Rheometer

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A rotational rheometer in use in a research laboratory Rheometer.jpg
A rotational rheometer in use in a research laboratory

A rheometer is a laboratory device used to measure the way in which a viscous fluid (a liquid, suspension or slurry) flows in response to applied forces. It is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. It measures the rheology of the fluid.

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There are two distinctively different types of rheometers. Rheometers that control the applied shear stress or shear strain are called rotational or shear rheometers, whereas rheometers that apply extensional stress or extensional strain are extensional rheometers. Rotational or shear type rheometers are usually designed as either a native strain-controlled instrument (control and apply a user-defined shear strain which can then measure the resulting shear stress) or a native stress-controlled instrument (control and apply a user-defined shear stress and measure the resulting shear strain).

Meanings and origin

The word rheometer comes from the Greek, and means a device for measuring main flow. [1] In the 19th century it was commonly used for devices to measure electric current, until the word was supplanted by galvanometer and ammeter. It was also used for the measurement of the flow of liquids, in medical practice (flow of blood) and in civil engineering (flow of water). This latter use persisted to the second half of the 20th century in some areas. Following the coining of the term rheology the word came to be applied to instruments for measuring the character rather than quantity of flow, and the other meanings are obsolete. (Principal Source: Oxford English Dictionary) The principle and working of rheometers is described in several texts. [2] [3]

Types of shear rheometer

Shearing geometries

Different shearing planes that can be employed to measure rheological properties. From the left - Couette drag plate flow; cylindrical flow; Poiseuille flow in a tube and plate-plate flow. Shearing geometries.png
Different shearing planes that can be employed to measure rheological properties. From the left - Couette drag plate flow; cylindrical flow; Poiseuille flow in a tube and plate-plate flow.

Four basic shearing planes can be defined according to their geometry,

The various types of shear rheometers then use one or a combination of these geometries.

Linear shear

One example of a linear shear rheometer is the Goodyear linear skin rheometer, which is used to test cosmetic cream formulations, and for medical research purposes to quantify the elastic properties of tissue. The device works by attaching a linear probe to the surface of the tissue under test, a controlled cyclical force is applied, and the resultant shear force measured using a load cell. Displacement is measured using an LVDT. Thus the basic stress–strain parameters are captured and analysed to derive the dynamic spring rate of the tissue under tests.

Pipe or capillary

Liquid is forced through a tube of constant cross-section and precisely known dimensions under conditions of laminar flow. Either the flow-rate or the pressure drop are fixed and the other measured. Knowing the dimensions, the flow-rate can be converted into a value for the shear rate and the pressure drop into a value for the shear stress. Varying the pressure or flow allows a flow curve to be determined. When a relatively small amount of fluid is available for rheometric characterization, a microfluidic rheometer with embedded pressure sensors can be used to measure pressure drop for a controlled flow rate. [4] [5]

Capillary rheometers are especially advantageous for characterization of therapeutic protein solutions since it determines the ability to be syringed. [6] Additionally, there is an inverse relationship between the rheometry and solution stability, as well as thermodynamic interactions.

Rotational geometries of different types of shearing rheometers Rotational geometries.png
Rotational geometries of different types of shearing rheometers

Dynamic shear rheometer

A dynamic shear rheometer, commonly known as DSR is used for research and development as well as for quality control in the manufacturing of a wide range of materials. Dynamic shear rheometers have been used since 1993 when Superpave was used for characterising and understanding high temperature rheological properties of asphalt binders in both the molten and solid state and is fundamental in order to formulate the chemistry and predict the end-use performance of these materials.

Rotational cylinder

The liquid is placed within the annulus of one cylinder inside another. One of the cylinders is rotated at a set speed. This determines the shear rate inside the annulus. The liquid tends to drag the other cylinder round, and the force it exerts on that cylinder (torque) is measured, which can be converted to a shear stress. One version of this is the Fann V-G Viscometer, which runs at two speeds, (300 and 600 rpm) and therefore only gives two points on the flow curve. This is sufficient to define a Bingham plastic model which was once widely used in the oil industry for determining the flow character of drilling fluids. In recent years rheometers that spin at 600, 300, 200, 100, 6 & 3 RPM have become more commonplace. This allows for more complex fluids models such as Herschel–Bulkley to be used. Some models allow the speed to be continuously increased and decreased in a programmed fashion, which allows the measurement of time-dependent properties.

Cone and plate

The liquid is placed on horizontal plate and a shallow cone placed into it. The angle between the surface of the cone and the plate is around 1–2 degrees but can vary depending on the types of tests being run. Typically the plate is rotated and the torque on the cone measured. A well-known version of this instrument is the Weissenberg rheogoniometer, in which the movement of the cone is resisted by a thin piece of metal which twists—known as a torsion bar. The known response of the torsion bar and the degree of twist give the shear stress, while the rotational speed and cone dimensions give the shear rate. In principle the Weissenberg rheogoniometer is an absolute method of measurement providing it is accurately set up. Other instruments operating on this principle may be easier to use but require calibration with a known fluid. Cone and plate rheometers can also be operated in an oscillating mode to measure elastic properties, or in combined rotational and oscillating modes.

Basic concepts of shear rheometer [7]

Strain-controlled rheometer: separate motor-transducer system. (Co = controller; M = torque; ph = deflection angle; n = rotational speed) Strain-controlled rheometer.png
Strain-controlled rheometer: separate motor-transducer system. (Co = controller; M = torque; φ = deflection angle; n = rotational speed)

In the past, devices with controlled strain or strain rate (CR rheometers) were distinguished from rheometers with controlled stress (CS rheometers) depending on the measuring principle.

In a controlled strain (CR) rheometer, the sample is subjected to displacement or speed (strain or strain rate) using a DC motor, and the resulting torque (stress) is measured separately using an additional force-torque sensor (torque compensation transducer). The electric current used to generate the displacement or speed of the motor is not used as a measure of the torque acting in the sample. This mode of operation is also referred to as separate motor transducer mode (SMT).

Stress-controlled rheometer: Combined motor-transducer system. (M = torque; ph = deflection angle; n = rotational speed) Stress-controlled rheometer.png
Stress-controlled rheometer: Combined motor-transducer system. (M = torque; φ = deflection angle; n = rotational speed)

In a controlled-stress (CS) rheometer, the torque acting in the sample is determined directly  from the electrical torque generated in the motor. With such a design, no separate torque sensor is required. Usually, this mode of operation is described as combined motor-transducer mode (CMT).

Nowadays, there are device concepts that allow both working modes, the combined motor transducer mode and the separate motor transducer mode, by using two motors in one device. The use of only one motor enables measurements to be made in the combined motor transducer mode. Using both motors allows working in the separate motor transducer mode, where one motor is used to deform the sample while the other motor is used to record the torque acting in the sample. Furthermore, this concept allows for additional modes of operation, such as counter-rotating mode, where both motors can rotate or oscillate in opposite directions. This mode of operation is used, for example, to increase the maximum achievable shear rate range or for advanced rheooptical characterization of samples.

Types of extensional rheometer

The development of extensional rheometers has proceeded more slowly than shear rheometers, due to the challenges associated with generating a homogeneous extensional flow. Firstly, interactions of the test fluid or melt with solid interfaces will result in a component of shear flow, which will compromise the results. Secondly, the strain history of all the material elements must be controlled and known. Thirdly, the strain rates and strain levels must be high enough to stretch the polymeric chains beyond their normal radius of gyration, requiring instrumentation with a large range of deformation rates and a large travel distance. [8] [9]

Commercially available extensional rheometers have been segregated according to their applicability to viscosity ranges. Materials with a viscosity range from approximately 0.01 to 1 Pa.s. (most polymer solutions) are best characterized with capillary breakup rheometers, opposed jet devices, or contraction flow systems. Materials with a viscosity range from approximately 1 to 1000 Pa.s. are used in filament stretching rheometers. Materials with a high viscosity >1000 Pa.s., such as polymer melts, are best characterized by constant-length devices. [10]

Extensional rheometry is commonly performed on materials that are subjected to a tensile deformation. This type of deformation can occur during processing, such as injection molding, fiber spinning, extrusion, blow-molding, and coating flows. It can also occur during use, such as decohesion of adhesives, pumping of hand soaps, and handling of liquid food products.

A list of currently and previously marketed commercially available extensional rheometers is shown in the table below.

Commercially available extensional rheometers

Instrument nameViscosity Range [Pa.s]Flow TypeManufacturer
Currently marketedRheotens>100Fiber spinningGoettfert
CaBER0.01-10Capillary breakupThermo Scientific
Sentmanat extensional rheometer>10000Constant lengthXpansion Instruments
FiSER1–1000Filament stretchingCambridge Polymer Group
VADER>100Controlled Filament stretchingRheo Filament
Previously marketedRFX0.01-1Opposed JetRheometric Scientific
RME>10000Constant lengthRheometric Scientific
MXR2>10000Constant lengthMagna Projects

Rheotens

Rheotens is a fiber spinning rheometer, suitable for polymeric melts. The material is pumped from an upstream tube, and a set of wheels elongates the strand. A force transducer mounted on one of the wheels measures the resultant extensional force. Because of the pre-shear induced as the fluid is transported through the upstream tube, a true extensional viscosity is difficult to obtain. However, the Rheotens is useful to compare the extensional flow properties of a homologous set of materials.

CaBER

The CaBER is a capillary breakup rheometer. A small quantity of material is placed between plates, which are rapidly stretched to a fixed level of strain. The midpoint diameter is monitored as a function of time as the fluid filament necks and breaks up under the combined forces of surface tension, gravity, and viscoelasticity. The extensional viscosity can be extracted from the data as a function of strain and strain rate. This system is useful for low viscosity fluids, inks, paints, adhesives, and biological fluids.

FiSER

The FiSER (filament stretching extensional rheometer) is based on the works by Sridhar et al. and Anna et al. [11] In this instrument, a set of linear motors drive a fluid filament apart at an exponentially increasing velocity while measuring force and diameter as a function of time and position. By deforming at an exponentially increasing rate, a constant strain rate can be achieved in the samples (barring endplate flow limitations). This system can monitor the strain-dependent extensional viscosity, as well as stress decay following flow cessation. A detailed presentation on the various uses of filament stretching rheometry can be found on the MIT web site. [12]

Sentmanat

The Sentmanat extensional rheometer (SER) is actually a fixture that can be field installed on shear rheometers. A film of polymer is wound on two rotating drums, which apply constant or variable strain rate extensional deformation on the polymer film. The stress is determined from the torque exerted by the drums.

Other types of extensional rheometers

Acoustic rheometer

Acoustic rheometers employ a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. This non-contact method applies an oscillating extensional stress. Acoustic rheometers measure the sound speed and attenuation of ultrasound for a set of frequencies in the megahertz range. Sound speed is a measure of system elasticity. It can be converted into fluid compressibility. Attenuation is a measure of viscous properties. It can be converted into viscous longitudinal modulus. In the case of a Newtonian liquid, attenuation yields information on the volume viscosity. This type of rheometer works at much higher frequencies than others. It is suitable for studying effects with much shorter relaxation times than any other rheometer.

Falling plate

A simpler version of the filament stretching rheometer, the falling plate rheometer sandwiches liquid between two solid surfaces. The top plate is fixed, and bottom plate falls under the influence of gravity, drawing out a string of the liquid.

Capillary/contraction flow

Other systems involve liquid going through an orifice, expanding from a capillary, or sucked up from a surface into a column by a vacuum. A pressurized capillary rheometer can be used to design thermal treatments of fluid food. This instrumentation could help prevent over and under-processing of fluid food because extrapolation to high temperatures would not be necessary. [13]

See also

Related Research Articles

Rheology is the study of the flow of matter, primarily in a fluid state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids.

A viscometer is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used. Thus, a rheometer can be considered as a special type of viscometer. Viscometers can measure only constant viscosity, that is, viscosity that does not change with flow conditions.

A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, that is, it has variable viscosity dependent on stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as custard, toothpaste, starch suspensions, corn starch, paint, blood, melted butter, and shampoo.

The Deborah number (De) is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It quantifies the observation that given enough time even a solid-like material might flow, or a fluid-like material can act solid when it is deformed rapidly enough. Materials that have low relaxation times flow easily and as such show relatively rapid stress decay.

Dynamic mechanical analysis is a technique used to study and characterize materials. It is most useful for studying the viscoelastic behavior of polymers. A sinusoidal stress is applied and the strain in the material is measured, allowing one to determine the complex modulus. The temperature of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this approach can be used to locate the glass transition temperature of the material, as well as to identify transitions corresponding to other molecular motions.

<span class="mw-page-title-main">Shear stress</span> Component of stress coplanar with a material cross section

Shear stress is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.

Hemorheology, also spelled haemorheology, or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit and mechanical properties of red blood cells. Red blood cells have unique mechanical behavior, which can be discussed under the terms erythrocyte deformability and erythrocyte aggregation. Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak-systole. Therefore, blood is a shear-thinning fluid. Contrarily, blood viscosity increases when shear rate goes down with increased vessel diameters or with low flow, such as downstream from an obstruction or in diastole. Blood viscosity also increases with increases in red cell aggregability.

<span class="mw-page-title-main">Magnetorheological fluid</span>

A magnetorheological fluid is a type of smart fluid in a carrier fluid, usually a type of oil. When subjected to a magnetic field, the fluid greatly increases its apparent viscosity, to the point of becoming a viscoelastic solid. Importantly, the yield stress of the fluid when in its active ("on") state can be controlled very accurately by varying the magnetic field intensity. The upshot is that the fluid's ability to transmit force can be controlled with an electromagnet, which gives rise to its many possible control-based applications.

In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

<span class="mw-page-title-main">Dilatant</span> Material in which viscosity increases with the rate of shear strain

A dilatant material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid. This behaviour is usually not observed in pure materials, but can occur in suspensions.

Rheometry generically refers to the experimental techniques used to determine the rheological properties of materials, that is the qualitative and quantitative relationships between stresses and strains and their derivatives. The techniques used are experimental. Rheometry investigates materials in relatively simple flows like steady shear flow, small amplitude oscillatory shear, and extensional flow.

<span class="mw-page-title-main">Melt flow index</span>

The Melt Flow Index (MFI) is a measure of the ease of flow of the melt of a thermoplastic polymer. It is defined as the mass of polymer, in grams, flowing in ten minutes through a capillary of a specific diameter and length by a pressure applied via prescribed alternative gravimetric weights for alternative prescribed temperatures. Polymer processors usually correlate the value of MFI with the polymer grade that they have to choose for different processes, and most often this value is not accompanied by the units, because it is taken for granted to be g/10min. Similarly, the test conditions of MFI measurement are normally expressed in kilograms rather than any other units. The method is described in the similar standards ASTM D1238 and ISO 1133.

<span class="mw-page-title-main">Shear thinning</span> Non-Newtonian fluid behavior

In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudo-plastic behaviour, and is usually defined as excluding time-dependent effects, such as thixotropy.

<span class="mw-page-title-main">Manfred Wagner</span> German chemical engineer

Manfred Hermann Wagner is the author of Wagner model and the molecular stress function theory for polymer rheology. He is a Professor for Polymer engineering and Polymer physics at the Technical University of Berlin.

An acoustic rheometer employs a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It applies an oscillating extensional stress to the system. System response can be interpreted in terms of extensional rheology.

Extensional viscosity is a viscosity coefficient when applied stress is extensional stress. It is often used for characterizing polymer solutions. Extensional viscosity can be measured using rheometers that apply extensional stress. Acoustic rheometer is one example of such devices.

Brookfield Engineering is an engineering and manufacturing company with headquarters in Middleboro, Massachusetts. It is a subsidiary of the conglomerate Ametek. Its product line includes laboratory viscometers, rheometers, texture analyzers, and powder flow testers as well as in-line process instrumentation. These instruments are used by research, design, and process control departments.

<span class="mw-page-title-main">Viscosity</span> Resistance of a fluid to shear deformation

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.

Constant viscosity elastic liquids, also known as Boger fluids are elastic fluids with constant viscosity. This creates an effect in the fluid where it flows like a liquid, yet behaves like an elastic solid when stretched out. Most elastic fluids exhibit shear thinning, because they are solutions containing polymers. But Boger fluids are exceptions since they are highly dilute solutions, so dilute that shear thinning caused by the polymers can be ignored. Boger fluids are made primarily by adding a small amount of polymer to a Newtonian fluid with a high viscosity, a typical solution being polyacrylamide mixed with corn syrup. It is a simple compound to synthesize but important to the study of rheology because elastic effects and shear effects can be clearly distinguished in experiments using Boger fluids. Without Boger fluids, it was difficult to determine if a non-Newtonian effect was caused by elasticity, shear thinning, or both; non-Newtonian flow caused by elasticity was rarely identifiable. Since Boger fluids can have constant viscosity, an experiment can be done where the results of the flow rates of a Boger liquid and a Newtonian liquid with the same viscosity can be compared, and the difference in the flow rates would show the change caused by the elasticity of the Boger liquid.

Capillary breakup rheometry is an experimental technique used to assess the extensional rheological response of low viscous fluids. Unlike most shear and extensional rheometers, this technique does not involve active stretch or measurement of stress or strain but exploits only surface tension to create a uniaxial extensional flow. Hence, although it is common practice to use the name rheometer, capillary breakup techniques should be better addressed to as indexers.

References

  1. Mezger, Thomas (2014). Applied Rheology (6th ed.). Austria: Anton Paar. p. 192. ISBN   9783950401608.
  2. Macosko, Christopher W. (1994). Rheology: Principles, Measurements, and Applications. Wiley-VCH. ISBN   0-471-18575-2.
  3. Ferry, JD (1980). Viscoelastic Properties of Polymers. Wiley. ISBN   0-471-04894-1.
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  7. Mezger, Thomas G. (2020). The Rheology Handbook (5th Revised ed.). Hanover: Vincentz Network GmbH & Co. KG, Hanover. pp. 400–403. ISBN   978-3-86630-532-8.
  8. Macosko, Christopher W. (1994). Rheology : principles, measurements, and applications. New York: VCH. ISBN   1-56081-579-5.
  9. Barnes, Howard A. (2000). A handbook of elementary rheology. Aberystwyth: Univ. of Wales, Institute of Non-Newtonian Fluid Mechanics. ISBN   0-9538032-0-1.
  10. Springer Handbook of Experimental Fluid Mechanics, Tropea, Foss, Yarin (eds), Chapter 9.1(2007)
  11. Sridhar, J. Non-Newtonian Fluid Mech., vol 40, 271–280 (1991); Anna, J. Non-Newtonian Fluid Mech., vol 87, 307–335 (1999)
  12. McKinley, G. "A decade of filament stretching rheometry". web.mit.edu.
  13. Ros-Polski, Valquíria (5 March 2014). "Rheological Analysis of Sucrose Solution at High Temperatures Using a Microwave-HeatedPressurized Capillary Rheometer". Food Science. 79 (4): E540–E545. doi:10.1111/1750-3841.12398. PMID   24597707.