Rheometer Concentric cylinder

Best for lower viscosity systems, 100 Pa-s Good for high shear rates 

Gravity settling of suspensions has less effect than in cone and plate 

Normd stresses hard to measure because of curvature and need to transmit signal through a rotating shaft Rod climbing is another option, eq. 5.3.36 

Equation 5.3.3 simply determines the hydrostatic pressure in the gap. Equation 5.3.1 governs the normal stress and eq. 5.3.2 the shear stress. The boundary conditions are  

The shear stress distribution across the gap between the cylinders is obtained by integrating eq. 5.3.2 

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The major sources of error in a concentric cylinder rheometer are the end-effects. One way of minimizing these effects is by providing a large gap between the inner cylinder end and the bottom of the closed end of the outer cylinder. 

Measurement of the flow properties of non-Newtonian fluids is typically accomplished via rotational techniques. The rotational methods fall into two basic types, concentric cylinder and cone and plate rheometers. In a concentric cylinder rheometer, a bob is placed inside a cylinder so that the fluid to be studied may be placed into the gap between the cylinders. This arrangement helps approximate a uniform shear rate throughout a sample by shearing only a thin film of sample fluid between... 

Fig. 5. Diagram illustrating an ultrasonic instrument designed to measure the speed of sound in a fluid under known shea conditions. The design is based on a combination of a pulse-echo ultrasonic reflectometer and a controlled-strain concentric cylinder rheometer.

Figure 6. Marsh funnel and concentric cylinder rheometer. (Reproduced with permission from reference 65. Copyright 1985 IHRDC.)...

A number of Fann or Baroid rheometers have been used for the rig site measurement of fluid rheology (62, 63). The design of the rheometers is similar and the various viscometer types differ largely in the control of shear rate. Early models of the concentric cylinder rheometer were limited to two shear rate measurements made at rotation speeds of r = 300 rpm and r = 600 rpm. Later models have extended the number of rotational speeds (shear rates) at which the torque can be measured, enabling a more complete rheogram to be constructed. 

The major sources of errors associated with concentric cylinders are the end effects and turbulent flow in the end region. Princen (1986) proposed a modification to eliminate the end effects in a concentric cylinder rheometer. He proposed adding a pool of mercury at the bottom of the cup that essentially eliminates the torque exerted on the bottom of the inner cylinder and on the sample in the gap. However, the limitation of this modification is that the fluid to be tested must be considerably more viscous than mercury, and the angular velocity of the cup must be kept below the levels where centrifugal force or normal force effects start to significantly alter the shape of the sample/air and sample/mercury interfaces. 

A range of rotational instruments are available which function like the concentric cylinder rheometer described earlier. For example, the Fann viscometer. 

Predicting the pressure drop for pipeline transportation of such a fluid has not been an easy task. The rheological behavior of Orimulsion , as measured in concentric cylinder rheometers of flie Couette type, is shear thinning and only slightly viscoplastic and viscoelastic (63). At first, it was thought that these rheological data was reliable enough to predict the pressure drop in the pipeline. However, the field data have repeatedly showed that the actual pipeline pressure drop is systematically lower than the one predicted from the rheometric data (10). 

The concentric cylinder or Couette flow rheometer is schematically depicted in Figure 1. The torque, T, and rotational speed, Q, can easily be measured. The torque is related to the shear stress that acts on the inner cylinder wall. The major sources of error in a concentric cylinder rheometer are the end-effects. One way of minimizing these effects is by providing a large gap between the inner cylinder end and the bottom of the closed end of the outer cylinder. 

In order to accoimt for a change in bed state, some investigators have adopted empirical stress train models based wholly on rheometric tests, because simple mechanical analogs caimot accoimt for such a change. An illustrative case is the model of Isobe et which was developed for a mud tested in a concentric-cylinder rheometer. A sample stress-shear (strain) rate relationship is shown in Fig. 27.8. The model (Fig. 27.9) attempts to mimic the characteristic hysteresis loop arising out of a phase lag between the applied stress and the resulting shear rate. Based... 

Fig. 11 Schematic diagrams of rotational rheometers (a) concentric cylinder rheometer (b) cone-plate rheometer (c) parallel-plate rheometer.

The apparatus constants for the concentric cylinder rheometer are given by... 

The attempt to relate the nonlinear and steady flow behavior with the plasticity (the yield stress) of the solutions of styrene (S) and butadiene (B) block copolymers were carried out by using a concentric cylinder rheometer [8]. Nonsinusoidal responses of the outer cylinder found in the SB sample were analyzed to obtain G - and G J by Eq. (78). Figure 54 shows the frequency dependence of the nonlinear dynamic modulus G - and GJ (/ = 1 and 3) for the system. Typical nonlinear behavior, that is, a large contribution of the higher odd harmonics and a plateau region in the fundamental harmonics, can be seen in the data with 60 = 2 and 4, whereas in those with 1.1° the response is nearly linear and elastic. The ratio of the amplitude of the 7th harmonics to that of the fundamental harmonics, Gj/Gj, can be used as a measure of the nonlinearity of the system, where Gj = [(Gj)+(GJ)]. Figure 55 shows the frequency dependence of Gj/G for the SB system with various... 

Many concentric cylinder rheometers, including Couette s original, use a fairly narrow gap, 0.5 < < 1.0. To find the shear rate in this case, we expand eq. 5.3.18 in a Maclaurin series (Krieger and Elrod, 1953 Yang and Krieger, 1978)... 

Three common designs for eliminating end effects in concentric cylinder rheometers (a) conicylinder, (b) recessed bottom, and (c) double Couette. 

To use eq. 6.2.9 to get the true shear rate, we must have additional data near the point of interest Furthermore, numerical differentiation of data is notoriously inaccurate. Fortunately, this correction does not greatly alter the shtqw of the viscosity versus shear rate function. The apparent (Newtonian) shear rate Yaw is multiplied by (3 -I-1 /n )/4 and the viscosity is divided by it Thus data points are shifted to the right and down along a line with slope —I on a log-log plot as illustrated in Figure 6.2.2. The correction is similar to that for a wide gap concentric cylinders rheometer (Figure 5.3.2). 

To study suspensions, the first choice is a narrow gap, concentric cylinder rheometer. The outer cylinder should rotate to avoid inertia problems. If there are no settling, large particle, or sensitivity limitations, the cone and plate is a good second choice. For either geometry, stress-controlled instruments (see Figure 8.2.10) provide the lowest shear rate data and best measure of yield stress. Most of the stress-controlled instruments can also do sinusoidal oscillations that allow determination of Yc and structure breakdown and recovery measures (see C hapter 10). 

On-line concentric cylinder rheometer with torque sensor on the rotating bob. Similar to commercial designs from Brookfield, Haake, and Mettler. 

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