Concentric cylinder instruments

Coaxial (Concentric Cylinder) Viscometer. The earliest and most common type of rotational viscometer is the coaxial or concentric cylinder instrument. It consists of two cylinders, one within the other (cup and bob), keeping the specimen between them, as shown in Figure 27. The first practical rotational viscometer consisted of a rotating cup with an inner cylinder supported by a torsion wire. In variations of this design the inner cylinder rotates. Instruments of both types are useful for a variety of applications. 

Solution Equation (16) shows that the velocity gradient is not uniform in a capillary viscometer any more than it is in a concentric-cylinder instrument. The rate of shear dvldr is directly proportional to the radial distance from the axis of the cylinder. At the wall it has its maximum value, which is proportional to Rc] at the center of the tube it equals zero. Some intermediate value, say, the average, might be used to characterize the gradient in a given instrument. This quantity will be different for capillaries of different radii. All of this is similar to the situation in concentric-cylinder viscometers. 

In a wide-gap concentric cylinder instrument, the shear rate at a given location depends on the rheological behavior of the sample. This complicates, but does not prohibit, evaluation of shear rate. In a narrow-gap concentric cylinder instrument (bob radius/cup radius >0.97), the shear rate may be considered constant at the average value in the gap shear rate then depends only on radii and rotational speed, making its evaluation easy (Barnes et al., 1989). 

The vane viscometer is yet another form of the concentric cylinder instrument, in which the bob is replaced by a rotor with four blades or vanes each attached by one edge to a vertical shaft, at 90° intervals around the shaft (Figure 22.7). This geometry, which can be used either with a cup or in the infinite sample mode, is particularly useful for measuring yield stress, and can also be used to measure the rheological properties of non-Newtonian liquids. Its advantages are described by Gunasekaran and Ak (2002). 

Departures from laminar flow, which are attributed to inertia and/or viscoelasticity, result in turbulences, i.e., an uneven flow pattern with locally clear deviations from the flow direction. In the extreme, the flowing sample can start to circulate locally, which is known as Taylor vortices and mainly observed in concentric cylinder instruments, where the inner cylinder rotates,i.e., in cup and bob viscometers. ... 

Concentric Cylinder Instruments. Saverborn (68) developed an instrument that requires the pectin mixture be poured between two concentric, corrugated cylinders and allowed to set. The inner cylinder is twisted by a torsion wire and the extent of torsion caused in the gel is measured. The corrugations prevent slippage of the gel. Kertesz (3 ) cites this as one of the finest instruments devised for jelly strength measurements. 

The Brookfield TTIOO is a typical on-line instrument that fulfils the criteria set out above, in that it follows the 3Rs, i.e., representative sampling, relatabihty, reliability and robustness of operation. It is manufactured by the Brookfield Engineering Company of the USA, who are the longest-standing manufacturers of commercial rotational viscometers in the world. It is a concentric-cylinder instrument that can operate in- or on-line, and has an open-ended variant that can be mounted into the wall of a vessel - the TT200. 

The first practical rotational rheometer was the concentric cylinder instrument of Maurice Couette (1890). As shown in Figure... 

A number of concentric cylinder instruments rotate the outer cylinder f2o and hold the inner cylinder fixed. For this case we can just replace with 2o in eq. 5.3.24 and S.3.2S. 

Figure 2.4 A commercial instrument, the Brookfield Digital Viscometer, based on the geometry of the concentric cylinder viscometer. (Photo courtesy of Brookfield Engineering Laboratories, Inc., Stoughton, Mass. 02072.)...

The concentric cylinder viscometer described in Sec. 2.3, as well as numerous other possible instruments, can also be used to measure solution viscosity. The apparatus shown in Fig. 9.6 and its variations are the most widely used for this purpose, however. One limitation of this method is the fact that the velocity gradient is not constant, but varies with r in this type of instrument, as noted in connection with Eq. (9.26). Since we are not considering shear-dependent viscosity in this chapter, we shall ignore this limitation. 

Historically, viscosity measurements have been the single most important method to characterize fluids in petroleum-producing applications. Whereas the ability to measure a fluid s resistance to flow has been available in the laboratory for a long time, a need to measure the fluid properties at the well site has prompted the development of more portable and less sophisticated viscosity-measuring devices [1395]. These instruments must be durable and simple enough to be used by persons with a wide range of technical skills. As a result, the Marsh funnel and the Fann concentric cylinder, both variable-speed viscometers, have found wide use. In some instances, the Brookfield viscometer has also been used. 

A computer-controlled rheology laboratory has been constructed to study and optimize fluids used in hydraulic fracturing applications. Instruments consist of both pressurized capillary viscometers and concentric cylinder rotational viscometers. Computer control, data acquisition and analysis are accomplished by two Hewlett Packard 1000 computers. Custom software provides menu-driven programs for Instrument control, data retrieval and data analysis. 

The relationship between viscosity, angular velocity, and torque for a Newtonian fluid in a concentric cylinder viscometer is given by the Maigules equation (eq. 26) (21,146), where M is the torque on the inner cylinder, h the length of the inner cylinder, Q the relative angular velocity of the cylinder in radians per second, R the radius of the inner cylinder wall, Rr the radius of the outer cylinder wall, and k an instrument constant. 

The Ravenfield model BS viscometer is a wide shear rate range instrument with several possible measurement systems cone—plate, parallel plates, concentric cylinders, and taper plug. The last gives shear rates of up to 106 s-1, and the cone—plate of up to 8 x 104 -1. The viscosity range is 102 108 mPa-s. Measurements can normally be made up to 170°C, but with special modifications even higher temperatures can be achieved. A computer interface permits two-way communication with a computer. 

In the next section we consider an experimental approach to viscosity. We generate the apparatus of interest by wrapping —in our imagination —the fluid in Figure 4.1 into a closed ring around the z axis. The two rigid surfaces then describe concentric cylinders, and the instrument is called a concentric-cylinder viscometer. 

To successfully measure non-Newtonian fluids, a known shear field (preferably constant) must be generated in the instrument. Generally, this situation is known as steady simple shear. This precludes the use of most single-point viscometers and leaves only rotational and capillary devices. Of these, rotational devices are most commonly used. To meet the criterion of steady simple shear, cone and plate, parallel plates, or concentric cylinders are used (Figure HI. 1.1). 

Concentric cylinder and cone and plate instruments are particularly useful for studying the flow behaviour of non-Newtonian liquids. 

Concentric-cylinder viscometers are in widespread use. Figure 3d represents a partial section through such an instrument in which liquid is contained and sheared between the stationary inner and rotating outer cylinders. Either may be driven, but the flow regime... 

Viscometers can be divided into rotational instruments and axial flow instruments. Rotational instruments include concentric cylinder (cup and bob), cone and plate and parallel disc viscometers, while axial flow instruments include capillary, slit and extrusion rheometers. 

In rotational instruments, one member (e.g., the cup in a concentric cylinder viscometer) rotates while the other (e.g., the bob) remains stationary. The sample is held, and sheared, in the gap between the two. In a controlled shear rate measurement, the rotational speed is constant, and the torque on one member caused by the viscous resistance to flow exerted by the sample is measured. In a controlled stress measurement, a constant torque is applied to one member and its speed of rotation measured. Controlled stress instruments are particularly useful for measuring yield stress, the minimum stress causing flow of a plastic material. 

A variation of the concentric cylinder viscometer is the rotating cylinder in an infinite sample . In this controlled (low) shear rate instrument, the sample is contained in a vessel of such large diameter relative to the cylinder s diameter that the vessel wall exerts no influence on the shear... 

Conventional rheometer geometries such as concentric cylinders, cone and plate and parallel discs are unsuitable, even when the rheometer is designed to allow measurement of normal forces. Many of the disadvantages of such geometries are overcome in the sliding-plate viscometer (Gunasekaran and Ak, 2002). In this instrument (Figure 22.9), the sample (the exact shape and size of which need not be known) is held between a... 

The second instrument was a Deer rheometer (model PDR881, Integrated Petronic Systems Ltd., London) fitted with concentric cylinder platens. This instrument was used to measure of the yield value by applying a series of stress values of equal increments and recording the response until flow occurred. 

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