The effects of small misalignment in the cone-and-plate rheometer on t
he flow of a Newtonian fluid, an upper-convected Maxwell fluid, and a
White-Metzner fluid are examined in detail. The method of domain pertu
rbation and the lubrication approximation are employed to calculate ve
locity and stress profiles to first order in the misalignment paramete
r epsilon. Results for the Newtonian fluid show symmetric velocity and
stress profiles around the plane at the widest gap. The two elastic f
luids studied exhibit asymmetry in their velocity and stress profiles
caused by fluid memory effects. Misalignment effects on torque and thr
ust measurements in the cone and plate are also discussed, and results
are compared with a similar calculation made for flow in the journal
bearing.