Rheometer
| Continuum mechanics |
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| File:BernoullisLawDerivationDiagram.svg |
A rheometer is a laboratory device used to measure the way in which 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.
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).
Contents
Meanings and origin
The word rheometer comes from the Greek, and means a device for measuring flow. 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 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 excellent texts.[1] [2]
Types of shear rheometer
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.[3] [4]
For Newtonian fluids, the pressure drop increases linearly with flow rate and the measured viscosity does not depend upon applied deformation rate or stress. On the other hand, since non-Newtonian fluids or complex fluids can display shear thinning or shear thickening, the pressure drop versus flow rate data must be analyzed using Weissenberg-Rabinowitch-Mooney equation.
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 used to be 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 been used. 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 of the order of 1 degree—i.e. it is a very shallow cone. Typically the plate is rotated and the force 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.
Linear Shear
One example of a linear shear rheometer is the Goodyer 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 test.
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.
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.[5]
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 Name | Viscosity Range [Pa.s] | Flow Type | Manufacturer | |
|---|---|---|---|---|
| Currently Marketed | Rheotens | >100 | Fiber spinning | Gottfert |
| CaBER | 0.01-10 | Capillary breakup | ThermoFisher | |
| Sentmanat extensional rheometer | >10000 | Constant length | Xpansion Instruments | |
| FiSER | 1-1000 | Filament stretching | Cambridge Polymer Group | |
| Previously Marketed | RFX | 0.01-1 | Opposed Jet | Rheometric Scientific |
| RME | >10000 | Constant length | Rheometric Scientific | |
| MXR2 | >10000 | Constant length | Magna Projects |
Rheotens
The 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 is based on the works by Sridhar et al. and Anna et al. [6]. 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 McKinley Group web site [1]
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.
- Fiser.jpg
FiSER (filament stretching extensional rheometer)
Other Types of Extensional Rheometers
Acoustic
Acoustic rheometers employ a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It 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 column by a vacuum.
See also
References
- ↑ Script error
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- ↑ Springer Handbook of Experimental Fluid Mechanics, Tropea, Foss, Yarin (eds), Chapter 9.1(2007)
- ↑ Sridhar, J. Non-Newtonian Fluid Mech., vol 40, 271-280 (1991); Anna, J. Non-Newtonian Fluid Mech., vol 87, 307-335 (1999)
- K. Walters (1975) Rheometry (Chapman & Hall) ISBN 0-412-12090-9
- A.S.Dukhin and P.J.Goetz "Ultrasound for characterizing colloids", Elsevier, (2002)
External links
- [2] - Research Rheometers, Capillary Rheometers, Viscometers, Rheology Consulting and Testing by ATS RheoSystems
- [3] - Rotational and Capillary Rheometers from Malvern Instruments
- [4] - Physica Rheometer from Anton Paar
- [5] - Brookfield Rheometer
- [6] - Thermo Fisher Scientific
- [7] - MonTech Rubber Testing Instruments, Germany
- [8] - Rheometer/Viscometer from RheoTec Messtechnik GmbH
- [9] - A R Series Rheometer from T A instruments Inc
- [10] - Metravib DMA+ series from ACOEM
- [11] - CaBER extensional rheometer
- [12] - Rheotens rheometer
- [13] - Sentmanat Rheometer
- [14] - FiSER Extensional Rheometers
- [15] - Goodyer Linear Skin Rhometerde:Rheometer
