Article for the 29th Sensing Forum

Characteristics of Tuning-fork Vibration Rheometer
RHEO-VISCO RV-10000

Presented by: Naoto Izumo, Yuji Fukami, and Masahiro Kanno
R&D Division 5, A&D Company, Limited
Organized by: The Society of Instrument and Control Engineers (SICE)

September 27 to 28, 2012
Hitachi Campus, Ibaraki University
Ibaraki, JAPANCharacteristics of Tuning-fork Vibration Rheometer
RHEO-VISCO RV-10000
Naoto Izumo, Yuji Fukami, Masahiro Kanno A&D Company Limited
Higashi-Ikebukuro, Toshima-ku, Tokyo 170-0013 Japan
Abstract
We’ve developed a new rheometer for which shear rate can be changed by the sensor plate
amplitude in stages, based on the tuning-fork vibration viscometer SV series. Also we report on
the physical properties for non-newtonian fluid using the newly developed rheometer
RHEO-VISCO RV-10000, which works using the tuning-fork vibration method.
Keywords
Newtonian fluid, Bingham fluid, Dilatant fluid, Thixotropic fluid1) Introduction
As a means of measuring viscosity, in May 2011, vibration viscometers were recognized as aJapan industrial standard (JIS). Vibration viscometers are also among the viscometers to becalibrated in the Japan Calibration Service System (JCSS). To meet these viscometer standards,
A&D has taken the only tuning-fork vibration viscometer in the world for the past 20 years andmade it into a product, now sold as the SV Series.
Tuning-fork vibration viscometers have a low resonance frequency of 30 Hz, and the amount ofenergy they transmit to materials through these slight vibrations is low. For this reason, they
have high resolution (minimum digit of 0.01 mPa•s) and consistency, able to perform continuous
measurements from a low viscosity of 0.3 mPa•s (equivalent to the viscosity of acetone) all theway up to a high viscosity of 10,000 mPa•s. Because of this, using viscosity variation
measurement, the instrument can measure things like the cloud points of nonionic surface-active
agents, concentration of alcohol, and cure processes of proteins and adhesives. With this uniquevibrational system, researchers, who mostly measure non-Newtonian fluids, often asked us
whether it is possible to change the fixed shear rate.
With this in mind, we took the tuning-fork vibration viscometer SV as a base, and developed arheometer which allowed graded adjustment of the shear rate (the amplitude of the oscillators).
We will report on physical properties of non-Newtonian fluids we measured with ournewly-developed tuning-fork vibration rheometer, RHEO-VISCO RV-10000.
2) Principles of the tuning-fork vibration rheometer * 2, 3
With the tuning-fork vibration viscometer, twooscillators are made to resonate in a horizontal direction
like a tuning-fork, and the vibrational energy needed tomaintain a fixed amplitude for the oscillators iscompensated for using electromagnetic energy. In otherwords, a driving force equivalent to the fluid’s viscous
Flat spring

resistance is applied, and because this driving force is in

Displacement
sensorElectromagnetic
drive section

proportion to the viscous resistance, the viscosity isTemperature
sensorviscosity × density. We call this viscosity × density “staticsought. Additionally, with a vibrational viscometer, inprinciple the viscous resistance is sought throughviscosity” *4 to differentiate it from kinetic viscosity andSample

viscosity.

Oscillator

With the tuning-fork vibration method, by calculating
the equation of motion including the driving force

Fig 1．Composition of the viscosity
detectornecessary to cause the oscillators to resonate, inertia
term, viscosity term, and elasticity term, it can beunderstood that the power required to drive theoscillators is proportional to viscosity × density.

Here we will explain the theoretical model behind the vibration viscometer, abbreviating someintermediate steps. With the structure shown in Fig. 1, when the oscillator vibrates withfrequency f, the mechanical impedance Rz which the oscillator receives from the fluid isRz  A πf
and the parameters in the equation are f : vibration frequency (Hz), A : planar dimensions ofboth sides of the oscillator,  : viscosity of the fluid, : density of the fluid. Then, if the force bywhich the electromagnetic drive unit gives the oscillator the constant vibration velocity Ve

F , thenRz it

isF
 A πfVeit

The above equation makes it clear that the power applied by the electromagnetic drive unit is
proportional to the static viscosity (product of viscosity  and density )*４. During actual

measurements, the instrument controls the torque generated in the electromagnetic drive unit tomaintain the constant amplitude of the oscillator against the sample fluid, and uses the fact thatthe electric current needed for said control is proportional to “viscosity × density”, namely, static
viscosity. In developing a rheometer (RHEO-VISCO) utilizing a tuning-fork vibration viscometer,
maintaining high sensitivity was the most critical issue, so it was difficult to make the naturalvibration frequency (the built-in resonance point) adjustable. Instead, the shear rate is changedby adjusting the oscillator amplitude in steps, and from the oscillator surface areas and thetorque generated for driving the oscillator at each shear rate, the shear stress is calculated,which in turn is used to arrive at the static viscosity.
In this report, for the sake of convenience, wenondimensionalize values by assuming the sample’sdensity to be 1.00 g/cm3, equivalent to water, andexpress the viscosity by mPa•s. In Fig. 2, we haveincluded an external view of the instrument. The
instrument’s structure is the same as that of ourviscometer. At present, the shear rate range measurable
by the RHEO-VISCO is 0.2 to 1.2 mm for oscillator
amplitude, and 10 to 2000s-1 for shear rate conversion,based on water and JS2000. Because the oscillators on
the RV-10000 experience repeated sine-wave vibrations
like conventional vibration viscometers do, unlike
rotational viscometers, a constant shear rate is not
Fig.2 RV-10000

maintained. It is for that reason that the constantly
varying shear rate is converted and expressed as aneffective value. In other words, one must be aware thatthe shear rate varies with time. For information on theRV-10000’s measurable viscosity range and shear rate,please refer to Fig. 3.

Fig. 3 Relationship between amplitude, viscosity, and shear
velocity for Newtonian fluids3) Sample measurements for the RHEO-VISCO: RV-10000
1. Concerning Newtonian fluids
Here, we explain the measurement results for water and JS2000. Water is a chemicallystable substance which can be used as a standard for viscosity measurements, and isdetermined to have a viscosity of 1.00 mPa•s at 20. Though temperature variation isrelatively small, at room temperature there is a change of about -2% for every 1˚C intemperature change, and so temperature must be managed when conducting viscosity
measurements. In Fig. 4 and 5, with water and JS2000 as subjects, we plotted viscosity
values when oscillation amplitude was changed from 0.2 (0.07) to 1.2 mm by peak to peak(from highest to lowest point) at a temperature of 25˚C.

Fig. 4 Ion exchange water:

Fig. 5 Standard fluid JS2000:

Amplitude-Viscosity, Driving current

Amplitude-Viscosity, Driving current

It is shown in Fig.４ that there is a proportional relationship between amplitude (shearrate) and shear stress for Newtonian fluids. In addition, it can be judged that the JS2000
exhibits good Newtonian properties as a standard viscous fluid.
2. Bingham fluids (skin moisturizing cream)
We now explain measurement results for moisturizing cream. Fig. 6 contains viscosity
data from adjusting the oscillator amplitude each minute according to the following values:
0.07 / 0.10 / 0.20 / 0.4 / 0.6 / 0.8 / 1.0 / 1.2mm - roughly Δ0.2 ｍｍ intervals - taking one cyclefrom the minimum amplitude value to the maximum, and then back to the minimum again.
The x axis is time, the left y axis is viscosity, and the right y axis is the oscillating drive(current). Fig. 7 takes Fig. 6’s data and makes the x axis the oscillator amplitude, and the yaxes viscosity and oscillator drive current. When the amplitude exceeds a certain value, theviscosity drops quickly, revealing its properties as a Bingham fluid. Additionally, thesample’s thixotropy can be seen by the fact that even if the shear rate is reduced viscosity
does not return to its value when measurement commenced. With moisturizing cream, if its
viscosity does not decrease when you rub it between your hands, then its stretchiness will

become worse, and it will be more difficult to apply to the skin. Additionally, there is lessrisk of having the solution seep away if viscosity after applying to the skin is higher. For
these reasons, it is thought that this product was designed as a Bingham fluid in order toobtain the above properties.

Fig. 6 Moisturizing cream:

Fig. 7 Moisturizing cream:Time-Viscosity, Driving currentAmplitude-Viscosity, Driving currnt

Fig.8 shows a graph of the effects ofchanging

temperatureonmoisturizing

cream with regards to oscillator amplitudeand viscosity. The temperature dependenceof viscosity can be seen, as well as the factthat even if temperature is changed, thetendency of viscosity to rise at low shear
rates does not change.
Fig. 8 Moisturizing cream:
Amplitude-Viscosity relative to Temperature change

3. Dilatant fluid (corn starch water solution: corn starch 62% + water 38%)
The graphs in Fig. 9, 10, 11 show measurement data using a corn starch and watersolution. If a spoon is moved rapidly through a corn starch and water solution thenresistance will be high, but if the spoon is moved slowly then one will feel little resistance atall. In other words, it is recognized that when shear rate increases, viscosity grows rapidly.
It has been confirmed while measuring this corn starch and water solution that when theoscillator amplitude exceeds 0.8 mm, the viscosity quickly increases.

Fig. 9 Corn starch (Concentration 62%):

Fig. 10 Corn starch (Concentration 62%):

Time-Viscosity

Time-Viscosity

As with Fig. 6, Fig. 9 graphs the oscillator’s driving current and viscosity at various
amplitudes. Fig. 10 puts oscillator amplitude on the x axis, and viscosity on the y axis. It canbe seen that when the oscillator’s amplitude exceeds 0.8 mm, the viscosity value, which waspreviously below 100 mPa•s, quickly rises to 2000 mPa•s.
For Fig.11, we’ve added a graph showing
the same measurement but with the watermass proportion slightly changed. With thenewly created 60% corn starch sample,there was no evidence of a rapid rise inviscosity accompanying a rise in shear rate.
Measuring the quick elastic response ofdilatant fluid as a physical quantity ofFig. 11 Corn starch: Amplitude-Viscosity resulting fromviscosity

isprobably

afirst,anddifferent concentrations

measurement results indicating that just aFig. 11 Cornstarch: Amplitude-Viscosity

2% difference in blend ratio eliminates theat different concentration

phenomenon of rapidly rising viscosity arealso quite intriguing.

4. Thixotropic fluid (ketchup)
Lastly, we’ll discuss measurement results for tomato ketchup.

Tomato ketchup is said tohave thixatropic properties, and thus it has a tendency to decrease in viscosity as shear rateincreases.
In Fig.12, one can see that as the oscillator’s amplitude increases, the initial viscosity of2000 mPa•s decreases to 900 mPa•s. Fig. 13 shows oscillator amplitude on the x axis andviscosity on the y axis, and the characteristic tendency for viscosity to drop as amplitude isdecreased can be seen.

Fig. 12

Tomato ketchup:Time-Viscosity, Driving current

Fig. 13

Tomato ketchup:

Amplitude-Viscosity, Driving current4）Issues and direction for the future
We have enabled the tuning-fork vibration viscometer to alter the shear rate by changing
oscillator amplitude. Through this, it is now possible to gather clear data on characteristic
phenomena, such as fluid behavior, for non-Newtonian fluids. By graphing this data, it is easy
to quantify understandings of the particular phenomena generated by non-Newtonian fluids.
With the vibration design’s shear rate, because the oscillator must move with a cyclical,
reciprocating motion, it will go back and forth from zero to the maximum value. Because of this,it has the characteristic of expressing the shear rate and shear stress as effective values.
Additionally, at present the vibration type, including the tuning-fork vibration type, provides noclear opposite surface to construct shear rate like a rotational type does. Moreover, viscous
resistance picked up by the vibration design is expressed as “viscosity × density”. Within thesecharacteristics and thinking, it is recognized that there are elements that are counter toexisting viscometers and rheometers.
However, for example with the tuning-fork viscometer, there are notable capabilities such as:
1. the sensitivity is high, 2. the dynamic range is wide, 3. it can measure changes in properties
from fluid to solid state as viscosity, and it also has advantages such as 4. the energy necessary
for measurement is extremely low, and thus 5. the viscometer can measure without changing
the physical properties of the measured sample.
Viscosity is a field that is both old and new, but it is certain that advancements inmeasurement technology are encouraging the development of new materials. As part of this, wehope to consider the special characteristics of vibration designs and aim to raise the capabilities
and widen the applications of the design as an analysis tool for non-Newtonian fluids. For thisreason, we wish to present our instrument as a more capable instrument for measuring kinetic
viscoelasticity from liquids of low viscosity to soft solids of high viscosity, and as a material
development tool which can be used in a wide range of industries including magnetic fluids,
coatings, inks, petroleum products, polymers, adhesives, abrasives, ceramics, pharmaceuticals,cosmetics, and food products.

References*1 A&D Website – “Viscometer SV-A series Users’ Handbook”*2 “Revised viscosity”

Hiro Kawada – edited by the Weighing Management

Society, published by Corona Publishing Co., Ltd.
*3 “Prototype vibration viscometers” - Eichi Fukada, the Society of Polymer
Science, Japan, Polymers – January 1957 issue, insert*4 “Regarding Static Viscosity〔sv〕and Vibration Viscometers”, the Society ofInstrument and Control Engineers, measurement division, 24th SensingForum