Bob Couette Viscometer

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  

T = Force x Lever arm = Shear stress x Surface area x Radius 

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 viscosity is the shear stress at the bob, as given by Eq. (3-10), divided by the shear rate at the bob, as given by Eq. (3-12). The value of n in Eq. (3-12) is determined from the point slope of the log T versus log rpm plot at each data point. Such a plot is shown Fig. 3-3a. The line through the data is the best fit of all data points by linear least squares (this is easily found by using a spreadsheet) and has a slope of 0.77 (with r2 = 0.999). In general, if the 

Shear stress at bob (dyn/cm2) Shear rate at bob (1/s) Viscosity (poise) 

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Two common methods for measuring viscosity are the cup and bob (Couette) and the tube flow (Poiseuille) viscometers. 

Figure 8.8 Viscosity results obtained with a Couette viscometer on a series of emulsions of chlorobenzene stabilized A with 5% cetomacrogol 1000 and B with 10% cetomacrogol 1000. Results are given in arbitrary units deflection in degrees of inner bob versus Rev min of outer container. Phase volumes for both series are appended to lines as percentage oil. The diagram shows the inversion of A and B at a phase volume about 0.60 (see low viscosity of this one). B inverts before A. From Florence and Rogers [4] with permission.

One common device for measuring viscous properties is the cup-and-bob or Couette viscometer (Figure 16.4). The fluid is confined in the gap between two concentric cylinders, one of which rotates relative to the other at a known angular velocity while the torque on one is measured. This is a classic example of viscometric flow. In cylindrical coordinates, we assume only a tangential velocity component, so the 1 coordinate is the tangential or 6 direction and the 2 coordinate is the radial direction. 

Example 16.3 One means of minimizing end effects in a Couette viscometer is to make the bottom of a bob a cone, the apex of which contacts the base of the cup, so that the area beneath the bob is a cone-and-plate viscometer. For a Couette geometry in which the gap 8 is much smaller than the bob radius / , what must the cone angle a be to match the shear rates in the Couette and the cone-and-plate regions ... 

The viscosities of adhesives and sealants can be measured with various types of equipment such as the spindle (e.g. Brookfield), cone and plate, bob and couette viscometers, and torque rheometers. The viscosity value of an adhesive or sealant is dependent on the shear rate at which the measmement is made, as shown in Figme 2. 

Consider-a Couette viscometer (Fig. 16.6) in which pressure taps are drilled radially in the cup and bob at the same height. These taps are connected to vertical manometer tubes, and the difference in fluid height in these tubes... 

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. 

Among the different possible ways to measure viscosities in rotating viscometers, the coaxial cylinder apparatus is the most commonly used in practice. The measured liquid intersperses the annular gap between the stationary inner cylinder (bob) and the rotating outer cylinder (cup). Therefore a velocity gradient builds between the inner and outer cylinders (Couette flow). The momentum, which is transferred by this downward gradient to the inner cylinder, is directly proportional to the viscosity. Deflection is compensated by a torsion bar and the equilibrium deflection is measured electrically. The measurement of the angular velocity of the cup and the angular deflection of the bob makes it possible to determine the viscosity [4, 11]. 

Obviously, the analysis above is not valid in the area beneath the bob at the bottom of the viscometer. This is best taken into account by making measurements with two fluid depths, the lower being well above the bottom of the bob, and using the differences between the torques and depths in (16,28), thereby subtracting out the effects of non-Couette flow. Another approach is illustrated in Example 7. 

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