1/7“Measurement Technology” Monthly Periodical – Article for the February 2013 issue
Classification

Products and technology

1)

Title

Vibration Rheometer RV-100002)

Subtitle

Viscosity of various liquids measured by a new method rheometer

3)

Keywords

Tuning-fork vibration rheometer, static viscosity

4-1)

Introduction

What follows explains the measurement
principles, product specifications andmeasurement case studies for the world’s
only tuning-fork vibration rheometer.
The history of measurement of viscosity
is quite long, and to date has focused on
cup-type, capillary-type, rotational-type
or falling-ball- type. For example, for thecontrol of engine oils, a cone-shaped
container called a Ford cup is used with acup-type viscometer. This method ofmeasuring viscosity involved pooling oilin the cone-shaped Ford cup andmeasuring the rate at which it passed
through a narrow hole at the bottom ofthe cone.
Each of these different types of viscosity
measurement has been used to measurespecific types of liquid in specific kinds ofindustry, forming some of the historicalbackground to viscosity measurement. In
relation to oils used in the automobile
industry, for example, the standards of
the American Society for Testing andMaterials (ASTM) are generally adopted.
However, all of these earlier viscosity
measurement methods are generally
lacking in versatility, and it has beendifficult to measure various types ofliquids quantitatively over a wide rangeof viscosity. This is also obvious from thefact that many viscometers have beenstandardized not as measurement
devices but as testing equipment limited
in application to the particular object
being tested.
Now a tuning-fork vibration rheometerhas been developed through use of a highsensitivity
tuning-fork
vibration
viscometer,
whichmoves
twotuning-fork-type oscillators in the middleof the fluid. Using this rheometer, theuser is now able to measure liquids witha low viscosity around the level of water
to liquids with viscosity as high as a thickhoney (around 10000 mPa•s) in quick
succession. At the same time, bychanging the amount of displacement of
the tuning-fork oscillators it is possible tomeasure viscosity using shear rate as aparameter. By using this tuning-fork
vibration rheometer it is now possible toeasily measure fluids with strong
non-Newtonian characteristics, such asdilatants,
Binghamplasticandthixotropic fluids.
With the high sensitivity tuning-fork
method, as the energy needed to detectviscosity is extremely low any change inthe composition of the fluid is also kept toa minimum when measuring. In thefollowing sections will be reported theprinciples
behindthetuning-fork
vibration rheometer, some measurement
experiments conducted, and a newphysical quantity measured by vibration
method: static viscosity.
4-2) Background to development of thevibration viscometer
The book that has become the bible in theviscosity-relatedworld,“Viscosity(Revised)” was published in November
1958. It was written by Michio Kawata,
who at the time was working in themeasurement research laboratory ofJapan’s Agency of Industrial Science andTechnology. Sadly, this book is not being

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published at present, but in Chapter 6
the author details many theories andpotential characteristics of vibration
viscometers.
The book details a viscometer device witha vibrating reed which can measure
fluids across a wide range of just a few cP
to tens of thousands of cP; has ameasurement accuracy of 3 to 5%; canperform continuous measurements; isable to measure samples of just 2 to 3cm3,much smaller comparatively to otherviscometers available; can measure
non-transparent fluids; can obtainviscosity x density figures; and is subject
to the influence of elasticity in the case ofviscoelastic fluids; with all of thesecharacteristics being principles of thetuning-fork vibration rheometer.
Other than this book, in a supplement tothe January 1957 edition of the in-house
publication of the Japanese Society ofPolymer Sciences “Polymers” there is anarticle called “Experimental Productionof a Vibration Viscometer” by Eiichi
Fukada.
Inthispublication,measurement principles, relationshipbetween the wall and the oscillator plate,
and actual experimental data such as thegelatinization of polyvinyl chloride, etc.,
are presented.
These vibration viscometers did not use
two oscillators as a tuning-fork, but theyshow that more than 50 years ago thetheory behind the vibration viscometer
had been confirmed and development wasable to advance to almost commercialviability. When there is only one
oscillator being used, the reactive force
relative to the drive force needed to power
the back-and-forth motion of theoscillator is generated in the axial section
supporting the oscillator and interfereswith the driving system. Particularly inthe low viscosity range when the drive
force is low, the effect as a damper of thefluid being measured itself is quite small
and there are latent problems such as
variability in measurements or not being

able to increase the sensitivity. Therefore,
the tuning-fork viscometer using two
oscillators with zero reactive force wasdeveloped to solve this problem.
5)

Measurement principle of thetuning-fork vibration viscometer andstatic viscosity

With the tuning-fork vibration viscometer,
two oscillators are resonated horizontallyin a similar fashion to the tuning-forks,
and the vibration energy needed to keep
the amplitude of the oscillators fixed iscompensated by electromagnetic force. In
other words, drive force equivalent to theviscosity resistance of the liquid isexerted, and as that drive force is
proportional to the viscosity resistancethe viscosity value is actually beingsought. Also, with vibration viscometers,in principle viscosity x density is beingsought as viscosity resistance. Thisviscosity x density is expressed as “staticviscosity”*1 and is distinguished fromdynamicviscosity
andkinematicviscosity.
With the tuning-fork vibration model, by
calculating the drive force necessary forthe oscillators to resonate, as well as themotion equation involving the inertia
term, viscosity term and elasticity term,
one can understand how the drive force
power is proportional to viscosity xdensity.
To explain the theoretical model behindthe vibration viscometer summarily, inthe device in Diagram 1 above, if theoscillators are vibrating at a frequency off , the mechanical impedance (Rz) thatthe oscillators receive from the fluid is:Rz  A πf
withf

representing

thevibration

frequency (Hz), A representing thesurface area of both sides of the oscillator
plate,  representing the viscosity of
the fluid and  its density. Here, if we
define the force by which the3/7

electromagnetic drive section gives theitto thefixed vibration velocity Ve
oscillator plate as F, we get the following
equation:Rz F A πfVeit

From this graph we can understand how
the force induced by the electromagnetic
drive is proportional to static viscosity(the product of viscosity  x density  )*1.
In actual measurements, the torquegenerated in the electromagnetic drive
section is controlled so as to maintain the
fixed vibration amplitude of theoscillators while in the sample fluid. The
tuning-fork vibration viscometer draws
on the fact that the electrical current
required to control that torque is
proportional to (viscosity x density), thatis, static viscosity.

Photograph 16)

point of the device, but by incrementallychanging the vibration amplitude of theoscillators to adjust the shear rate andthen calculating the shear stress from thesurface of the oscillators and the torqueused to drive them at each shear rate.
Also, as the unit system for static
viscosity is not yet determined at thetime of writing this report, wenondimensionalize values by assuming
the sample’s density to be 1.00 g/cm3,
equivalent to water, and express theviscosity by mPa•s. In Photograph 1 you
can see the exterior of the product. Theframework is the same as the viscometer.
Also, at present, the shear rate range
measurable by the RV-10000 is, whenbased upon water and JS2000, 0.2 to 1.2
mm by the amplitude of the oscillators,
and 10 to 2000 s-1 by shear rate
conversion. Because the oscillators on theRV-10000 experience repeated sine-wave
vibrations like conventional vibration
viscometersdo,unlikerotational
viscometers, a constant shear rate is not
maintained. It is for that reason that theconstantly varying shear rate isconverted and expressed as an effective
value. In other words, one must recognizethat the shear rate varies with time. The
relationship between shear rate and themeasurable range of viscosity for theRV-10000 is shown in Diagram 2.

Product exterior

Development of a tuning-fork
typerheometer
andactualmeasurement examples

In applying the technology of thetuning-fork vibration viscometer to thedevelopment of the rheometer (RV-10000),
while holding the maintenance of highsensitivity as the most important criteria
to ensure in the new product, the static
viscosity value was sought not bychanging the natural vibration frequency,
which forms the structural resonanceDiagram 2. Relationship between amplitude, viscosity,and shear velocity for Newtonian fluids

4/76-1)

Measuring Newtonian fluids

Below is explained the results ofmeasurements of water (ion-exchanged)
and JS2000 (a viscosity standard). Water
is scientifically speaking a chemicallystable substance which can be used as astandard for viscosity measurements,
and is defined to have a viscosity of 1.00
mPa•s at 20°C temperature. Whiletemperature variation is relatively small,at around room temperature there is adecrease of about 2% in viscosity forevery1˚Ctemperature
increase,demonstrating the necessity of paying
attention to temperature management.
In Diagrams 3 and 4, under conditions ofa constant 25°C temperature, viscosity
values are plotted for water and JS2000,
changing the oscillation amplitude from
0.2 (0.07) to 1.2 mm by peak to peak(from highest to lowest point). Diagram 3shows the proportionate relationshipbetween amplitude (shear rate) andviscosity (shear stress) for Newtonian
fluids. The JS2000, being a standard
fluid for viscosity measurement, also
demonstrates good Newtonian properties.

Diagram 3. Ion exchange water:
Amplitude-Viscosity, Driving current

Diagram 4. Standard fluid JS2000:
Amplitude-Viscosity, Driving current

6-2)

Bingham fluid (skin moisturizingcream)

The results of measurement experiments
conducted on moisturizing cream will
now be explained. Diagram 5 shows theresults of altering the amplitude of theoscillators by taking measurements at
0.07 / 0.10 / 0.20 / 0.4 / 0.6 / 0.8 / 1.0 / 1.2
mm intervals, approximately Δ0.2 mm
each time, starting at the minimum
amplitude and increasing to themaximum amplitude, before returning tothe minimum again.
The x-axis in Diagram 5 represents time,the y-axis on the left represents viscosity,and the y-axis on the right represents thedrive force (current) on the oscillator.
Diagram 6 uses the same the data as
Diagram 5, but shows the amplitude of
the oscillators on the x-axis, while they-axes show viscosity and the drive
current on the oscillators. The Bingham
fluid characteristic of viscosity dropping
dramatically as the amplitude of theoscillators exceeds a certain point canclearly be seen. Further, the thixotropic
nature of the moisturizing cream can beconfirmed, as even if the shear rate is
reduced the viscosity does not return to
its level at the start of the experiment. If
the viscosity of a moisturizing cream did
not drop after squeezing some into one’s

5/7

hands and rubbing it between them, thecream would have poor stretch and would
be hard to apply. Also, after applying it to
one’s face, the viscosity rising again
ensures there are no concerns with itdripping off. Therefore, this product could
be thought of as designed to hold these
special properties of Bingham fluids.
Diagram 7 shows the relationshipbetween the amplitude of the oscillatorsand viscosity for moisturizing cream in
response to a change in temperature. It
also demonstrates viscosity’s dependence
on temperature and the fact thatviscosity’s tendency to increase under alow shear rate does not change evenwhen temperature changes.

Diagram 5. Moisturizing cream:Time-Viscosity, Driving current

Diagram 7. Moisturizing cream:
Amplitude-Viscosity relative to Temperature change6-3)

Dilatant
fluid(cornstarchwatersolution: corn starch 62% +water 38%)

Graphs in Diagrams 8, 9 and 10 show theresults of measurements of a cornstarch
and water mixture. In such a mixture,when a spoon is rapidly stirred in it there
is a strong resistance, yet if the spoon isstirred gently hardly any resistance canbe felt at all. In other words, one can see
the phenomenon of the viscosity rapidly
increasing in response to an increase in
shear rate. When this cornstarch mixture
was measured, it was found that theviscosity jumped dramatically when theamplitude of the oscillators exceeded 0.8mm.
Diagram 8 is a similar graph to Diagram
5, showing the viscosity and drive currentof the oscillators at a series of different
amplitudes. Diagram 9 shows theoscillators’ amplitude on the x-axis andviscosity on the y-axis. At the point of theoscillators’ amplitude exceeding 0.8 mm,
the viscosity with a value previously
under 100 mPa・s can be seen to suddenly
jump to around 2000 mPa•s.

Diagram 6. Moisturizing cream:
Amplitude-Viscosity, Driving current

In Diagram 10, a graph is displayed for asimilar experiment conducted whileslightly increasing the proportion ofwater in the mixture. In the new mixture
with just 60% cornstarch, the sudden

6/7

increase in viscosity due to an increase in
shear rate cannot be seen. It wasprobably the first time that the quick
elastic response of dilatant fluid wasmeasured by the physical quantity ofviscosity.
In these experiments, theslight change to the blend ratio of just 2%
producing the completely different resultof no rapid increase in viscosity could beconsidered an extremely fascinating
result.

Diagram 10. Cornstarch: Amplitude-Viscosity
at different concentration7)

Diagram 8. Corn starch(Concentration 62%): Time-Viscosity

Conclusion and future challenges

Sale of the new RV-10000 rheometerusing a tuning-fork vibration method has
begun. By applying some of thetechnology used in A&D’s earlier
tuning-fork vibration viscometer with aproven sales record, and by altering theamplitude of the oscillators, the shear
rate has been made adjustable. Byexperimenting with several sample fluidswith characteristic properties, it wasconfirmed that by this way of changingshear rate, and accordingly using it as aparameter for measurement, suddenchanges in the viscosity or behavior of
non-Newtonian fluids could be measured.
In the future, A&D would like to develop
an improved product and quantify thecharacteristics of various low-viscosity
fluids, which can be made possible by useof the tuning-fork vibration rheometer,
thereby increasing the range ofapplications where the rheometer can beused.

Diagram 9. Corn starch(Concentration 62%): Time-Viscosity<References>*1『Static viscosity (sv) and vibration-type
viscometers 』 Society of Instrument andControl Engineers (Incorporated Assoc.),
Measurement Division, 24th Sensing Forum

Izumo, Naoto

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A&D Company Ltd., 1st Design andDevelopment Division, 5th Section
Asahi 1-243, Kitamoto City, Saitama
Prefecture〒364-8585
TEL：048-593-1362
E-mail：n-izumo@aandd.co.jp