Editing Viscometer (section)

==Rectangular-slit viscometer==
The basic design of a rectangular-slit viscometer/rheometer consists of a rectangular-slit channel with uniform cross-sectional area. A test liquid is pumped at a constant flow rate through this channel. Multiple pressure sensors flush-mounted at linear distances along the stream-wise direction measure pressure drop as depicted in the figure:

[[File:Rectangular slit.png|center|m-VROC Rectangular Slit Viscometer/Rheometer|alt=Rectangular Slit Viscometer/Rheometer]]<ref>{{cite web | url=https://www.rheosense.com/technology | title=Viscometer/Rheometer-On-a-Chip, VROC Technology }}</ref>

'''Measuring principle:''' The slit viscometer/rheometer is based on the fundamental principle that a viscous liquid resists flow, exhibiting a decreasing pressure along the length of the slit. The pressure decrease or drop ({{math|∆''P''}}) is correlated with the shear stress at the wall boundary. The apparent shear rate is directly related to the flow rate and the dimension of the slit. The apparent shear rate, the shear stress, and the [[apparent viscosity]] are calculated:

: <math>\begin{align}
  \dot{\gamma}_\text{a} &= \frac{6Q}{wh^2}, \\
                 \sigma &= \frac{wh}{2(w + h)} \frac{\Delta P}{l}, \\
          \eta_\text{a} &= \frac{\sigma}{\dot{\gamma}_\text{a}},
\end{align}</math>

where
: <math>\dot{\gamma}</math> is the apparent shear rate (s<sup>−1</sup>),
: {{mvar|σ}} is the shear stress (Pa),
: {{math|''η''<sub>a</sub>}} is the apparent viscosity (Pa·s),
: {{math|∆''P''}} is the pressure difference between the leading pressure sensor and the last pressure sensor (Pa),
: {{mvar|Q}} is the flow rate (ml/s),
: {{mvar|w}} is the width of the flow channel (mm),
: {{mvar|h}} is the depth of the flow channel (mm),
: {{mvar|l}} is the distance between the leading pressure sensor and the last pressure sensor (mm).

To determine the viscosity of a liquid, the liquid sample is pumped through the slit channel at a constant flow rate, and the pressure drop is measured. Following these equations, the apparent viscosity is calculated for the apparent shear rate. For a Newtonian liquid, the apparent viscosity is the same as the true viscosity, and the single shear-rate measurement is sufficient. For non-Newtonian liquids, the apparent viscosity is not true viscosity. In order to obtain true viscosity, the apparent viscosities are measured at multiple apparent shear rates. Then true viscosities {{mvar|η}} at various shear rates are calculated using Weissenberg–Rabinowitsch–Mooney correction factor:<ref>{{Cite web | url=https://www.rheosense.com/en/en-us/en/thank-you-wrm-viscosity-correction | title=Viscosity Correction: Weissenberg-Rabinowitsch-Mooney (WRM) | archive-url=https://web.archive.org/web/20240129183201/https://www.rheosense.com/en/en-us/en/thank-you-wrm-viscosity-correction | archive-date=2024-01-29}}</ref>

: <math>\frac{1}{\eta} = \frac{1}{2\eta_\text{a}}\left(2 + \frac{\mathrm{d} \ln{\dot{\gamma}_\text{a}} }{\mathrm{d} \ln{\sigma}}\right).</math>

The calculated true viscosity is the same as the cone and plate values at the same shear rate.

A modified version of the rectangular-slit viscometer/rheometer can also be used to determine apparent [[extensional viscosity]].