= Rheometer
{wiki}
A <rheometer> imposes a controlled <stress> or <deformation> and measures the complementary response. In a rotational instrument, a sample fills a gap between surfaces such as concentric cylinders, parallel disks or a cone and plate. The directly controlled or measured quantities include <torque>, angular displacement and <angular velocity>; the geometry converts these into <shear stress>, <shear strain> and <shear rate>.<Rheology and DMA Theory, Instrumentation, and Basic Methods by TA Instruments>[slides 8–14: geometries and the distinction between raw rotational signals and calculated material variables]{ref}
For example, a small-angle <cone-and-plate rheometer> produces approximately uniform <shear rate> $\dot\gamma=\Omega/\alpha$ and <shear stress> $\tau=3\mathcal T/(2\pi R^3)$, with cone angle $\alpha$, radius $R$, rotation rate $\Omega$ and measured <torque> $\mathcal T$. A <parallel-plate rheometer> instead has a radius-dependent <shear rate>. The conversion therefore requires the appropriate flow model. <Wall slip>, edge failure, <temperature> drift and the instrument's own <inertia> can mimic a material response, especially for very weak or rapidly varying signals.
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