Couette rotating-cylinder viscometer

A commonly employed instrument for measuring the viscosity of a liquid is the Oswald viscosimeter or viscometer, illustrated in Figure 11.16c. One measures the time that it takes, for a quantity of liquid to pass through the tube, from one position to another, under the force of its own weight. Usually the instrument is calibrated by the use of a liquid of known viscosity.f Another apparatus used for viscosity measurements is the Couette rotating-cylinder viscometer (see Figure 11.16d). 

Figure 4-10a shows the basic schematic diagram for the operating parts of the Couette concentric cylinder viscometer. The liquid to be investigated is in a thin layer between two coaxial cylinders, the outer one with a radius R2 rotating with angular velocity n and the inner one... 

In a rotational viscometer the solution is filled in the annulus between two concentric cylinders of which either the external (Couette-Hatschek type) or the internal (Searle type) cylinder rotates and the other, which is connected to a torsion-measuring device, is kept in position. Let R, and Ro be the radii of the inner and outer cylinders, h the height of the cylinder which is immersed in the solution or its equivalent height if end effects are present, a> the angular velocity of the rotating cylinder, and T the torque (or moment of force) required to keep the velocity constant against the viscous resistance of the solution. It can be shown that the shearing stress (see, for example, Reiner, 1960) ... 

In the last decade of the nineteenth century, Maurice Couette invented the concentric cylinder viscometer. This instrument was probably the first rotating device used to measure viscosities. Besides the coaxial cylinders (Couette geometry), other rotating viscometers with cone-plate and plate-plate geometries are used. Most of the viscometers used nowadays to determine apparent viscosities and other important rheological functions as a function of the shear rate are rotating devices. 

Shear dependence of the limiting viscosity nvunber is probably only significant for values of [i ] of several hundred, but this has always to be confirmed. Measurements can be made in a modified capillary viscometer. Details of construction of one for this purpose have been given, and the instrument has been used to study dextran fractions. Shear dependence can also be measured in a rotating cylinder (Couette) viscometer, and a simplified model has been described. ... 

The flow-property or rheological constants of non-Newtonian fluids can be measured using pipe flow as discussed in Section 3.5E. Another, more important method for measuring flow properties is by use of a rotating concentric-cylinder viscometer. This was first described by Couette in 1890. In this device a concentric rotating cylinder (spindle) spins at a constant rotational speed inside another cylinder. Generally, there is a very small gap between the walls. This annulus is filled with the fluid. The torque needed to maintain this constant rotation rate of the inner spindle is measured by a torsion wire from which the spindle is suspended. A typical commercial instrument of this type is the Brookfield viscometer. Some types rotate the outer cylinder. 

Many types of rotational rheometers and viscometers have been developed. The cone and plate, couette (coaxial cylinder), torsional, and disc spindle types are the most common. 

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. 

Typical of this class of viscometer is the coaxial or Couette type of instrument described in Volume l, Section 3.7.4. The sample fluid is contained within the annular space between two coaxial cylinders, either of which may be rotated by a motor with the remaining cylinder suspended elastically in such a way that the torsional couple exerted on the latter can be measured. If the outer cylinder of radius r2 rotates with an angular velocity cou and the inner cylinder of radius r, is stationary, and the torque (or viscous drag) per unit length of cylinder exerted on the inner cylinder is T, then, for a Newtonian fluid(49) ... 

By taking into account that v = cor, the velocity profile of the fluid layers in the Couette viscometer with rotating inner cylinder is given in Figure 13.18. Equation (13.70) in combination with the first boundary condition in Eq. (13.69) gives... 

Dynamic crystallization under precise control of shear and temperature was studied in a prototype apparatus specially developed. The whole cell, similar to a Couette viscometer, was made out of glass. The inner cylinder rotated at a controlled speed, CO, while the outer wall was fixed. A double-mantel with a circulation of water allowed precise control of the temperature. Temperature of cocoa butter in the cell was measured with a chromel-alumel thermocouple. Measures were recorded with a data acquisition system. Shear rate imposed to cocoa butter in the system could be estimated from the rotation speed of the inner cylinder, assuming that the fluid is Newtonian and incompressible. There is no normal speed, only tangential speed. The shear rate, y> in the specimen is a single function of the radiu. In the rest of this work, shear in the cell was characterized by its average value, y, calculated by integration over the cell thickness (7). 

Finally, there are industrial rheological instruments in common use that allow determination of viscosities for liquids to within a few percent, which is sufficient for many purposes. These involve measuring the torque required to maintain a given velocity for a fluid confined in the annulus between two concentric cylinders, one of which is rotated (Couette viscometer), or a fluid confined between a flat plate and a rotating cone (cone-and-plate viscometer). 

The apparatus with a cylinder rotating in liquid in a fixed cylinder is usually called the Couette viscometer in the Pochettino viscometer6 the two cylinders rotate in opposite directions. In Searle s7 apparatus (Fig. 6.VIIIE) a brass cylinder C of radius a is supported on a vertical spindle A pivoted at its ends, and dips to a depth / in a liquid in a cylinder B of radius b. The cylinder C is rotated by weights mg in scale pans which pull on cords passing round a drum of diameter d attached to the spindle, on the top of which is a disc a used with an index b to measure the period of rotation, t0. Then ... 

Figure 4-10. Concentric cylinder rotational viscometer. (a) Basic scheme of operation. (b) Couette viscometer with guard rings and liquid seal.

A nearly identical flow pattern exists in the annular space between two concentric cylinders, one rotating and the other stationary, provided the width of the annulus, B, is small compared to the diameters of the cylinders. A device that makes use of this is the Couette viscometer. By measuring the torque required to rotate one cylinder at a known speed, the viscosity may be readily calculated from Eq. (5.70). 

The cone-and-plate viscometer is one of the rotational methods of measuring the polymer viscosity. It consists of a fiat horizontal plate and a cone with an obtuse angle. The cone touches the plate at its tip and rotates at a constant speed. The melt is charged into the gap forming between the horizontal plate and the cone. The rotational velocity determines shear rate and the torque applied gives shear stress. Shear rate is constant across the gap, thus it eliminates the need for non-Newtonian behavior of the melt. In a plate-plate viscometer, the cone is replaced by a second flat plate. The Couette viscometer is comprised of two concentric cylinders where one can be rotated at a constant speed. 

Rotational methods are particularly suitable for studying the flow of non-Newtonian liquids. An example is the concentric cylinder (or Couette) viscometer. The liquid is sheared between concentric cylinders, which are moving relative to one another. The outer cylinder can be rotated (or oscillated) at a constant rate and the shear measured in terms of the deflection of the inner cylinder, which is suspended by a torsion wire. Altema-... 

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]. 

Couette Flow n Shear flow in the annulus between two concentric cylinders, one of which is usually stationary while the other turns. By measuring the relative rotational velocity and the torque required to maintain steady flow, one can infer the viscosity of the liquid. See Rotational Viscometer. Flow in the metering section of a single-screw extruder resembles Couette flow, modified by the presence of the flight and, normally, by the pressure rise along the screw. 

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. 

The second type of viscometer, which is fairly often used in colloid science, is the CouETTE type, which exists in many constructions and the principle of which is illustrated by Fig. 11. A hollow cylinder A is set in rotation by some mechanism D a cylinder B is suspended by a wire c (on which is a mirror d) coaxially with A. In the space between A and B is the liquid, for wMch one wishes to determine tj. Thanks to the internal friction the cylinder B experiences a rotation and the wire a torsion the angle of rotation can be determined with the aid of a beam of light oti the mirror c and a reading telescope. The couple exerted on the cylinder B is Kyfn, in which K is a constant for the apparatus and ol the ai ular velocity of cylinder A as a result the cylinder B experiences a rotation, characterized by the angle of torsion of the suspension wire. If the apparatus is first calibrated with water (subscript ly) and then the torsion angle for a sol (subscript s) is measured, the expression... 

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