Editing Viscometer (section)

==Rotational viscometers==
Rotational viscometers use the idea that the torque required to rotate an object in a fluid is a function of the viscosity of that fluid. They measure the torque required to rotate a disk or bob in a fluid at a known speed.

"Cup and bob" viscometers work by defining the exact volume of a sample to be sheared within a test cell; the torque required to achieve a certain rotational speed is measured and plotted. There are two classical geometries in "cup and bob" viscometers, known as either the "Couette" or "Searle" systems, distinguished by whether the cup or bob rotates. The rotating cup is preferred in some cases because it reduces the onset of [[Taylor vortex|Taylor vortices]] at very high shear rates, but the rotating bob is more commonly used, as the instrument design can be more flexible for other geometries as well.

"Cone and plate" viscometers use a narrow-angled cone in close proximity to a flat plate. With this system, the shear rate between the geometries is constant at any given rotational speed.  The viscosity can easily be calculated from shear stress (from the torque) and shear rate (from the angular velocity).

If a test with any geometries runs through a table of several shear rates or stresses, the data can be used to plot a flow curve, that is a graph of viscosity vs shear rate. If the above test is carried out slowly enough for the measured value (shear stress if rate is being controlled, or conversely) to reach a steady value at each step, the data is said to be at "equilibrium", and the graph is then an "equilibrium flow curve". This is preferable over non-equilibrium measurements, as the data can usually be replicated across multiple other instruments or with other geometries.

===Calculation of shear rate and shear stress form factors===
Rheometers and viscometers work with torque and angular velocity. Since viscosity is normally considered in terms of shear stress and shear rates, a method is needed to convert from "instrument numbers" to "rheology numbers". Each measuring system used in an instrument has its associated "form factors" to convert torque to shear stress and to convert angular velocity to shear rate.

We will call the shear stress form factor {{math|''C''<sub>1</sub>}} and the shear rate factor {{math|''C''<sub>2</sub>}}.

: shear stress = torque ÷ {{math|''C''<sub>1</sub>}}.
: shear rate = {{math|''C''<sub>2</sub>}} × angular velocity.
:: For some measuring systems such as parallel plates, the user can set the gap between the measuring systems. In this case the equation used is
::: shear rate = {{math|''C''<sub>2</sub>}} × angular velocity / gap.
: viscosity = shear stress / shear rate.

The following sections show how the form factors are calculated for each measuring system.

====Cone and plate====
: <math>\begin{align}
  C_1 &= \frac{3}{2} r^3, \\
  C_2 &= \frac{1}{\theta},
\end{align}</math>

where
: {{mvar|r}} is the radius of the cone,
: {{mvar|θ}} is the cone angle in radians.

====Parallel plates====
: <math>\begin{align}
  C_1 &= \frac{3}{2} r^3, \\
  C_2 &= \frac{3}{4} r,
\end{align}</math>

where {{mvar|r}} is the radius of the plate.

'''Note:''' The shear stress varies across the radius for a parallel plate.  The above formula refers to the 3/4 radius position if the test sample is Newtonian.

====Coaxial cylinders====
: <math>\begin{align}
  C_1 &= 2\pi r_\text{a}^2 H, \\
  C_2 &= \frac{2 r_\text{i}^2 r_\text{o}^2}{r_\text{a}^2 \left( r_\text{o}^2 - r_\text{i}^2\right)},
\end{align}</math>

where:
: {{math|''r''<sub>a</sub> {{=}} (''r''{{sub|i}} + ''r''{{sub|o}})/2}} is the average radius,
: {{math|''r''<sub>i</sub>}} is the inner radius,
: {{math|''r''<sub>o</sub>}} is the outer radius,
: {{mvar|H}} is the height of cylinder.

Note: {{math|''C''<sub>1</sub>}} takes the shear stress as that occurring at an average radius {{math|''r''<sub>a</sub>}}.

===Electromagnetically spinning-sphere viscometer (EMS viscometer)===
[[File:EMS viscometer measuring principle.png|thumb|Measuring principle of the electromagnetically spinning-sphere viscometer]]

The EMS viscometer measures the viscosity of liquids through observation of the rotation of a sphere driven by electromagnetic interaction: Two magnets attached to a rotor create a rotating magnetic field. The sample ③ to be measured is in a small test tube ②. Inside the tube is an aluminium sphere ④. The tube is located in a temperature-controlled chamber ① and set such that the sphere is situated in the centre of the two magnets.

The rotating magnetic field induces eddy currents in the sphere. The resulting Lorentz interaction between the magnetic field and these eddy currents generate torque that rotates the sphere. The rotational speed of the sphere depends on the rotational velocity of the magnetic field, the magnitude of the magnetic field and the viscosity of the sample around the sphere. The motion of the sphere is monitored by a video camera ⑤ located below the cell. The torque applied to the sphere is proportional to the difference in the angular velocity of the magnetic field {{math|''Ω''<sub>B</sub>}} and that of the sphere {{math|''Ω''<sub>S</sub>}}. There is thus a linear relationship between {{math|(''Ω''<sub>B</sub> − ''Ω''<sub>S</sub>)/''Ω''<sub>S</sub>}} and the viscosity of the liquid.

This new measuring principle was developed by Sakai et al. at the University of Tokyo. The EMS viscometer distinguishes itself from other rotational viscometers by three main characteristics: 
* All parts of the viscometer that come in direct contact with the sample are disposable and inexpensive.
* The measurements are performed in a sealed sample vessel.
* The EMS viscometer requires only very small sample quantities (0.3&nbsp;mL).

===Stabinger viscometer===
By modifying the classic Couette-type rotational viscometer, it is possible to combine the accuracy of kinematic viscosity determination with a wide measuring range.

The outer cylinder of the Stabinger viscometer is a sample-filled tube that rotates at constant speed in a temperature-controlled copper housing. The hollow internal cylinder – shaped as a conical rotor – is centered within the sample by hydrodynamic lubrication<ref>Beitz, W. and Küttner, K.-H., English edition by Davies, B. J., translation by Shields, M. J. (1994). Dubbel Handbook of Mechanical Engineering. London: Springer-Verlag Ltd., p. F89.</ref> effects and [[centrifugal force]]s. In this way all bearing [[friction]], an inevitable factor in most rotational devices, is fully avoided. The rotating fluid's shear forces drive the rotor, while a magnet inside the rotor forms an [[eddy current brake]] with the surrounding copper housing. An equilibrium rotor speed is established between driving and retarding forces, which is an unambiguous measure of the dynamic viscosity. The [[speed]] and [[torque]] measurement is implemented without direct contact by a [[Hall-effect]] sensor counting the frequency of the rotating [[magnetic field]]. This allows a highly precise [[torque]] resolution of 50&nbsp;[[newton metre|pN·m]] and a wide measuring range from 0.2 to 30,000&nbsp;mPa·s with a single measuring system. A built-in [[density]] measurement based on the [[oscillating U-tube]] principle allows the determination of kinematic [[viscosity]] from the measured dynamic viscosity employing the relation
: <math>\nu = \frac{\eta}{\rho},</math>

where:
: {{mvar|ν}} is the kinematic viscosity (mm<sup>2</sup>/s),
: {{mvar|η}} is the dynamic viscosity (mPa·s),
: {{mvar|ρ}} is the density (g/cm<sup>3</sup>).