Viscometers cup and bob

Example 2-5 Suppose we wish to calculate the shear stress on the bob surface in a cup-and-bob viscometer from a measured value of the torque or moment on the bob. The equation for this is... 

As the name implies, the cup-and-bob viscometer consists of two concentric cylinders, the outer cup and the inner bob, with the test fluid in the annular gap (see Fig. 3-2). One cylinder (preferably the cup) is rotated at a fixed angular velocity ( 2). The force is transmitted to the sample, causing it to deform, and is then transferred by the fluid to the other cylinder (i.e., the bob). This force results in a torque (I) that can be measured by a torsion spring, for example. Thus, the known quantities are the radii of the inner bob (R ) and the outer cup (Ra), the length of surface in contact with the sample (L), and the measured angular velocity ( 2) and torque (I). From these quantities, we must determine the corresponding shear stress and shear rate to find the fluid viscosity. The shear stress is determined by a balance of moments on a cylindrical surface within the sample (at a distance r from the center), and the torsion spring ... 

Example 3-1 The following data were taken in a cup-and-bob viscometer with a bob radius of 2 cm, a cup radius of 2.05 cm, and a bob length of 15 cm. Determine the viscosity of the sample and the equation for the model that best represents this viscosity. 

The quantities that are measured in a cup-and-bob viscometer are the rotation rate of the cup (rpm) and the corresponding torque transmitted to the bob. These quantities are then converted to corresponding values of shear rate (j>) and shear stress (r), which in turn can be converted to corresponding values of viscosity if. ... 

What is the difference between shear stress and momentum flux How are they related Illustrate each one in terms of the angular flow in the gap in a cup-and-bob viscometer, in which the outer cylinder (cup) is rotated and the torque is measured at the stationary inner cylinder (bob). 

You have obtained data for a viscous fluid in a cup-and-bob viscometer that has the following dimensions cup radius = 2 cm, bob radius = 1.5 cm, bob length = 3 cm. The data are tabulated below, where n is the point slope of the log T versus log N curve. 

A number of techniques have been developed to measure melt viscosity. Some of these are listed in Table 3.8. Rotational viscometers are of varied structures. The Couette cup-and-bob viscometer consists of a stationary inner cylinder, bob, and an outer cylinder, cup, which is rotated. Shear stress is measured in terms of the required torque needed to achieve a fixed rotation rate for a specific radius differential between the radius of the bob and the cup. The Brookfield viscometer is a bob-and-cup viscometer. The Mooney viscometer, often used in the rubber industry, measures the torque needed to revolve a rotor at a specified rate. In the cone-and-plate assemblies the melt is sheared between a flat plate and a broad cone whose apex contacts the plate containing the melt. 

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. ... 

Fig. 15 Cup and bob viscometer ri[equals] radius of the inner cylinder, ro = radius of the outer cylinder, h = length length of the inner cylinder immersed in the liquid.

The schematic principle of a simple arrangement, i.e., the cup and bob viscometer, is shown in Fig. 15. The driveshaft rotates with a given number of rotations per minute. If there were no friction between the two concentric cylinders, the spring would transfer the rotation completely. However, the material to be investigated, which fills the gap between the two concentric cylinders, is viscous and causes resistance against the rotation. As a result, the spring cannot follow the rotation of the drive shaft and gets twisted. Thus, a torque is produced, which is proportional to the shear stress applied. 

A common problem for the viscosity measurements of suspensions is the presence of wall effects due to the presence of particles in the suspension. Some work has been done on the wall effects [see, e.g., Yoshimura and Prud homme (52)]. Despite the efforts put into this subject, the words of Mewis (56) still stand that there are no acceptable means in accounting for the wall effects or usable procedures to avoid wall effects available either experimentally or analytically. As shown by Wen et al. (57), the wall effects can lead to serious errors in viscosity measurements (Figure 9). The solid line in Figure 9 is the stress versus shear rate relation that they thought to be true for the system, whereas the symbols represent the experimental results from a rotational (cup-and-bob) viscometer with different gap size settings. 

Viscosity is a property sometimes difficult to assess, as figures can be measured on any one of several types of viscometer. One common type is the rotating disk viscometer, which must be used in a container big enough to eliminate wall effects. The main alternative is the cup-and-bob viscometer, where the viscous drag of the liquid between stationary and rotating concentric cylinders is indicated by a spring-loaded pointer moving over a dial. 

In order to simplify end corrections in a cup-and-bob viscometer, the ends can be conical. If each end of the bob is the cone of a cone-plate viscometer, what is the ratio of the torque due to the ends of the bob to the torque due to flow in the annulus in the cylindrical part Assume a bob of length L and radius KR, a cup of radius R, and a cone angle of 1 -Assume a Newtonian fluid and refer torque in the annulus to the geometric mean radius. 

For a Bingham plastic, qualitatively, what unusual feature must a velocity profile in pipe flow exhibit In a cup-and-bob viscometer, what discontinuity might be expected in the flow field for the same model In a cone-plate viscometer, would any discontinuities be expected ... 

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