Couette device

Mechanical rheometry requires a measurement of both stress and strain (or strain rate) and is thus usually performed in a simple rotating geometry configuration. Typical examples are the cone-and-plate and cylindrical Couette devices [1,14]. In stress-controlled rheometric measurements one applies a known stress and measures the deformational response of the material. In strain-controlled rheometry one applies a deformation flow and measures the stress. Stress-controlled rheometry requires the use of specialized torque transducers in conjunction with low friction air-bearing drive in which the control of torque and the measurement of strain is integrated. By contrast, strain-controlled rheometry is generally performed with a motor drive to rotate one surface of the cell and a separate torque transducer to measure the resultant torque on the other surface. 

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

Tardos, G. I., and Khan, M. I., Study of Granulation in a Constant Shear Granular Flow Couette Device, Paper presented at the Annual AIChE Meeting, Miami Beach, Florida (1995)... 

The Couette rheometer. Another rheometer commonly used in industry is the concentric cylinder or Couette flow rheometer schematically depicted in Fig. 2.48. The torque, T, and rotational speed, 0, can easily be measured. The torque is related to the shear stress that acts on the inner cylinder wall and the rate of deformation in that region is related to the rotational speed. The type of flow present in a Couette device is analyzed in detail in Chapter 5. 

Figure 3.21 [19] shows another variation of initial orientation and arrangement of the secondary component. Here, the secondary phase cuts across all streamlines, which leads to a homogeneous mixture throughout the Couette device, under appropriate conditions. 

For this problem, we will consider a Couette device, schematically represented in Fig. 6.46 in which the inner cylinder rotates at a speed Cl and with a secondary component made up of a black tracer line with an initial thickness S0. As the tracer line is deformed, it spirals... 

Figure 6.48 Striation thickness reduction as a function of number of revolutions in a Couette device.

Temperature distribution in a polymer confined in a narrow-gap Couette device. 

To illustrate the techniques presented in the last sections, in this example we will model the heat transfer within a Couette device shown in Fig. 9.5. In the analysis we will assume that viscous dissipation plays a significant role and we are seeking the temperature profile across the gap with the effects of viscous heating. 

Figure 9.6 Simplified model of the Couette device of Fig. 9.5 with its finite element discretization.

Here, Br is the Brinkman number, which is a ratio of the viscous heating to the heat conducted through the gap of Couette device. From Eq. (4.28), we obtain the temperature gradient... 

Figure 4.4 shows the temperature profile for T2 = 300 K and -2.0 < Br < 8.0. The rise of temperature in the middle part of the Couette device is considerably large for high values of Br. Inserting Eqs. (4.26) and (4.29) into Eq. (4.23) yields an expression for the volumetric entropy production rate for a Couette flow. 

An increase in Be indicates a competition between the irreversibilities caused by heat transfer and friction. At high Reynolds numbers, the distribution of Be is relatively more uniform than at lower Re. For a circular Couette device, the Reynolds number (Re = wr2lv) at the transition from laminar to turbulent flow is strongly dependent on the ratio of the gap to the radius of the outer cylinder, 1 — n. The critical Re reaches a value 50,000 at 1 n 0.05. We may control the distribution of the irreversibility by manipulating various operational conditions such as the gap of the Couette device, the Brinkman number, and the boundary conditions. 

Using a Couette device, which consists of a pair of concentric cylinders, with the inner one rotating, it is possible to generate approximately uniform shear on chocolate. The temperature of the device can be controlled and varied this allows a controlled temperature-time-shear pattern to be provided. Figure 22.5 shows the DSC trace for milk chocolates processed at different shear rates (Stapley, Tewkesbury and Fryer 1999). The phase change temperatures are lower than those shown in Table... 

GAP-DEPENDENT APPARENT SHEAR RATE. Indirect evidence of slip, as well as a measurement of its magnitude, can be extracted from the flow curve (shear stress versus shear rate) measured at different rheometer gaps (Mooney 1931). If slip occurs, one expects the slip velocity V (a) to depend on the shear stress a, but not on the gap h. Thus, if a fluid is sheared in a plane Couette device with one plate moving and one stationary, and the gap h is varied with the shear stress a held fixed, there will be a velocity jump of magnitude Vs(ct) at the interfaces between the fluid and each of the two plates. There will also be a velocity gradient >(a) in the bulk of the fluid thus the velocity of the moving surface will be y = 2V,(a) + y (a)/i. The apparent shear rate V/h will therefore be... 

Figure 3-5. Typical rheometer geometries (a) parallel disk, (b) concentric cylinder (Couette) geometry, (c) cone-and-plate. Either the angular velocity is set and one measures the torque required to produce this rotation rate, or the torque is set and one measures the angular velocity. We analyze the Couette device in this section.

Hence, to achieve the best possible approximation to a linear shear flow, the Couette device must have a very thin gap relative to the cylinder radius. 

In a rheological experiment, one of the two cylinders is typically rotated with a known angular velocity, and the torque required to produce this motion is measured. Let us suppose that the torque is measured on the inner cylinder. Now, if we ignore the finite length of the Couette device, we have seen that there is a single nonzero component of the velocity ug(r). Hence, if we examine the various components of the rate-of-strain tensor E,... 

Table 3-1. Ratio of inferred-to-true viscosities in a Couette device versus gap width...

The last of these conditions is the same as w = 0, as we can see from the continuity equation (12-124). The condition on v comes from the kinematic condition at the walls of the Couette device, and the conditions on u and w are the no-slip conditions. 

In this laboratory, an ex vivo test system was developed and utilized to delineate some of the factors affecting thrombus formation on surfaces. The system consisted of a flow-through couette device (Figure 1) placed in an arteriovenous shunt in a dog. The device was designed to allow independent control of blood flow and shear by separate control of the flow rate through the chamber, and of the rotation speed of a central rod, which is coated with the material to be studied. The validation of the method with respect to flow conditions, hematological considerations, and reproducibility has been reported previously (2—4). 

The ex vivo flow-through couette method provides a very convenient model for assessing the effect of drugs on the thrombogenic process. By directly monitoring the accumulation of radioisotope in the couette device, a direct measure of the kinetics of thrombus accumulation can be obtained. An example of the deposition of platelets on the rod surface after the administration of systemic heparin is shown in Figure 10 (4). In this experiment... 

Typically, simple shear flow is generated in cone-and-plate, plate-plate, or couette devices. Simple extensional flow is generated by devices in which a cylindrically shaped specimen is deformed in such a manner that the length increases exponentially with time. Th ogic of rheometry is reviewed and discussed in... 

Figure 9 Schematic representation of the fluidized bed Couette device. 

Experiments were performed with the fluidized bed Couette device described above (see also Khan and... 

Figure 10 Experimental results. Elongation parameter (Z>) vs. Stokes number for granules produced in a constant shear Couette device.

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