Technological Background and Latest Market Requirements
concerning “Static Viscosity” Measurement with a Tuning-fork
Vibration Viscometer
Naoto IZUMO, and Atsushi KOIWAIR&D Division, A&D Company, Limited.
Tokyo, Japan
ABSTRACT
We introduce a new method viscometer “Sine Wave Vibro Viscometer” which principle is different from conventional
viscometers, such as the capillary viscometers or the rotational one.
And also We propose a new viscosity unit “static viscosity[sv]  viscosity[Pa·s]  density[kg/m3]”.
This sine wave vibro viscometer features a small amount of sample and wide range measurements without replacing
the sensor.
The SV-1A requires only 2ml sample and has measuring range from 0.3mPa·s to 1000mPa·s.
The SV-10A requires only 10ml and has measuring range from 0.3m Pa·s to 10000m Pa·s.
Also describing the measuring method and features of this vibro viscometer. And explaining about JCSS and themeasurement uncertainty evaluation for viscosity.
Finally showing the viscosity measurement result of various substances measured with this vibro viscometer.
(For example: the cloud point of a surface-active agent, the concentrations for ethanol solutions, the cure process ofsilicone adhesive and the coagulation process of egg white.)
Keywords: Sine Wave Vibro Viscometer, Static Viscosity, JCSS, Uncertainty

1. INTRODUCTION
Various methods have been invented for measuring viscosity. Each of these methods is selected and used in theindustry where it is most suitable. However, applications of viscosity measurements are recently expanding into newfields such as measurements of polymeric solutions, adhesive agents, coating materials, abrasives, engine oils, biodiesel
fuels, and even soft drinks, cosmetics and human blood. Meanwhile, demands are rising for a measuring system that canminimize the energetic interference to a sample liquid such as rotative force and barycentric shift in order to measure
the viscous property that is inherent to the liquid. Moreover, there are increasing requirements for measuringcontinuously a wide range of viscosities in order to observe a viscosity change caused by a temperature change, thecuring of an adhesive agent, etc. The following will present an explanation of the tuning-fork vibration viscometer as adevice that satisfies the above requirements, the technical background of its JCSS standardization and actual
measurement examples. In addition, the physical quantity measured by the new viscometer, “static viscosity (sv)”[viscosity × density] will be discussed.

2. TUNING-FORK VIBRATION VISCOMETERIn the field of liquid viscosity measurements, the capillary viscometer and the rotational viscometer have a long
history and are widely recognized. Meanwhile, although the principle for the vibration viscometer was proposed a longtime ago, it was only about 20 years ago that the theory was put into actual practice due to various technologicaldifficulties. The recently developed, tuning-fork vibration viscometer not only realized downsizing and price-reductionof the instrument but also made it possible to perform wide-range, continuous measurements from 0.3 mPa·s(equivalent of acetone) up to 10,000 mPa·s. More recently, measurements with as small as 2ml sample liquid havebecome possible, whose applications including the viscosity measurements of such fluids as resist inks for liquid
crystals and human blood. The high-performance, tuning-fork vibration viscometer is rapidly expanding its scope of
applications to where viscosity measurements used to be impossible. Meanwhile, due to quality control requirements inoffshore manufacturing, the precision and the user-friendliness of the tuning-fork vibration viscometer have also been
gaining attention at the production level (although delocalization has been decreasing lately).

2.1 MEASUREMENT PRINCIPLES OF THE VIBRATION VISCOMETERS
The damped vibration of a spring in a liquid is influenced by the restorative force of the spring and the viscous
resistance of the liquid. Based on this idea, the characteristics of the damped vibration can be represented in adifferential equation, which is then integrated to obtain a viscous resistance. This viscous resistance is then used to
calculate the viscosity value. The formula that expresses this principle is a linear motion equation involving the inertial
force due to the mass of the oscillator, the restorative force of the spring and the damping force due to the viscous
resistance. Based on the solution of the equation, it could be deduced that the product of viscosity and density governs
damping. When the oscillator is vibrated at the frequency f, the mechanical impedance Rz that the oscillator receives
from the liquid will be:

Rz  A f(1)

In the above equation, f is vibration frequency (Hz), A is planar dimensions of the both sides of the oscillator in theliquid, η is the viscosity of the liquid, and ρ is the density of the liquid. Then if the force by which the electromagnetic
driving unit gives the oscillator the constant vibration velocity Ve

Rz 

it

is F, the following equation is valid:F A f
Ve iwt(2)

Therefore, it is evident that the force generated in the electromagnetic driving unit to maintain the constant amplitudeof the oscillator against the viscous resistance is proportional to the product of the viscosity η and the density ρ; that is,
the “static viscosity.”
2.2 STRUCTURE OF THE TUNING-FORK VIBRATION VISCOMETER
The tuning-fork vibration viscometer utilizes the same measurement principle as the vibration method, which was
proposed a long time ago. However, the difference is that with the tuning-fork vibration viscometer, the vibromotive
force generated due to the vibration—a problem inherent in the vibration method—has been eliminated by the adoptionof a tuning-fork structure with two oscillator plates. The tuning fork and two oscillator plates function as a resonancesystem that is a highly sensitive viscosity sensor. Moreover, the viscous resistance of the liquid and the driving force
generated in the electromagnetic unit are successfully balanced because the amplitude of the oscillators is always
feedback-controlled to remain constant. By adopting the same measuring system as the electromagnetic weighing
sensor of a balance (called the “null method”), it is now possible to perform a wide, dynamic range of highly sensitive
viscosity measurements.
Spring Plate
Displacement Sensor
Electromagnetic Drive

Temperature Sensor

SampleOscillator

Figure 1: Structure of Viscosity Detection Unit

Figure 2: Tuning-fork Vibration Viscometer SV-A

(2ml sample measurement is possible)

Recently, viscosity measurements that require only 2ml sample liquid while measuring the temperature of the liquidhave been realized, responding to the need for small sample measurements for expensive liquids. When the sample
volume is 2ml, the size of a sample cup becomes very small. Therefore, in order to make the positioning of the sample
cup easier, the precisive X-Y-Z stage is provided as standard. In addition, the oscillator and the temperature sensor are
now made of titanium because there are growing demands for measuring the viscosities of strongly-acid or stronglyalkaline liquids along with the expansion of viscosity measurement applications.

3. “STATIC VISCOSITY” MEASURED BY THE TUNING-FORK VIBRATION VISCOMETER
As illustrated in the solution of the motion equation (1), the physical quantity measured by the vibration viscometer isviscous resistance, and this viscous resistance consists of “viscosity × density.” If we define “viscosity × density” as“static viscosity,” the relationships between each viscosity measuring method and physical quantity to be measured willbe the “kinetic viscosity” (viscosity / density) for the capillary viscometer, the “viscosity” for the rotational viscometer,
and the “static viscosity” (viscosity × density) for the vibration viscometer. The following is a brief summary of each
viscometry device, its features and unit system:-

Kinetic viscosity: Determined by measuring the time taken by a liquid to go through a flow channel inaccordance with gravity. This method is accompanied by a barycentric shift of the liquid, and the measured
time is proportional to the viscosity, but inversely proportional to density.
Viscosity: Determined directly from the difference in the rotational torque generated within a liquid inaccordance with rotational movement. The liquid is always measured in a rotational state.
Static viscosity: Determined based on the driving force torque loaded on the oscillator within a liquid. The
driving force is proportional to the product of viscosity and density, and there is no barycentric shift of theliquid. The minute amplitude of the oscillators causes little change to the physical properties of the measured
sample.
Terms

Kinetic Viscosity

Viscosity

Static Viscosity

Definition

Viscosity / Density

Viscosity

Viscosity × Density

SI Unit2

m /sec

Pa·s

Pa·s × kg/m3

Dimension

L2/T

ML−1T−1

M2L−4T−1

CGS UnitSt

cP

cP × g/cm3 = sv

1 m2/sec = 106 cSt

1 Pa·s = 103 cP

1 Pa·s × kg/m3 = 1 sv

Measurement Method

Capillary method, etc.

Rotational method

Vibration method

Conversion to Viscosity

Density correction required――

Density correction required

Unit Conversion

Table1: Comparison between Kinetic Viscosity, Viscosity & Static Viscosity

4. JCSS STANDARDIZATION OF VISCOSITY
After modeling the above measurement principle and determining the uncertainties based on the measurement errors
inherent in the product, the vibration viscometers were accredited as a Japan Calibration Service System (JCSS)
standard device along with the standard liquids of viscosity, capillary viscometers and the rotational viscometers as ofApril 24, 2006, although at present the JCSS of viscosity is yet to be put into practice. The documents demonstrating themodeling and the uncertainties of the vibration viscometers have greatly contributed to the JCSS standardization of theother viscometry devices as well. Fore reference, the uncertainties estimated for the tuning-fork vibration viscometerSV-10 when calibrated using standard liquids for calibrating viscometers under a temperature of 20˚C are shown in
Table 2.

Uncertainty Factor
Uncertainty based on Calibration Liquid
Uncertainty based on Temperature
Measurement
Uncertainty based on Calibration
Procedure
Uncertainty based on Other Factors

Uncertainty
Component
Calibration Liquid
Accuracy

Distribution

Liquid Surface
Adjustment
Repeatability
Rounding Error

Rectangular

0.72

0.72

NormalRectangular

1.00
0.21

1.00
0.04

1.74
3.48

2.86
5.72

NormalRectangular

Relative Contribution Of Uncertainty (%)
JS20
JS14000
0.062
0.111
1.20
2.58

Combined Standard Uncertainty
Expanded Uncertainty (k = 2)

Table 2: Estimated Uncertainties of a Tuning-fork Vibration Viscometer(2 Standard Liquids for Calibrating Viscometers, 20˚C)
What follows is an explanation of some distinctive uncertainty components of the tuning-fork vibration viscometer.
From the certificate of properties for the standard liquids for calibrating viscometers based on JISZ8809, the uncertainty
based on the calibration liquid us and the static viscosity S can be obtained as follows where η: Viscosity, ν : Kinetic
viscosity, ρ: Density

S       2(3)When the standard uncertainty of kinetic viscosity is uν and that of density is uρ based on the certificate of properties,
the below formula is valid:
2

 u

u
u s       2   



 


2

(4)

As shown in Table 2, the uncertainty based on calibration procedure is largely influenced by the uncertainty based on
temperature measurement. This is due to the fact that the temperature coefficient of the static viscosity is −4.1%/˚C for
JS20 and −9.8%/˚C for JS14000. In order to minimize the uncertainty based on calibration procedure, it is necessary tolessen the temperature distribution inside the sample cup and the difference in temperature between the temperature
sensor and the oscillators. The sample cup of the SV-10 is as small as 35ml (the optional cup of 10ml is also available),and it is possible to control the temperature of the sample liquid with a water jacket and a constant heat water tank.
Therefore, the temperature distribution will be smaller than using a beaker, etc. However, it will be difficult to lessen
the temperature distribution actively when the viscosity of a sample liquid exceeds 1000 mPa·s because the rotator of astirrer for churning the liquid will not rotate. For example, when setting the liquid temperature of JS14000 at 40˚Cunder a room temperature of around 25˚C, a temperature difference by approx. 0.3˚C between the temperature sensor
and the oscillators will be present, which will result in an error of approx. 3% in viscosity value. To combat this, theviscometer and the standard liquids for calibrating viscometers were placed in a temperature-controlled chamber so thatthe temperature difference could be reduced to within 0.02˚C, virtually eliminating any influence of temperature.
Consequently, the uncertainty based on the temperature measurement was narrowed down to the uncertainty based on
the temperature sensor, which was 2.6%. The uncertainty based on calibration procedure is attributable to theuncertainty caused by an operator being unable to position the oscillators always on the same level against the liquidsurface. With viscometers other than the capillary type, the display value will be by principle influenced if the depth ofthe oscillator in the liquid varies. This problem was solved by making a narrow area in each oscillator as well as
equipping the device with a liquid level adjustment plate, which reduced the uncertainty to 0.7%.

5. MEASUREMENT EXAMPLES OF THE TUNING-FORK VIBRATION VISCOMETER SV-10
Now, let us examine various examples of static viscosity measurements using the tuning-fork vibration viscometerSV-10. The physical quantity measured in these examples is the “static viscosity” (sv). However, to avoid confusion,
the vertical axis of the graphs will indicate the “viscosity” with the unit being either Pa·s or mPa·s, assuming that thedensities of the samples were all 1.0 g/cm3.

5.1 MEASURING THE CLOUD POINT OF A SURFACE ACTIVE AGENT (SEE FIGURE 3)
This is an example of a cloud-point measurement of a nonionic surface-active agent. The viscosity increased graduallyas the liquid temperature was raised, but there was an abrupt fall in viscosity at 35.4˚C. This point is the cloud point of
this liquid, where the surface-active agent starts dissociating its hydrogen bond and becoming oil soluble and cloudy.
Detecting the cloud point of a surface-active agent is the most important measurement in designing the basic
performance and function of the surface-active agent. In the past, there existed cloud-point meters with which a cloud
point was optically measured. On the other hand, being able to detect a cloud point by measuring changes in static
viscosity, which is a physical property, is groundbreaking, and for this reason the tuning-fork vibration viscometer ishighly evaluated.

Figure 3: Cloud-point Measurement of a Surface-active Agent

5.2 RELATIONSHIP BETWEEN THE CONCENTRATION AND THE VISCOSITY OF ETHANOLSOLUTION (SEE FIGURE 4)
Viscosity measurement examples of solutions of different alcohol/water ratios. The viscosity value increases as thealcohol concentration becomes higher until 40%. After 40%, the viscosity value decreases the higher the alcohol
concentration. This phenomenon is consistent with past experiments, and the same viscosity change was observed withthe tuning-fork vibration viscometer.

Figure 4: Concentration and Viscosity of Ethanol Solution

5.3 INFLUENCE OF AMBIENT TEMPERATURE ON THE CURE PROCESS OF MORTAR(SEE FIGURE 5)
The viscometer and a commercially-available mortar material were placed inside a temperature-controlled room,
where water and the mortar were mixed under different temperatures in order to measure the influence of differences inambient temperature on curing. It is possible with the SV-10 to measure the cure process while checking directly thetemperature of the sample since the temperature sensor is placed between the two oscillators of the device. Consistent
with what is already known from experience, a relationship was found to exist between the temperature and the cureprocess by means of the static viscosity measurement. When the cure process was under a temperature of 40˚C, there
existed an unstable viscosity variation around 8000 mPa·s. This is supposedly due to slipping between the sample andthe oscillators, which means that a state change of the sample around the oscillator surfaces was measured as a variationin viscosity value.

Figure 5: Cure Processes of Mortars under Different Ambient Temperatures

5.4 CURE PROCESS OF PLASTER (SEE FIGURE 6)
The cure processes when the water-plaster ratio was 67, 60 and 50% are shown. Here, it is easy to understand how
plaster hardens rapidly in a few minutes and that curing speed varies greatly depending on the mixing ratio.

Figure 6: Cure Process of Plaster at Different Temperatures

5.5 CURE PROCESS OF A SILICON ADHESIVE AGENT (SEE FIGURE 7)
In general, silicon adhesive agents require a long time for curing. As shown in the example in Figure 7, the measured
sample took 22 hours for its slow curing. This and other measurement examples of a long curing process are very rare,
but these kinds of measurements are important for examining the physical properties of an adhesive agent during its
cure process and for designing its adhesion characteristics.

Figure 7: Cure Process of a Silicon Adhesive Agent

5.6 CONCENTRATIONS AND COAGULATION TEMPERATURES OF GELATIN (SEE FIGURE 8)
The graph shows an example of viscosity measurement of 2.5% and 5% gelatin solutions while varying thetemperatures. It can be observed that the coagulation point depends on the concentration of the solution.

Figure 8: Concentrations and Coagulation Temperatures of Gelatin

5.7 CURING OF EGG WHITES DUE TO TEMPERATURE (SEE FIGURE 9)
The process in which protein becomes irreversibly hardened was measured by heating egg whites. Based on thethermal history of the graph (the horizontal axis indicates temperature and the vertical axis viscosity), the process can be
described as (1) softening due to heat until 60˚C, (2) starting to harden suddenly from 60˚C, (3) passing a small peakaround 68˚C, and then (4) fully hardening. The peak around 68˚C indicates that the egg white contains several kinds ofproteins with different curing characteristics.

Figure 9: Increase in Viscosity of Egg White along with Rise in Temperature

5.8 MEASUREMENT OF THE GELATION POINT OF A SOLDERING FLUX DUE TO HEAT (SEE FIGURE
10)
In the graph, the horizontal and vertical axes indicate temperature and viscosity respectively. At around 70˚C there isan inflection point where viscosity changes drastically. It can be inferred that a soldering flux is also designed to have aphase transition point at a certain temperature.

Figure 10: Measurement of the gelation point of a soldering flux due to heat6. SUMMARY
For a long time, viscometers were limited to the capillary type, rotational type and the cup type, etc. It is true that thesedevices were forming a staple market. At the same time, advancing technological levels including the upgrading of
R&D frameworks and enhancing sensitivities of measuring instruments has been increasingly an important issue in theindustrial arena. In addition, standards and regulations concerning production lines are becoming more and more strictworldwide. For example, it is now essential to enhance qualities all the way from basic research to production lines,
which involves evaluating and understanding the physical characteristics and properties of materials such as liquids.
Consequently, there are emerging demands for measuring viscosities more accurately and efficiently as basic data thatshow the characteristics of the liquids. The tuning-fork vibration viscometer has the capabilities to satisfy such needs,
and it should be possible to cultivate new technological fields through “static viscosity” measurements using thisviscometer. For example, the tuning-fork vibration viscometer is already adopted and recommended by a leading engine
oil manufacturer as a device for measuring viscosities of engine oils. It is also beginning to be used for blood viscosity
measurements. As these examples indicate, it is expected that static viscosity measurements will be utilized in widerranging industrial fields including the medical industry in the near future.

7. REFERENCES
1. Micho KAWATA., Viscosity, CORONA PUBLISHING, Tokyo, 1958, pp. 134-145.
2. National Institute of Technology and Evaluation, Estimation Examples of Uncertainty(Title Viscometer),NITE,
Tokyo, 2007, pp. 14-18
3. Naoto IZUMO, ”Quantity of physics measured in a vibration-type viscometer” Proc. 23th Sensing Forum, Tukuba,
2006 pp. 149-152.
4. Naoto IZUMO and Atsushi KOIWAI, ”Static Viscosity[SV] and Vibration type Viscometer”
Proc. 23th Sensing Forum, Sendai, 2007 pp. 141-146.
*corresponding author information: Naoto IZUMO phone+81-3-5391-6132; Fax:+81-3-5391-6148;
Higashi-Ikebukuro, Toshima-ku, Tokyo 170-0013 Japan