Viscometers disk-plate

t is constant, and can be taken outside the integral, because t = t (yX and y is constant, as shown by (16.30). 

Cone-and-plate viscometers of the type shown here are usually limited to fairly low shear rates. At higher shear rates, solutions tend to be flung from the gap by centrifugal force, and melts tend to ball up (like rubbing a finger over dry rubber cement). These problems can be overcome by enclosing the fluid around a biconical rotor, giving, in effect, two cone-and-plate viscometers back-to-back. The flow curves in Chapter XV were obtained with such a device. 

Example 7. One means of minimizing end effects in a Couette viscometer is to make the bottom of the bob a cone, the apex of which contacts the base of the cup, so that the area beneath the bob is a cone-ahd-plate viscometer. For a Couette geometry in which the gap b is much smaller than the bob radius U,-, what must the cone angle a be to match the shear rates in the Couette and cone-and-plate regions  

Solution. By equating the expressions for shear rate from Examples 5(A) and 

Another type of viscometer which finds occasional use is the disk-plate viscometer (Fig. 16.8). A disk of radius R rotates with an angular velocity of CO relative to a parallel plate. The disk and plate are separated by a distance d(d R with the test fluid in between. The torque M on either the disk or plate is measured. This is known as torsional (twisting) flow, and is another example of a viscometric flow. 

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Similar reasoning leads to the conclusion that in cone-and-plate or disk-plate viscometers (Sections 16.7 and 16.8) there will be forces tending to push the cone and plate or the disk and plate apart. Indeed, there are, and the measurement of these forces provides a means of determining the functions Ni j) and Also, for the case of torsional flow, Maxwell and Scalora showed that if a hole is drilled through the plate along the axis of rotation, a screwless extruder is obtained, as the axial normal stress pushes a polymer melt through the hole. Unlike a screw extruder, however, this device works only with viscoelastic fluids. 

Parallel-plate viscometer n. (1) An instrument consisting of two circular parallel plates, the lower one stationary, the upper one rotatable, the disk-shaped specimen being confined between the plates. An example of this type of viscometer is the Mooney viscometer. 

Viscosities of liquid resins are typically determined with a Cannon-Fenske capillary viscometer at 25°C, or a Brookfield viscometer. The viscosity depends on the temperature, as illustrated in Figure 2. Viscosities of soUd epoxy resins are determined in butyl carbitol (diethylene glycol monobutyl ether) solutions (40% solids content) and by comparison with standard bubble tubes (Gardner-Holdt bubble viscosity). The Gardner color of the same resin solution is determined by comparison with a standard color disk. Recently, data have been reported for solid epoxy resins using the ICI Cone and Plate viscometers, which are much more time-efficient because they do not require sample dissolution. 

The Mooney viscometer, used particularly in the rubber industry, is a variant of the cone-and-plate viscometer it restricts the sample to a disk-shaped cavity (ASTM D1646) [4]. 

The parallel-disk viscometer used for measuring the shear stress and normal stress difference of molten thermoplastics is similar in principle to the cone-n-plate viscometer except that the lower cone is replaced by a smooth circular disk. This type of viscometer was initially developed for measuring the rheological properties of rubber [29-33] and therefore made use of serrated disks placed in a pressurized cavity to prevent rubber slippage. When it was adapted for thermoplastic melts [1534,35], measurements were performed using smooth disks and without pressure. 

Oscillatory shear measurements can be done with the parallel-disk arrangement in a manner similar to the case of the cone-n-plate viscometer and, similarly, the material fimcdons i), G, C, and others can be generated. However, a slightly different tedinique [36] is at times used wherein the polymer melt sample is deformed between two oscillating parallel eccentric disks as shown in Fig. 3.2. In this case, too, it has been shown that the fluid elements undergo a periodic sinusoidal deformation and the forces exerted on the disk are thus interpreted in terms of G and G" [4]. 

Somewhat higher viscosities, up to 10 poise or so, are measured using a parallel plate viscometer (see ASTM C1351M-96). In the parallel plate viscometer, a suitably sized disk (about 8 mm in diameter by 3 to 6 mm thick) of glass is sandwiched between two parallel plates (inconel plates covered with platinum foil or thin alumina substrates). The top plate is loaded with known weights. Viscosity can be calculated by measuring the rate of decrease in the thickness of the specimen with a linear variable differential transformer (LVDT) device. 

Another type of viscometer that finds occasional use is the disk-and-plate viscometer (Rgure 16.6). A disk of radius R rotates with an angular velocity of co relative to a parallel... 

The cone-n-plate viscometer is a widely used instrument for measurement of shear flow rheological properties of polymer melts [9-20]. The principal features of this viscometer are shown schematically in Fig. 3.1. The sanaple, whose rheological properties are to be measured, is trapped between the circular conical disk at the bottom and the circular horizontal plate at the top. The cone is connected to the drive motor which rotates the disk at various constant speeds, whereas the plate is connected to the torque-measuring device in order to evaluate the resistance of the sample to the motion. The cone is truncated at the top. The gap between the cone and plate is adjusted in such a way as to represent the distance that would have been available if the untruncated cone had just touched the plate. The angle of the cone surface is normally very small (0o 4° or 0.0696 radians) so as to maintain [4] cosec Op = 1. The cone angles are chosen such that for any point on the cone surface, the ratio of angular speed and distance to the plate is constant. This ensures that the shear rate is constant from the cone tip to the outer radius of the conical disk. Similarly, the shear... 

With several springs, which function as torque gauges, and a number of spindles, viscosities can be measured up to 10 mPa-s with the Brookfield viscometer. The shear rates depend on the model and the sensor system they are ca 0.1 100 for the disk spindles, <132 for concentric cylinders, and <1500 for the cone—plate forlow viscosity samples. Viscosities at very low (ca 10 — 1 )) shear rates can be measured with the concentric... 

The Nametre Rotary B rotational viscometer measures torque in terms of the current needed to drive the d-c motor at a given speed while a material is under test. The standard sensors are coaxial cylinders or Brookfield disk-type spindles, but a cone—plate system is also available. The viscosity range for the coaxial cylinder sensors is 5 to 5 x 1(T mPa-s, and the maximum shear rate is 200. ... 

For a parallel disk viscometer (i.e., cylindrical coordinates), the tangential velocity vg on the rotating plate is ftr. This reveals the radial dependence of vg at any axial position z between the rotating and stationary plates, because if one moves into the fluid in the z direction from the moving plate at constant r and a separation of variables solution to the 0-component of the equation of motion is valid, then the r... 

Oscillating-disk viscometers consist of an axially symmetric disk placed between two fixed parallel plates and suspended fi om a torsion wire, so that it performs oscillations in the fluid about its axis of symmetry. Such a viscometer has been used by several researchers as an instrument for viscosity measmements (see, for example, DiPippo et al, 1966 Kestin et al, 1977, 1978a,b, 1980 Correia et al., 1979 Correia and Kestin, 1980 Kestin and Shankland, 1981b, 1984b and Krall et al, 1987, 1992). The theoretical and experimental problems of this technique have been... 

In the particular case of viscometers consisting of a disk of thickness d and radius R, oscillating between two fixed horizontal plates, and provided 5 lb + d (where b is the separation between the disk and one of the fixed horizontal plates), the solution for D(s), is Kestin and Shankland (1981b)... 

Rotational Viscometers. These relatively complex instruments can be used in the steady state or in an oscillatory, dynamic mode. Some are useful up to the glassy state of the polymer. The working mechanism, in all cases, is one part that moves past another. Designs include concentric cylinders (cup and bob), cone-and-plate, parallel-plate, and disk, paddle, or rotor in a cylinder. 

For thermoplastic melt studies, rotational viscometers with either the cone-n-plate or parallel-disk configuration are used. 

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