52 Rates

# Rotational Viscometry

Viscosity testing is one of the most important methods used to check the quality of materials. Various industries rely on viscosity checks of their products to produce a product with consistent texture. Many important parameters for the production control of materials and also for the development of new products are directly related to the product’s viscosity. In nearly all production stages, the viscosity of the material has a major impact (e.g., in the mixing process, while pumping liquids through pipes). Incoming liquid raw materials also have to be checked using viscosity measurements. Rotational viscometers are perfect for determining the viscosity of a wide range of different samples. Viscosity testing with rotational viscometers is suitable for everything from liquid samples to semi-solid ones.

## Rotational viscosity

The physical quantity “viscosity” refers to how thick a fluid is and how easily it flows. In scientific terms, viscosity is the measure of a fluid’s internal flow resistance. It is the resistance that a fluid shows when being deformed. Rotational viscometers measure the viscosity of the sample by turning a spindle in a cup.[1] You can determine viscosity by measuring the torque on a vertical shaft that rotates a spindle.

## Types of rotational viscometers

Although there are two setups available to measure viscosity with a rotational viscometer –  spring-type instruments and servo motor instruments – we only cover spring-type instruments here.

How do these work? The rotation of the spindle deflects a spring. Optical sensors detect the deflection and the viscosity of the sample is then calculated from it.[2]

The test sequence is the following: The user attaches a spindle to the rotational viscometer, sets a speed, and receives the dynamic viscosity and the torque (mostly in %). The resulting driving torque depends on the rotational speed w, the spindle geometry, and the sample viscosity.

In case of low-viscosity substances, the spring needs to be sufficiently sensitive, whereas for samples in the high-viscosity range, a more robust spring is required. Different instrument models are available that have different spring types to cover a broad range of applications.

There are three different rotational viscometer models:

• Spring type to measure low-viscosity samples ("L-type")
• Spring type to measure medium (regular)-viscosity samples ("R-type”)
• Spring type to measure high-viscosity substances (“H-type”)

There are two types of spring-type viscometers:[3]

• Dial reading: The torque value in % is shown by the pointer on the dial. To convert the torque % reading to viscosity in mPa·s, the dial reading has to be multiplied by the appropriate factor for the spindle and speed in use (Equation 1).

• Digital reading: The viscosity is automatically calculated and displayed on a screen for every spindle/speed combination. There are no further calculations necessary.

### What torque model for what application?

Viscosity measurement is important for various liquid and semi-solid materials we know from daily life (Figure 1). You can use a spring-type rotational viscometer for countless applications in various industries, particularly the chemical, petrochemical, food, beverage, personal care, and pharmaceutical ones.

Depending on the viscosity of the sample, you need to use a certain instrument with the accurate torque range (Table 1).

• The L-model is suited for the measurement of low-viscosity samples, such as solvents, oils, juices, ink, and mouthwash.
• The R-model is suited for the measurement of medium-viscosity samples, such as paints, coatings, adhesives, and dairy products.
• The H-model is suited for the measurement of high-viscosity samples, such as mayonnaise, peanut butter, pastes, and ointments.

Table 1: Overview of torque models and their typical applications

Chemicals & petrochemicals Food & beverage Pharma & cosmetics
Application Torque Application Torque Application Torque
Solvents, inks L Juices L Mouthwash L
Oils, lubricating oils L Dairy R Shower liquid L
Liquid wax L Dressing, sauces R Shampoo, lotion, cream R
Paints, coatings R Blancmange, vanilla sauce R Detergents R
Adhesives, epoxies R Chocolate and cocoa products H Ointments, gels H

### What spindle for what application?

For each torque model, different spindles exist so that samples with different viscosities can be measured. Usually, interchangeable spindles in the form of disks and cylinders are used. They are fixed on the coupling of the instrument. For a given viscosity, the flow resistance is related to the spindle’s speed of rotation and its shape and size. The flow resistance increases with the speed and size of the spindle. What does that mean? The lowest viscosity range can be covered by measuring with the biggest spindle at maximum speed. The highest viscosity range can be covered by measuring with the smallest spindle at the lowest speed. For a better reproducibility, you should use the same spindle/speed combination for multiple tests.[4]

The maximum measurable viscosity of the spindle at a given speed is called the full-scale range (FSR).[5] In other words, the FSR is the maximum viscosity that can be measured with the chosen spindle/speed combination. The minimum viscosity that can be measured is one tenth of the full-scale range. By knowing the FSR of the spindle/speed combination, you can determine whether that spindle/speed combination fits to the viscosity of the sample. If the viscosity of the sample is unknown, the viscosity is tested by taking the smallest spindle first and replacing it in ascending order by the next largest spindle until a valid measurement result is achieved. To obtain a valid measurement, the torque value must be between 10 % and 100 %.[6] If the torque value is higher than 100 %, you need to use a smaller spindle. If the torque value is lower than 10 %, you need to use a bigger spindle. The higher the torque value, the better the accuracy – since the accuracy of the measuring system depends on the full-scale range (usually 1 % of FSR).

An overview of typical available spindle types for rotational viscometers is shown in table 2.

 Spindle Absolute / relative Defined gap / shear-rate calculation Sample types Particles Sample volume Temperature equilibration Cleaning Liquid bath Peltier-tempered Standard Relative No Liquids <2 mm ~ 500 mL Long n.a. Easy Cylindrical Absolute Yes Liquids <0.1 mm 2 mL to 20 mL Medium Fast More intense Small sample adapter Relative Yes Liquids <0.1 mm to 0.5 mm 2 mL to 16 mL Medium Fast More intense Double-gap Absolute Yes Low-viscosity liquids <0.01 mm 7.5 mL Medium Fast More intense UL Relative Yes Low-viscosity liquids <0.1 mm 16 mL Medium Fast More intense Cone-plate Absolute Yes Liquids up to semi-solids <15 µm 0.5 mL to 2 mL Medium n.a. Easy T-bar (+ motorized stand adapter) Relative No Non-flowing samples None ~ 500 mL Long n.a. Easy Vane Relative No Non-flowing samples <2 mm ~ 20 mL to 500 mL Long Easy

n.a. = Not applicable

### Standard spindles

Each instrument model typically has a set of standard spindles (Figure 2, 3). The set depends on the torque range of the instrument. An L-instrument, such as ViscoQC 100-L, usually contains four spindles, and an R/H-instrument usually contains six spindles.[7] Standard spindles produce accurate and reproducible results. Nevertheless, it is crucial that these spindles are relative systems because the shear gap is not defined (so-called “infinite gap” systems).[8] Standard spindles are used in 600 mL beakers with a minimum inner diameter of 83 mm. They measure viscosity according to ISO 2555. The viscosity value is only comparable to results of the same instrument type with the same setup.

An accessory used for standard spindles is the spindle protector. It consists of a metal plate that has a “U” form.[9] You should always use the spindle protector for measurements on both the L-model and the R-model. While protecting the spindle against bending – the spindle protector also influences the measurement results, which causes a different flow behavior of the sample in the beaker. For the H-model, you do not need a spindle protector for viscosity measurement. To get reliable results, it is necessary to always use the spindle protector when it is mandatory and to use a 600 mL beaker with a defined geometry (approx. 83 mm inner diameter).

### Concentric cylinder spindles

Concentric cylinder spindles, when used with the corresponding cup, are called concentric cylinder systems (Figure 4). Concentric cylinder systems are absolute measuring systems. Due to the defined spindle geometry, you can calculate shear rate values. This means the concentric cylinder systems measure viscosity according to ISO 3219 and DIN 53019 because of the defined shear gap.[10] You can use concentric cylinder systems for liquid samples that contain particles with a maximum size of 100 µm.

There are several reasons to prefer absolute measuring systems:

• Defined gap of the measuring system: provides constant shear conditions so that measurements are independent of the instrument and measuring system
• Mathematical models to analyze flow/viscosity curves: Mathematical models such as the “Bingham yield point calculation” can be applied by using such measurement systems
• Low sample volume: The sample volume needed for the measurement is relatively low in comparison to the volume needed for standard spindles

Small sample adapter (SSA) spindles , also called “SC4” spindles, are cylindrical spindles. The spindles are available in various sizes to cover a large viscosity range. Most of the spindles are used in the same cup, although the spindle size varies (Figure 5). For this reason, the spindles are relative measuring systems. However, it is possible to calculate a shear rate and use mathematical regression models. Using small sample adapter spindles lets you reduce the sample volume (approx. 2 mL to 16 mL) and control temperature easier when compared to standard spindles. The maximum allowed particle size inside the sample depends on the specific spindle and gap size. Rule of thumb: The particle size must be lower than a tenth of the gap size.

### Double-gap spindles

A double-gap measuring system (Figure 6) is suited for measuring low-viscosity samples (≥1 mPa·s) according to DIN 54453.[11] It is an absolute measuring geometry, but based on the small gaps between spindle and cup, it is very sensitive to particles, agglomerates, etc. The maximum particle size must be >10 µm. In comparison to the UL system, the double-gap measuring system requires less sample volume and delivers absolute viscosity results.

### UL spindle

The UL (ultra low) spindle has a cylindrical geometry and is also used in a small cup. In comparison to concentric cylinder spindles, it is very large in order to measure very low-viscosity samples. If the spindle is used with an L-model viscometer, you can measure a minimum viscosity of 1 mPa.s. The geometry does not follow any standard, so it is not an absolute measuring geometry. But since there is a defined, small gap between spindle and cup, you can calculate a shear rate and use mathematical regression models.

### Cone-plate spindles

Cone-plate spindles (Figure 7) are absolute measuring systems[12] and are, in particular, suitable if very low sample volume is available (0.5 mL to 2 mL). Moreover, temperature control is done very fast due to the low sample volume. Cleaning of cone and plate systems is also done very easily. Because the gap between cone and plate is very narrow, samples must not contain any particles (<15 µm) for a measurement with cone-plate spindles. The gap between cone tip and plate is approx. 15 µm for typical cone-plate spindles of a rotational viscometer. Cone-plate measuring systems are also typically used for rheometers. However, the geometry, accuracy, and test methods (rotation/oscillation) are different for rheometers and rotational viscometers.

### T-bar spindles with motorized stand adapter

T-bar spindles in combination with a motorized stand adapter let you measure non-flowing samples (Figure 8). Typical samples are cream, sauces, gel, and wax. For such sample types, you do not need a high-priced high-end rheometer. A T-bar spindle with motorized stand adapter is a low-cost solution for a rotational viscometer. During the measurement, the motorized stand adapter moves the spindle up and down within the sample at a slow speed. It eliminates the so-called “channeling” problem. Any spindle that rotates constantly at the same height will create an air channel within the sample, which leads to meaningless viscosity values because the sample is not in contact with the spindle anymore. The moving viscometer head with T-bar spindles eliminates this problem by continuously measuring the intact sample due to the helical spindle movement.[13]

### Vane spindles

Vane spindles are especially used for paste-like and gel-like samples when yield point values are required (Figure 9). Such sample types cannot be tested with concentric cylinder spindles, which allow the yield point determination with mathematical models. Vane spindles immersed in a sample will create a cylinder during a measurement. This means you can calculate shear stress values. You can also analyze the yield point of a sample.[14] Vane spindles are used for viscosity tests, at low speeds (max. 12 rpm), for samples containing particles.

## How to get comparable viscosity results

The type of measuring system affects the comparability of the measurement data. If you use an absolute measuring geometry, you get instrument- and measuring-geometry-independent viscosity results. In other words, the measured value is comparable with results gathered from other absolute measuring configurations. In case the sample is non-Newtonian or is thixotropic/non-thixotropic, the shear rate and measurement time need to be the same for comparison.

If you use a relative measuring geometry, you need to use the same measurement configuration and measurement settings to get the same result. To get comparable results, you need to ensure these variables are all the same:

• Instrument torque model (e.g., L-model viscometer)
• Spindle geometry
• Cup/beaker size
• Spindle protector used/not used
• Speed or shear rate
• Measurement time
• Temperature

## Tips for a successful rotational viscosity measurement

• If available, the sample should be prepared according to a suitable standard test method, guide, or practice.
• The sample preparation can have a considerable effect on the measurement results. Thixotropic materials in particular are affected by stirring/mixing/pouring procedures. Thixotropic behavior of materials is characterized by a decrease in viscosity at constant shear conditions over time[15].
• For a good reproducibility the appropriate sample container has to be used for the measurement and placed concentric to the spindle.
• A sufficient sample filling height is important because the tip of the standard spindle should be at least ten mm above the vessel’s base. If used, a spindle should be immersed as far as the mark on its shaft.
• To avoid changing the rheological structure of the sample, spindles should be slowly dipped into the sample vessel. Incline disk spindles to avoid trapping air bubbles at the base of the spindle.
• In order to get reliable measurement results, the spindle should have completed at least five full turns before a value is taken. If not applicable the readings should be taken after a specified period of time . In particular for non-Newtonian samples viscosity/torque % readings may not stabilize after five full turns because of their thixotropic behavior. In that case the readings should be taken after a defined period of time. Rule of thumb: 20 seconds for speed >5 rpm, 60 seconds at least for speeds <5 rpm
• An error source during measurements might be turbulences which occur at high speeds. Turbulences (Eddy currents) can cause higher viscosity readings.
• In the case of high-viscosity substances (>30,000 mPa·s) shear heating is a potential error source during measurement. It is not recommended to set a speed higher than 100 rpm.
• As viscosity is strongly temperature-dependent a constant temperature of the liquid during the whole measurement is very important. Tracing the sample temperature with a Pt100 temperature sensor is recommended.

## References

1. Mezger, T. 2011. The Rheology Handbook. 3rd revised ed. Hanover: Vincentz Network.
2. ISO (International Organization for Standardization). 2017. Plastics – Resins in the liquid state or as emulsions or dispersions – Determination of apparent viscosity using a single cylinder type rotational viscometer method. ISO 2555:2017.
3. ASTM (American Society for Testing and Materials). 2017. Standard Test Method for Calibration of Concentric Cylinder Rotational Viscometers. ASTM E2975-15. https://www.astm.org/e2975-15.html.
4. ISO (International Organization for Standardization). 2017. Plastics – Resins in the liquid state or as emulsions or dispersions – Determination of apparent viscosity using a single cylinder type rotational viscometer method. ISO 2555:2017.
5. ISO (International Organization for Standardization). 2017. Plastics – Resins in the liquid state or as emulsions or dispersions – Determination of apparent viscosity using a single cylinder type rotational viscometer method. ISO 2555:2017.
6. ASTM (American Society for Testing and Materials). 2017. Standard Test Method for Calibration of Concentric Cylinder Rotational Viscometers. ASTM E2975-15. https://www.astm.org/e2975-15.html.
7. ISO (International Organization for Standardization). 2017. Plastics – Resins in the liquid state or as emulsions or dispersions – Determination of apparent viscosity using a single cylinder type rotational viscometer method. ISO 2555:2017.
8. Mezger, T. 2011. The Rheology Handbook. 3rd revised ed. Hanover: Vincentz Network.
9. ISO (International Organization for Standardization). 2017. Plastics – Resins in the liquid state or as emulsions or dispersions – Determination of apparent viscosity using a single cylinder type rotational viscometer method. ISO 2555:2017.
10. DIN (Deutsche Institut für Normung). 2008. Viscometry - Measurement of viscosities and flow curves by means of rotational viscometers - Part 1: Principles and measuring geometry. DIN 53019-1:2008-09. https://www.beuth.de/de/norm/din-53019-1/108532850.
11. DIN (Deutsche Institut für Normung). 1982. Testing of adhesives for metals and of bonded metal joints; dynamic viscosity determination of anaerobic adhesives by rotation viscometer. DIN 54453:1982-01. https://www.beuth.de/de/norm/din-54453/935492.
12. ISO (International Organization for Standardization). 1994. Plastics – Polymers/resins in the liquid state or as emulsions or dispersions – Determination of viscosity using a rotational viscometer with defined shear rate. ISO 3219:1994-10.
13. Barnes, H. 2001. “An examination of the use of rotational viscometers for the quality control of non-Newtonian liquid products in factories.” Applied Rheology 11, 2: 89-101.
14. Sun, A., and Gunasekaran, S. 2009. “Yield Stress in Foods: Measurements and applications.” International Journal of Food Properties, 12: 70-101.
15. Mezger, T. 2011. The Rheology Handbook. 3rd revised ed. Hanover: Vincentz Network.