How do we measure viscosity? Download the webinar to view how great engineering minds have tackled this question over the years. We trace the historical development of viscosity and viscometers; starting with the fundamental principles established by Sir Isaac Newton and leading up to modern-day viscometry methods. www.RheoSense.com http://www.rheosense.com/viscosity-webinars http://www.rheosense.com/applications

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1Rheology: An Historical Perspective; R.I Tanner and K.Walkers, Elsevier 1998
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Source: Wikipedia, “Viscosity.gif” https://en.wikipedia.org/wiki/File:Viscosity.gif

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• This method requires large
sample volumes and is only
accurate for Newtonian fluids
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SUS (at 37.8oC) cSt
32.6 2
97.8 20
463 100

9. • We jumped straight from the era of Greek philosophers to the 20’th
century, using the term ‘viscosity’ that was only introduced in 1929!1
• But how did the concept of viscosity develop in between?
• For a very long time…. it didn’t!
• That is to say…the underpinnings of viscosity have been developed
over the last two millennia-topics such as buoyancy or density,
uniformly accelerated motion and drag. Because viscosity
measurement relies on many other concepts, it is difficult to concisely
explain it’s history. As a result, we’ll only mention the major
developments.
91Rheology: An Historical Perspective; R.I Tanner and K.Walkers, Elsevier 1998

10. • One of the largest early developments was Newton’s work
on conservation of momentum (1687) and the concept of
pressure, which was later expanded upon by Pascal.
Newton calls the viscosity “the lack of slipperiness of the
parts of the liquid”1 . Newton postulated on the idea of a
fluid exhibiting a friction force, and how it relates to shear
stress.
• The deformation and flow of materials was expanded
upon Daniel Bernoulli (1743); with the Bernoulli principle.
• At around this time (1757), Leonhard Euler developed his
equations governing inviscid flows (known as Euler’s
equations)- leading to a complete, modern statement of
mass-conservation. Interestingly enough, the earliest
references to these relations date back to 2’nd century AD.
101Sir Isaac Newton, Principia, 1687
"GodfreyKneller-IsaacNewton-1689" by Sir Godfrey
Kneller -
http://www.newton.cam.ac.uk/art/portrait.html

11. • In 1822, Claude-Loise Navier and George Stokes publish
the Navier-Stokes equations, which expand upon Euler’s
equations and are a key underpinning of studies
involving fluid behavior.
• In 1840, Gotthilf Heinrich Ludwig Hagen and Jean
Léonard Marie Poiseuille published the Hagen-Poiseuille
equation, dictating the pressure drop of a
incompressible, Newtonian fluid in laminar pipe flow.
• A short while later the Darcy-Weisbach equation was put
in its final form, relating the pressure loss due to friction
to the average velocity of a fluid.
• Many more developments occurred since then, but we
will not focus on them at this time.
11
Licensed under Public Domain via Commons -
https://commons.wikimedia.org/wiki/File:Poiseuille
.jpg#/media/File:Poiseuille.jpg

12. These viscometers are known by many names,
such as U-tube viscometers, Ostwald
viscometers (after Wilhelm Ostwald, 1853-
1932, one of the major founders of physical
chemistry), and Ubbelohde viscometers (after
Leo Ubbelohde, 1877-1964, another notable
German chemist)
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"Ostwaldscher Zähigkeitsmesser" by Wilhelm Ostwald
https://commons.wikimedia.org/wiki/File:Ostwaldscher_Z%C3%A4higkeitsmesser.jpg#/media/File:Ostwaldscher_Z%C3%A4higkeitsmesser.jpg
𝜈 = 𝑡𝑖𝑚𝑒 × 𝐶

13. Operation:
Fluid is first drawn into the upper bulb via
suction
The fluid is then allowed to flow back into the
lower bulb, and the time it takes to move
from one marking to the next (labelled ‘c’ and
‘d’) is observed
This time is then used to calculate kinematic
viscosity, either via a manufacturer-provided
equation or by comparison with a standard.
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"Ostwaldscher Zähigkeitsmesser" by Wilhelm Ostwald
https://commons.wikimedia.org/wiki/File:Ostwaldscher_Z%C3%A4higkeitsmesser.jpg#/media/File:Ostwaldscher_Z%C3%A4higkeitsmesser.jpg

14. • Patented in 1932 by Fritz Hoppler
• First viscometer to measure dynamic
viscosity!
• Based on Stoke’s Law
• A sphere of known weight and size is
dropped into fluid, and is allowed to reach
terminal velocity
• The terminal velocity is measured, and the
frictional force (Stoke’s Drag) is calculated.
From there, dynamic viscosity can be
determined.
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𝜂 =
2
9
𝑟2
𝑔(𝜌𝑠 − 𝜌 𝑓)
𝑉𝑠

15. • All of the preceding viscometers have several
similar disadvantages
• They all rely on gravity-driven flow
• This means that highly viscous samples will have long
measurement times
• In addition, this means that shear rates cannot be
controlled or changed
• For Newtonian fluids, this does not matter, but it makes
accurate characterization and comparison of Non-Newtonian
fluids impossible.
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16. • Also similar to cup-and-bob or
Coutte viscometers
• Mentions of similar types of
rotational viscometers date back to
at least 1931
• These viscometers feature a
cylindrical element (the spindle, or
bob) suspended in a cup of fluid.
• The spindle is rotated inside the fluid
by a motor, and the torque required
to rotate the spindle at a certain
speed is measured
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𝜂 = 𝐾
𝑇𝑜𝑟𝑞𝑢𝑒
𝜔

17. • This torque value can then be
converted to dynamic viscosity
values using manufacturer-
provided calculations
• Compared to cone and plate
viscometers, spindle-type
viscometers typically require
greater sample volumes, but have
improved resolution for low
viscosity fluids
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𝜂 = 𝐾
𝑇𝑜𝑟𝑞𝑢𝑒
𝜔

18. Fluid
• Similar in mechanism to
spindle-type viscometers.
• Instead of a cylindrical
element suspended in the
fluid, these feature a
conical element on the
surface of the fluid.
• This design allows for
accurate characterization of
shear rates.
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Cone
Plate
𝜂 =
𝜏 (𝑡𝑜𝑟𝑞𝑢𝑒, 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦)
𝛾 (𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦)

19. Fluid
• This makes a cone and plate
design superior to a spindle-
type design for Non-Newtonian
fluids
• The design allows for:
• smaller sample volumes than
spindle type
• increases complexity of setup
(‘setting the gap’, cone must be
carefully aligned with surface of
the fluid)
• sensitivity to particulates, and
reduced resolution at low
viscosity (surface area is lower, so
friction will be lower for same
viscosity)
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Cone
Plate
𝜂 =
𝜏 (𝑡𝑜𝑟𝑞𝑢𝑒, 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦)
𝛾 (𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦)

20. • Combination of old principles and new technology
• Old principle: Hagen-Poiseuille flow for incompressible fluids
• New technology: fabrication of microfluidics and MEMS technology
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21. Microfluidic Viscometers
• As fluid passes through the flow channel at a
fixed flow rate, it experiences a drop in
pressure that is measured with multiple
sensors
• This pressure drop is directly related to shear
stress, which in turn can be used to calculate
fluid viscosity
• This technique allows for accurate
determination of viscosity and control of
shear rate
• Allows for characterization of Non-
Newtonian samples, small sample volume
measurements, and a broad shear rate range
(no turbulence concerns)
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𝜏 ~ Δ𝑃
𝛾 ~ 𝑄
𝜂 =
𝜏
𝛾

22. Other Modern Viscometry methods
• In the last several decades, the assortment of instruments used for
viscometry has exploded into a vast arrangement. We’ve mentioned the
most common viscometry methods above, but here is a handful of others:
• Oscillating Piston viscometer
• Analyzes travel time of piston oscillating in fluid to calculate shear stress
• Stabinger viscometer
• Modified version of a Couette viscometer (inverted version of standard spindle
viscometer, where the sample container rotates and the spindle is stationary
• Bubble viscometer
• Measures rise time of bubbles in low viscosity fluid to calculate the viscosity
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