Newtonian Fluid Dynamics in a Misaligned Parallel-Plate Rheometer

A rheometer is a fluid viscosity measurement device in which a fluid is commonly placed in between two parallel plates, and one of the plates rotates relative to the other in order to induce a shear on the fluid of interest. By measuring the torques and forces applied on the plates by the fluid as a function the rotation rate of the moving plate, the viscosity of the fluid can be characterized. Many studies and experiments are conducted under the assumption that the two plates of the rheometer are perfectly parallely aligned; however, unintentional misalignment in the plates can commonly occur through small errors in the manufacturing process. To examine the effect that misalignment plays on viscosity measurements taken by a rheometer, we derive a theoretical model for the behavior of a general Newtonian fluid in a rheometer with misaligned plates. We show that this misalignment can produce additional secondary velocity components and pressures in the fluid, which can greatly affect the forces and moments present in the rheometer and lead to underestimation of the viscosity of the fluid, especially at small rheometer gap heights. We also perform 3D numerical simulations of the system using OpenFOAM to validate the theoretical results, and these simulations provide additional detail to the flow structure inside the rheometer.