Cylinder geometry, rheology

A sphere vibrating at a specific frequency can be used to obtain magnitudes of G and G" at a specific frequency. Such an instrument was used to follow sol-gel transition of 5,7, and 10% starch dispersions (Hansen et ah, 1990). However, such instruments seem to have a limited range of oscillation frequencies (e.g., 676-680 Hz). In addition, the reliability of the data obtained in comparison to data from dynamic rheological tests in which cone-plate, parallel plate, and concentric cylinder geometries have been used needs to be established. 

While the concentric cylinder geometry is relatively easy to use in rheological studies, some of its limitations should be recognized as shown in Figure 3-44. 

Even the measurement of the steady-state characteristics of shear-dependent fluids is more complex than the determination of viscosities for Newtonian fluids. In simple geometries, such as capillary tubes, the shear stress and shear rate vary over the cross-section and consequently, at a given operating condition, the apparent viscosity will vary with location. Rheological measurements are therefore usually made with instraments in which the sample to be sheared is subjected to the same rate of shear throughout its whole mass. This condition is achieved in concentric cylinder geometry (Fi re 3.37) where the fluid is sheared in the annular space between a fixed and a rotating cylinder if the gap is small compared with the dimneters of the cylinders, the shear rate is approximately... 

Rheological measurements were performed on a Haake RV20 with an MVII concentric cylinder geometry. The temperature was controlled at 25 C and the shear stress measured as a function of shear rate (1 to 4(X) s ). The shear rate was linearly varied from 0 to 400 s over 10 minutes. 

In simple geometries the shear rate—and hence the shear stress—are the same ever)rwhere in the liquid, and cone-and-plate and narrow-gap concentric-cylinder geometries are examples of this situation used in viscometers, see chapter 6. In some other situations, either the shear rate or the shear stress varies in a known manner independently of the rheology of the test liquid, and this information can be used to reduce the measured data to viscosity/shear-rate or viscosity/shear-stress, however we must make some assumption about the form of the viscosity/shear-rate curve, for example that it approximately obeys a power-law relationship. Examples of this known relationship are found in... 

For a properly designed and operated cyclone, the sharpness iadex is constant, typically 0.6. The cut size and apparent bypass are a function of the cyclone geometry, the volumetric feed rate, the material relative density, the feed soflds concentration, and the slurry rheology. The relationship for a standard cyclone geometry, where if is the cylinder diameter ia cm and inlet area = 0.05 vortex finder diameter = 0.35 ... 

Experimentally, the dynamic shear moduli are usually measured by applying sinusoidal oscillatory shear in constant stress or constant strain rheometers. This can be in parallel plate, cone-and-plate or concentric cylinder (Couette) geometries. An excellent monograph on rheology, including its application to polymers, is provided by Macosko (1994). 

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). 

In the extrusion die, the flow is driven simply by the pressure drop, as shown in Figure 13.23 and Figure 13.24. This type of flow can be analyzed relatively easUy, even for complicated rheological behavior. We will look at two geometries in detail flow between two flat plates and flow in the annular space between two cylinders. Both these geometries are used commonly to make floor tiles, cylindrical pipe pieces, and by cutting in half, semicylindrical roof tiles. 

All the major manufacturers of viscometers and rheometers have Internet sites that illustrate and describe their products. In addition, many of the manufecturers are offering seminars on rheometers and rheology. Earlier lists of available models of rheometers and their manufacturers were given by Whorlow (1980), Mitchell (1984), and Ma and Barbosa-Canovas (1995). It is very important to focus on the proper design of a measurement geometry (e.g., cone-plate, concentric cylinder), precision in measurement of strain and/or shear rate, inertia of a measuring system and correction for it, as well as to verify that the assumptions made in deriving the applicable equations of shear rate have been satisfied and to ensure that the results provided by the manufecturer are indeed correct. 

In the last decade of the nineteenth century, Maurice Couette invented the concentric cylinder viscometer. This instrument was probably the first rotating device used to measure viscosities. Besides the coaxial cylinders (Couette geometry), other rotating viscometers with cone-plate and plate-plate geometries are used. Most of the viscometers used nowadays to determine apparent viscosities and other important rheological functions as a function of the shear rate are rotating devices. 

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

A more sensitive rheological techniques for following the stability of multiple emulsions is to use oscillatory techniques. In this case, a sinusoidal strain or stress is applied to the sample, which is placed in the gap of the concentric cylinder or cone-and-plate geometry the resulting stress or strain sine wave is followed at the same time. For a viscoelastic system, as is the case with multiple emulsions, the stress and strain sine waves oscillate with the same frequency, but out of phase. 

One very important point that must be considered in any rheological measurement is the possibility of slip during the measurements. This is particularly the case with highly concentrated dispersions, whereby the flocculated system may form a plug in the gap of the platens, leaving a thin liquid film at the walls of the concentric cylinder or cone-and-plate geometry. This behaviour is caused by some syneresis of the formulation in the gap of the concentric cylinder or cone and plate. In order to reduce sHp, roughened walls should be used for the platens an alternative method would be to use a vane rheometer. 

Figure 10. Rheological measurements performed with a coaxial cylinder viscometer and different geometries. The fact that the curves are not superimposed implies that the measurements are affected by wall slip. (Reproduced with permission from reference 13. Copyright 1991 E.irF.N. Spon.)...

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