Couette rheometer ($\mathcal{T}=4\pi \eta L\Omega R_i^2{R}_o^2/(R_o^2-R_i^2)$)

Concentric cylinders impose shear while torque and rotation measure a material's response. The displayed calibration holds for Newtonian laminar flow, inner-cylinder rotation and a stationary outer cylinder. In a narrow gap, the rate is approximately $\Omega R_i/(R_o-R_i)$ and inner-wall stress is $\mathcal{T}/(2\pi L{R}_i^2)$. End effects, wall slip and inertial secondary flow require control.