Rotating viscometer

Fig. 19.7. A rotation viscometer. Rotating the inner cylinder shears the viscous glass. The torque (and thus the shear stress aj is measured for a given rotation rate (and thus shear strain rate y).

For viscometers having a cup-to-bob diameter ratio which is essentially infinite, as for the case of the Brookfield Synchrolectric cylindrical-bob viscometers rotating in a large beaker or tank, the shear rate at the bob is given (A3, Kl) by the relation... 

In rotational instruments, one member (e.g., the cup in a concentric cylinder viscometer) rotates while the other (e.g., the bob) remains stationary. The sample is held, and sheared, in the gap between the two. In a controlled shear rate measurement, the rotational speed is constant, and the torque on one member caused by the viscous resistance to flow exerted by the sample is measured. In a controlled stress measurement, a constant torque is applied to one member and its speed of rotation measured. Controlled stress instruments are particularly useful for measuring yield stress, the minimum stress causing flow of a plastic material. 

The cone-and-plate viscometer is an in vitro flow model used to investigate the effects of bulk fluid shear stress on suspended cells. Anticoagulated whole blood specimens (or isolated cell suspensions) are placed between the two platens (both of stainless steel) of the viscometer. Rotation of the upper conical platen causes a well-defined and uniform shearing stress to be applied to the entire fluid medium as described by Konstantopolous et al. (1998). The shear rate (y) in this system can be readily calculated from the cone angle and the speed of the cone using the formula i/ = where y is the shear rate in sec-1, mis the... 

Type of viscometer Rotating Capillary type, Capillary type,... 

Rotational Viscometers. Rotational viscometers are the most widely used instruments for the measurement of the rheological properties of a fluid (e.g., a pure liquid, emulsion, or suspension). The test fluid is placed in a gap formed by either two coaxial rotating cylinders, two flat discs, or a flat disc and a cone. The major advantages of the rotational viscometers are... 

Stormer viscometers, concentric cylinder viscometers, rotating spindles, falling spheres, etc. Because these viscometers expend part of their energy in accelerating the particles, this produces change in their orientation, and because voidage in the bed is affected by the immersed objects, the data on apparent viscosity of fluidized beds have to be carefully examined. 

The dynamic viscosity test determined by a rotating spindle viscometer (rotational viscometer test) is also covered by ASTM D 2196 (2010). 

Cranking Simulator), by a pumpability temperature limit measured by a rotating mini viscometer, and by the minimum kinematic viscosity at 100°C. The five summer grades are defined by bracketing kinematic viscosities at 100°C. 

Rotating cone viscometers are among the most commonly used rheometry devices. These instruments essentially consist of a steel cone which rotates in a chamber filled with the fluid generating a Couette flow regime. Based on the same fundamental concept various types of single and double cone devices are developed. The schematic diagram of a double cone viscometer is shown in... 

Figure 2.3 Definition of variables for concentric cylinder viscometers (a) the rotating cylinder and (b) the coaxial cylinders.

Wagner and DUlont have described a low-shear viscometer in which the inside diameter of the outer, stationary cylinder is 30 mm and the outside diameter of the inner, rotating cylinder is 28 mm the rotor is driven by an electromagnet. The device operates at 135°C and was found to be free of wobble and turbulence for shear rates between 3 and 8 sec V The conversion of Eq. (2.7) to Eq. (2.9) shows that F/A = (i7)(dv/dr) (instrument constant) for these instruments Evaluate the instrument constant for this viscometer. 

Rheology. Flow properties of latices are important during processing and in many latex appHcations such as dipped goods, paint, inks (qv), and fabric coatings. For dilute, nonionic latices, the relative latex viscosity is a power—law expansion of the particle volume fraction. The terms in the expansion account for flow around the particles and particle—particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle—particle interactions must be considered (92). A relative viscosity relationship for concentrated latices was first presented in 1972 (93). A review of empirical relative viscosity models is available (92). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rpleologicalmeasurement). 

The study of flow and elasticity dates to antiquity. Practical rheology existed for centuries before Hooke and Newton proposed the basic laws of elastic response and simple viscous flow, respectively, in the seventeenth century. Further advances in understanding came in the mid-nineteenth century with models for viscous flow in round tubes. The introduction of the first practical rotational viscometer by Couette in 1890 (1,2) was another milestone. 

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

Viscometers may be separated into three main types capillary, rotational, and moving body. There are other kinds, usually designed for special apphcations. For any given type there usually is a choice of several different instmments. The choice depends on the particular requirements of the investigator and the price range. 

Orifice viscometers should not be used for setting product specifications, for which better precision is required. Because they are designed for Newtonian and near-Newtonian fluids, they should not be used with thixotropic or highly shear-thinning materials such fluids should be characterized by using multispeed rotational viscometers. 

A number of instmments are based on the extmsion principle, including sHt flow and normal capidary flow (Table 6). These instmments are useful when large numbers of quahty control or other melt viscosity test measurements are needed for batches of a single material or similar materials. When melt viscosities of a wide range of materials must be measured, rotational viscometers are preferable. Extmsion rheometers have been appHed to other materials with some success with adhesives and coatings (10,161). 

Rotational viscometers often were not considered for highly accurate measurements because of problems with gap and end effects. However, corrections can be made, and very accurate measurements are possible. Operating under steady-state conditions, they can closely approximate industrial process conditions such as stirring, dispersing, pumping, and metering. They are widely used for routine evaluations and quahty control measurements. The commercial instmments are effective over a wide range of viscosities and shear rates (Table 7). 

Coaxial (Concentric Cylinder) Viscometer, The eadiest and most common type of rotational viscometer is the coaxial or concentric cylinder instmment. It consists of two cylinders, one within the other (cup and bob), keeping the specimen between them, as shown in Figure 27. The first practical rotational viscometer consisted of a rotating cup with an inner cylinder supported by a torsion wire. In variations of this design the inner cylinder rotates. Instmments of both types ate useful for a variety of apphcations. 

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. 

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. 

Controlled Stress Viscometer. Most rotational viscometers operate by controlling the rotational speed and, therefore, the shear rate. The shear stress varies uncontrollably as the viscosity changes. Often, before the stmcture is determined by viscosity measurement, it is destroyed by the shearing action. Yield behavior is difficult to measure. In addition, many flow processes, such as flow under gravity, settling, and film leveling, are stress-driven rather than rate-driven. 

OtherRota.tiona.1 Viscometers. Some rotational viscometers employ a disk as the inner member or bob, eg, the Brookfield and Mooney viscometers others use paddles (a geometry of the Stormer). These nonstandard geometries are difficult to analy2e, particularly for an infinite bath, as is usually employed with the Brookfield and the Stormer. The Brookfield disk has been analy2ed for Newtonian and non-Newtonian fluids and shear rate corrections have been developed (22). Other nonstandard geometries are best handled by determining iastmment constants by caUbration with standard fluids. 

Another type of rotational viscometer is the hehcal-screw rheometer (176). This iastmment is basically a screw-type metering pump that does not pump. The measure of force is the pressure difference resulting from the rotational motion. It is possible to use a bank of pressure transducers of different sensitivities to measure viscosity over a wide range. The iastmment can be used for high temperature rheometry and to foUow polymerkation, shear and heat degradation, and other developments. 

Specific Commercial Rotational Viscometers. Information on selected commercial rotational viscometers can be found ia Table 7. The ATS RheoSystems Stresstech rheometer is an iastmment that combines controlled stress as well as controlled strain (shear rate) and oscillatory measurements. It has a torque range of 10 to 50 mN-m, an angular velocity range of 0 to 300 rad/s, and a frequency range of seven decades. Operation and temperature programming (—30 to 150°C higher temperatures optional) are computer controlled. 

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