Article for the 30th Sensing ForumStudy of Shear Rates Relating to the Measurement of“Static Viscosity”

Presenters:

Naoto IZUMO, Masahiro KANNO, Yuji FUKAMI, Sachiko
SHIMIZU
R&D Headquarters 1, A&D Company, Limited

Host:

The Society of Instrument and Control Engineers (SICE), Measurement
Section

Date:

August 29-30 (Thu, Fri), 2013

Venue: Faculty of Textile Science & Technology, Shinshu University (Ueda City, Nagano
Prefecture)

Study of shear rates relating to the measurement of “static viscosity”
Naoto Izumo, Masahiro Kanno, Yuji Fukami, Sachiko Shimizu

A&D Company, Limited

ABSTRACTMaking use of a tuning-fork vibro rheometer (viscometer), we measured and studied the viscosity of both
Newtonian and non-Newtonian fluids in relation to the parameters of shear rates or the gaps between
the sensor plate and the wall surface of cup.
Keywords
Static viscosity {= viscosity x density}, shear rate, tuning fork vibro method, effective value of shear rates,
propagation constant of shear rates1) Introduction
When evaluating the properties of fluids, change in shear rate cannot be ignored. Using a rotationalrheometer, let’s consider the differences between Newtonian and non-Newtonian fluids in relation todifferences in shear rate. For Newtonian fluids, change in shear rate is proportional to shear stress, andits proportionality constant, or the viscosity value, is fixed. On the other hand, for non-Newtonian fluids
there is no proportional relationship between changes in shear rate and shear stress, and as a result, theviscosity value as defined as a proportionality constant does not become a fixed value.
From this it can be understood that with a constant shear rate applied to the fluid, if the uniform
composition of the fluid, which has a proportional relationship to the change caused by the shear rate, ismaintained, the shear stress proportional to shear rate can be obtained, resulting in a constant viscosity
value. In other words, it can be said that when the change in composition of the material is in proportion
to shear rate for a non-Newtonian fluid, the nonlinearity of the non-Newtonian fluid is attributable tothe shear rate generated within the fluid not being proportional to the number of rotations of therotational viscosity measurement device.
For a non-Newtonian fluid, if it is presumed that there are no changes to the composition other than that
proportional to the shear rate, and that the viscosity value points to various forms of nonlinearity, it canbe said this means that the shear rate, which is decided by the geometrical shape of the rotational
viscosity measurement device, actually differs according to the number of rotations for each type of fluid,or even for identical fluids.
For example, for dilatants such as a suspension of sand and water, potato starch or cornstarch, the sharpchange in viscosity demonstrated in relation to shear rate is quite apparent, and the sudden change inviscosity can even be confirmed by the touch of one’s hand. As for the change in the value of viscosity for
regular non-Newtonian fluids other than dilatants, there is also the fact that, unlike general changes inphysical properties caused by stress on materials such as solids or Newtonian fluids, the measurement

results are often incongruent with what is felt by touch.
From the above considerations, if the true state of the shear rate, which is inferred to be the main
deciding factor of the viscosity of the fluid, can be found, it will probably become a clue in solving
questions regarding the behavior of fluids, including non-Newtonian ones. In this study, in order toelucidate the true state of the shear rate, (1) the shear rate is changed by altering the amplitude of thetuning fork vibro viscometer, and (2) by changing the distance between the sensor plates which are used
to detect viscosity values and the walls of the container holding the fluid, the case of secondarilychanging the shear rate is tested and the influence on the viscosity value from a difference in the shear
rate applied to a fluid is examined.
2) Principles and framework of the tuning fork vibro rheometer / Recommendations
 Measurement principle: The history of vibration-type viscometers is long, with publications andresearch material already available in 1955, more than half a century ago.*1*2 Such literature
introduced the principles of vibration-type devices, explained that the physical quantity amountobtained by measurement was a product of [viscosity x density], and mentioned that the method wasalso adaptable to non-Newtonian fluids associated with viscoelasticity.
The tuning fork vibro viscometer uses a method developed from the vibration-type above. In
particular, it is a method that uses two oscillators (sensor plates), resonating like a tuning fork, andreduces the reactive force transmitted out of the sensors while heightening the sensitivity. Themethod also finds the viscosity value from the drive force needed to vibrate the oscillators, under the
fixed conditions for displacement (amplitude) called the zero method, using similar constituent parts
as an electromagnetic balance.*3
 Framework of the device
The framework of the RV-10000 tuning fork vibro rheometer is presented below in Fig. 1 (externalappearance) and Fig. 2 (diagram of the sensor unit). The sensor unit of the tuning fork vibro device
consists of an electromagnetic component which generates drive torque, a displacement sensor
component which detects the movement of the oscillators and the oscillators themselves which aresupported by spring materials with constant elasticity. In fact, these constituent parts are the sameas those used in precision electronic balances, and the resolution obtained by dividing 10000 mPa·s– the maximum value of viscosity that can be measured continuously – by the minimum displayable
viscosity of d=0.01 mPa·s is equivalent to a precision balance’s resolution, which is one scale in amillion.

Flat spring
Displacement
sensorElectromagnetic drive
sectionTemperature sensor

SampleOscillator

Fig.2

Fig.1 Photograph of RV-10000

Diagram of measurement unit Static viscosity
With capillary viscometers, [viscosity ÷ density] is measured as kinetic viscosity. With a rotational
viscometer (dynamic) viscosity is measured. In contrast to these methods, with vibration-type
viscometers [viscosity x density] is obtained, which we defined as “static viscosity”.*4
 Effective value of the shear rate
It is easy to define the shear rate in such a way that when the space between two parallel plates,
spreading out to an infinite degree, is filled with a fluid, a constant shear rate is applied between thetwo plates when one of the plates is moved. However, a viscometer, rheometer, or other viscosity
measurement device which faithfully delivers this principle to reality does not yet exist. As theoscillators of the tuning fork vibro method move in a back and forth motion the shear rate keeps onchanging over time. Therefore, considering the movement which vibrates as a sine wave, bysquaring the amplitude (velocity) of the oscillators at each point in time and adding these values,
then calculating the square root of this total, the effective value of the shear rate was defined. The
shear rate at each viscosity value measured by the tuning fork vibro rheometer is shown in Fig. 3.
The border of the graph shows the viscosity
measurement

rangeinrelation

toeachamplitude of the oscillators. The curves in thegraph express the shear rates at each viscosity of
Newtonian fluids. The change in the propagation
distance of the shear rate according to theviscosity value even when the same amplitude isappliedsuggests

thatshearratechangesaccording to viscosity value even at the sameFig.3 Amplitude of vibrator and viscosity
measurement range & shear rate distribution

amplitude, at least for Newtonian fluids.

 Propagation constant of shear rate

Fig.4

With the tuning fork vibro method, the oscillators are moved in a liquid of known viscosity and thedrive torque required to move them at that time can be measured. The effective value of shear stressis calculated by dividing the shearing force obtained from this drive torque by the area of the wetted
surface of the oscillators. Dividing this shear stress by the viscosity value of a known fluid gives theshear rate. Also, the propagation range of the shear rate (stress) with a vibro method can be foundwith a theoretical formula. It is also possible to infer the propagation range from actual
measurements of viscosity using the distance to walls, which forms a boundary condition with theoscillators, as a parameter.
The propagation distance of the shear rate shallbe newly examined. Fig.4 shows propagation
ranges for each viscosity value, assuming an
各粘度での液体の速度の減衰率 ［川田式：μ＝μ0・exp(-√(ωρ/η)・у)］※１

1mPa・s

10mPa・s

50mPa・s

200mPa・s

1000mPa・s

5000mPa・s

63.2%

each shear rate propagation curve with the100.00

straight horizontal line which intercepts the90.00
各粘度におけるずり速度の伝播距離(%表示)infinite receptacle. The points of intercepts of80.00
70.00

Y-axis at 0.632 can be measured, with this

63.2%

straight line representing the time constant

60.00
50.00

relative to the maximum propagation distance of

40.00
30.00

the shear rate. This distance is defined as thePropagation
constant
伝播定数

20.00

propagation constant (mm) of the shear rate and10.00

shall be used for reviewing the shear rate

0.00
012

Propagation
伝播定数
constant

34

56

7

89

振動子から鉛直方向の距離(mm)10hereinafter. From this graph it can be seen thateven when the viscosity value is as high as

Fig.4 Graph of propagation constant

5000mPa·s, the propagation constant of theviscosity is around 6mm and the damping of theshear rate is rapid.

3) Experiment method
Fig. 5: Devices used and format of experiment
Tuning fork vibro rheometer – RV-10000 and its accessories: repeated measurements of viscosity weremade using a water circulation jacket, a 13ml glass container and a constant heat water tank widely
available for sale to ensure a fixed temperature. The distance between the oscillators and the walls of
the container were adjusted using the Y direction mechanism of an XYZ Stage which comes as anaccessory of the RV-10000. Also, the amplitude of the oscillators changed in incremental steps of 0.07, 0.1,0.2, 0.4, 0.6, 0.8, 1.0, and 1.2mm.

Fig.5 Frontal photographFig.6 Side photograph: thermometer andvibrators in central unit

4) Results of experiment
Rheometer using tuning fork vibro method: The RV-10000 was used altering the amplitude of theoscillators and measuring the viscosity at each different amplitude. The behavior of Newtonian andnon-Newtonian fluids was revealed from the measured viscosity values. Data was also collected on theinfluence of a change in shear rate on a fluid by changing the distance between the oscillators and acontainer wall and changing the boundary conditions of the shear rate.
 Measurement of change in viscosity when the amplitude of the oscillators and distance between
oscillators and wall have been changeda) Measurement results for purified water

Fig.7

Purified water is representative of a Newtonian fluid. Even though the amplitude of the oscillators wasaltered over 6 steps from 0.2mm (300/s) to 1.2mm (1800/s), if the distance from the wall was kept at acertain level the change in viscosity in relation to the change in amplitude (shear rate) was within theguaranteed repeatability range and an influence could not be seen. However, an increase in viscosity wasconfirmed the closer the oscillators got to the wall.
2013.07.23
温度：20.5℃
循環水ｼﾞｬｹｯﾄ20℃設定

RV-10000 ｲｵﾝ交換水 振幅変更
壁面までの距離
0.5mm

1mm

2mm

3mm

4mm

5mm

The sensitivity of the change in viscosity
created as the oscillators approach the wall

1.2

was higher in comparison to the time constant
粘度(mPa・s)

1.1of the shear rate. At 2mm or below, a marked
increase in viscosity was confirmed.

10.9

0.8
00.2

0.4

0.6
振幅(mm)

0.8

11.2

Fig.7 Measurement results for purified waterb) Measurement results for a standard viscosity liquid (JS20)
2013.07.24
温度:21.0℃
循環水ｼﾞｬｹｯﾄ20℃設定

RV-10000 JS20 振幅変更
壁面までの距離
0.5mm
1mm

2mm

3mm

4mm

5mm

17

the hydrocarbon standard viscosity liquid
JS20. A similar trend was seen to that ofpurified water, with an increase in viscosity

16粘度(mPa・s)

Fig.8 shows the results of measurements ofconfirmed as the oscillators grew closer to15

the wall, regardless of amplitude. Theviscosity is approximately 10 times that of

14water, but the rate of increase in viscosity in
13
00.2

0.4

0.6
振幅(mm)

0.8

11.2

relation to the closeness of the wall followed
a trend close to water.

Fig.8 Measurement results for standard
viscosity solution JS20c) Measurement of fresh cream2013.06.27
温度：8.5℃
循環水ｼﾞｬｹｯﾄ5℃設定

RV-10000 生ｸﾘｰﾑ脂肪分36% 振幅変更
壁面までの距離

粘度(mPa・s)

1mm

2mm

3mm

4mm

5mm

6mm

Fig.9 shows the results of measurement of22fresh cream. Fresh cream is an uncommon

20material showing stable dilatant properties.

18Its viscosity value rises when amplitude rises.

16It also showed a trend similar to water or

14

JS20 of the viscosity rising as the oscillators

12got closer to the wall.

10
80

0.2

0.4

0.6
振幅(mm)

0.8

11.2

Fig.9 Measurement results for fresh cream5) Conclusions
 With a tuning fork vibro method, by changing the amplitude of the oscillators it is possible todistinguish between Newtonian and non-Newtonian fluids.
 Further, by changing the amplitude of the oscillators it becomes possible to judge a change inviscosity in relation to shear rate for a non-Newtonian fluid.
 When the distance between the oscillators and a wall changed, a change in viscosity was measured.
When the distance to the wall became closer than a certain value, a sudden rise in viscosity appears
and this phenomenon has been confirmed for both Newtonian and non-Newtonian fluids.

6) Considerations and issues
 By newly introducing and defining the concept of propagation constant of the shear rate, it is now
possible to quantify the comparison between theoretical values and actual measurement values withregard to the propagation area of shear rate.
 The influence of the walls of the container on the viscosity value of each fluid becomes noticeable
when their distance becomes closer than a certain fixed value. The reach of shear rate propagation
was theoretically developed a long time ago as the “damping rate of the velocity of the liquid”*1, but
it differs greatly from the actual measurement data obtained by the RV-10000.
 This is the first time actual measurement values have been able to be compared to theoretical values
for vibration-type measurement; however, including the scaling, consideration of the influence of thecontainer walls has now become an issue.
 The propagation distance (propagation constant) of the shear rate derived from a theoretical formula
is for when the boundary conditions are presumed to be infinite, with the distances for water,
viscosity of 10 mPa·s and 50 mPa·s being 0.07mm, 0.25mm and 0.55mm respectively. However, it is
now clear from the change in viscosity as measured by the tuning fork vibro method that even when
there is a distance of a few millimeters between the oscillators and a wall of the containers,
interference exists as a boundary condition and influences a change in the viscosity value.
 In the past, for low viscosity ranges close to water, examples of experiments performing
measurements changing the distance between the sensor unit and the walls of the container, whileat the same time changing the shear rate to study their correlation, could not be confirmed. One of
the reasons for this is the low sensitivity of rotational viscometers which are predominant at present,
meaning that (1) the repeatability of measurements in a low viscosity range is particularly poor, and(2) the force applied to the fluid is too strong, creating a change in the constitution of the fluid,
meaning they are considered unsuitable for experiments where the distance between the rotor andthe circumference is a parameter.
 It was confirmed that the viscosity of water and JS20 were not influenced by shear rate. However,regarding the influence of the distance from a wall, it was clear that if the wall became closer than afew millimeters to the oscillators, similarly to non-Newtonian fluids such as fresh cream there was astrong influence from the wall.
 It is conjectured that the reasons for this are (1) even if the wall is further away than a theoreticallimit of reach of the shear rate generated from the oscillators, the shear rate generated from theoscillators and the shear rate reflected from the wall will create an interference with each other, (2)as the oscillators and the wall become close, slipping on the wetted surfaces occurs, and (3) similarly,
the influence from interference between the edges of the oscillators and the wall becomes significant.
 The fundamentals of viscosity measurement are shear rate, shear stress and viscosity. Among these,
the undetermined element in viscosity measurement is shear rate. Therefore, for the establishmentof a basic model relating to viscous properties, it is necessary to continue raising the precision of thetheorization of shear rate or attempts at quantification through actual measurements.

References*1 Hiroaki KAWATA, “Revising Viscosity”, Corona Publishing Co. Ltd*2 Eiichi Fukuda, “Experimental Vibration-type Viscometer”, Society of Polymer Science, January 1957
*3 APMF2009: [Technological Background and Latest Market Requirements concerning "StaticViscosity" Measurement with a Tuning-fork Vibration Viscometer]*4 29th Sensing Forum, Society of Instrument and Control Engineers “Characteristics of Tuning Fork
Vibration Rheometer: RHEO-VISCO RV-10000”