even for small mis-alignments.