Cone-plate

Chaturani, P, and Narasimman, S., 1990. Flow of power-law fluids in cone-plate viscometer. Acta Mechanica 82, 197-211. 

Normal Stress (Weissenberg Effect). Many viscoelastic fluids flow in a direction normal (perpendicular) to the direction of shear stress in steady-state shear (21,90). Examples of the effect include flour dough climbing up a beater, polymer solutions climbing up the inner cylinder in a concentric cylinder viscometer, and paints forcing apart the cone and plate of a cone—plate viscometer. The normal stress effect has been put to practical use in certain screwless extmders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

Cone—Plate Viscometer. In a cone—plate viscometer (Fig. 28), alow angle (<3°) cone rotates against a flat plate with the fluid sample between them. The cone—plate instmment is a simple, straightforward device that is easy to use and extremely easy to clean. It is well suited to routine work because measurements are rapid and no tedious calculations are necessary. With careful caUbration and good temperature control it can also be used for research. Heated instmments can be used for melt viscosity measurements. 

Fig. 28. Cone—plate viscometer. R is the radius of the cone, a is the angle between cone and plate, and Q is the relative angular velocity.

In most rotational viscometers the rate of shear varies with the distance from a wall or the axis of rotation. However, in a cone—plate viscometer the rate of shear across the conical gap is essentially constant because the linear velocity and the gap between the cone and the plate both increase with increasing distance from the axis. No tedious correction calculations are required for non-Newtonian fluids. The relevant equations for viscosity, shear stress, and shear rate at small angles a of Newtonian fluids are equations 29, 30, and 31, respectively, where M is the torque, R the radius of the cone, v the linear velocity, and rthe distance from the axis. 

Dyna.mic Viscometer. A dynamic viscometer is a special type of rotational viscometer used for characterising viscoelastic fluids. It measures elastic as weU as viscous behavior by determining the response to both steady-state and oscillatory shear. The geometry may be cone—plate, parallel plates, or concentric cylinders parallel plates have several advantages, as noted above. 

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... 

Brookfield has introduced a new digital cone—plate viscometer in two versions. The CAP 1000 is a single speed instmment (12,000 or 3, 000 with 60 Hz current) that upgrades the ICl cone—plate design (ASTM D4287). The CAP 2000 is a multispeed viscometer with a viscosity range of 1 15, 000 mPa-s. This instmment covers a wide range of shear rates (166-26, 600 ) and complements the low shear WeUs-Brookfield viscometer. 

The Ferranti-Shidey viscometer was the first commercial general-purpose cone—plate viscometer many of the instmments stiU remain in use in the 1990s. Viscosities of 20 to 3 x 10 mPa-s can be measured over a shear rate range of 1.8-18, 000 and at up to 200°C with special ceramic cones. Its features include accurate temperature measurement and good temperature control (thermocouples are embedded in the water-jacketed plate), electrical sensing of cone—plate contact, and a means of adjusting and locking the position of the cone and the plate in such a way that these two just touch. Many of the instmments have been interfaced with computers or microprocessors. 

The ICI cone—plate device is a simple, iaexpensive, one-speed iastmment designed for routine determination of paint viscosities at a shear rate comparable to that of bmshing or sprayiag (12, 000 at 60 H2 and 10, 000 at 50 H2) (180,181). The viscosity range at that shear rate is limited to 5-1000 mPa-s. A wider-angle cone allows measurement to 10, 000 mPa-s, but at a lower shear rate of 3, 000. A lower shear rate version (600 )... 

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. ... 

The Ravenfield model BS viscometer is a wide shear rate range iastmment with several possible measurement systems cone—plate, parallel plates, concentric cylinders, and taper plug. The last gives shear rates of up to 10 , and the cone—plate of up to 8 x lO". The viscosity range is... 

A number of viscometers have been developed for securing viscosity data at temperatures as low as 0 °C (58,59). The most popular instmments in current use are the cone plate (ASTM D3205), parallel plate, and capillary instmments (ASTM D2171 and ASTM D2170). The cone plate can be used for the deterniination of viscosities in the range of 10 to over 10 Pa-s (10 P) at temperatures of 0—70°C and at shear rates from 10 to 10 5 . Capillary viscometers are commonly used for the deterniination of viscosities at 60 —135°C. 

FIG. 4 Viscosity (cone-plate rheometer, D = 3.23 s1, at 25°C) and clear point of 10% sodium lauryl ether (2 EO) sulfate solutions with 0.5% of added NaCl vs. percentage of dialkanolamide [77],... 

When compared to standard (open cavity) cone-plate or parallel disks rheometers, closed cavity torsional rheometers such as the RPA or the PPA have unique high-strain capabilities, which prompted us to modify the instmment in order to investigate the promises of FT rheometry, as outlined a few years ago by the pioneering works of Wilhelm. The technique consists of capturing strain and torque signals and in using FT calculation algorithms to resolve it into their harmonic components, as detailed below. 

Model reactors, e.g. viscosimeters (cylinder or cone-plate systems), channel currents and jets (see Table 2) have been used very often to test the shear stress... 

Rheological Property Determination. The rheology of an emulsion is often an important factor in determining its stability. Any variation in droplet size distribution, degree of flocculation, or phase separation frequently results in viscosity changes. Since most emulsions are non-Newtonian, the cone-plate type device should be used to determine their viscosity rather than the capillary viscometer. 

Zero shear viscosities have been determined in solution over a wide range of concentrations with a cone-plate Rheometrics Stress Rheometer. For linear macromolecules, the viscosity is proportional to c below the so called "entanglement concentration", c above c, is proportional to c. However, the viscosity will rise steeply at some concentration below c in the case where particular interconnections are formed at the concentration at which the molecules come into contact with one another. Ideally this will be the overlap threshold c. Below c, the molecules may associate partially but cannot form a network continuous over the entire sample space. Above c, plastic flow will require separation and... 

Two main types of viscometers are suitable for the determination of the viscosity of a polymer melt The rotation viscometer (Couette viscometer, cone-plate viscometer) and the capillary viscometer or capillary extrusiometer. The latter are especially suitable for laboratory use since they are relatively easy to handle and are also applicable in the case of high shear rates. With the capillary extrusiometer the measure of fluidity is not expressed in terms of the melt viscosity q but as the amount of material extruded in a given time (10 min). The amount of ex-trudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MFI/2 (190 °C)=9.2 g/10 min means that at 190 °C and 2 kg load, 9.2 g of poly-... 

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