Newtonian fluids rotational viscometers

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. 

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. 

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. 

The unsuitable nature of many commercial instruments which are in common use clearly illustrates the confusion prevalent in the field of viscometric measurements. Many instruments measure some combination of properties which depend only partly on the fluid consistency since the flow is not laminar. In others the shear rates are indeterminate and the data cannot be interpreted completely. Examples of such units include rotational viscometers with inserted baffles, as in the modified Stormer instruments in which the fluid flows through an orifice, as in the Saybolt or Engler viscometers instruments in which a ball, disk, or cylinder falls through the fluid, as in the Gardiner mobilometer. Recently even the use of a vibrating reed has been claimed to be useful for measurement of non-Newtonian viscosities (M14, W10), although theoretical studies (R6, W10) show that true physical properties are obviously not obtainable in these instruments for such fluids. These various instru-... 

Chapter HI relates to measurement of flow properties of foods that are primarily fluid in nature, unithi.i surveys the nature of viscosity and its relationship to foods. An overview of the various flow behaviors found in different fluid foods is presented. The concept of non-Newtonian foods is developed, along with methods for measurement of the complete flow curve. The quantitative or fundamental measurement of apparent shear viscosity of fluid foods with rotational viscometers or rheometers is described, unithi.2 describes two protocols for the measurement of non-Newtonian fluids. The first is for time-independent fluids, and the second is for time-dependent fluids. Both protocols use rotational rheometers, unit hi.3 describes a protocol for simple Newtonian fluids, which include aqueous solutions or oils. As rotational rheometers are new and expensive, many evaluations of fluid foods have been made with empirical methods. Such methods yield data that are not fundamental but are useful in comparing variations in consistency or texture of a food product, unit hi.4 describes a popular empirical method, the Bostwick Consistometer, which has been used to measure the consistency of tomato paste. It is a well-known method in the food industry and has also been used to evaluate other fruit pastes and juices as well. 

If one considers fluid flowing in a pipe, the situation is highly illustrative of the distinction between shear rate and flow rate. The flow rate is the volume of liquid discharged from the pipe over a period of time. The velocity of a Newtonian fluid in a pipe is a parabolic function of position. At the centerline the velocity is a maximum, while at the wall it is a minimum. The shear rate is effectively the slope of the parabolic function line, so it is a minimum at the centerline and a maximum at the wall. Because the shear rate in a pipe or capillary is a function of position, viscometers based around capillary flow are less useful for non-Newtonian materials. For this reason, rotational devices are often used in preference to capillary or tube viscometers. 

To successfully measure non-Newtonian fluids, a known shear field (preferably constant) must be generated in the instrument. Generally, this situation is known as steady simple shear. This precludes the use of most single-point viscometers and leaves only rotational and capillary devices. Of these, rotational devices are most commonly used. To meet the criterion of steady simple shear, cone and plate, parallel plates, or concentric cylinders are used (Figure HI. 1.1). 

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) ... 

Since the apparent viscosity of a non-Newtonian fluid holds only for the shear rate (as weii as temperature) at which it is determined, the Brookfield viscometer provides a known rate of shear by means of a spindle of specified configuration that rotates at a known constant speed in the fluid. The torque imposed by fluid friction can be converted to absolute viscosity units (centipoises) by a multiplication factor. See viscosity, shear stress. The viscosities of certain petroleum waxes and wax-polymer blends in the molten state can also be determined by the Brookfield test method ASTM D 2669. 

For the impeller ribbon viscometer technique, the power number of an impeller is inversely proportional to the impeller Reynolds number (Eq. 1). As the impeller rotational speed increases, the flow will gradually change from laminar to turbulent, passing through a transition region. Parameter c can be obtained from the calibration fluids. If the same value for c is assumed to apply to a non-Newtonian fluid, then Eq. 4 can be used to calculate the apparent viscosity of that fluid. The range of the impeller method is determined by the minimum and maximum torques that can be measured (5). 

The impeller method is a technique commonly used to determine rheologic properties of fluids subject to particle settling. The impeller method utilizes a viscometer along with Newtonian and non-Newtonian calibration fluids to obtain constants that relate shear stresses and shear rates to experimentally measured values of torque and rotational speed. Newtonian calibration fluids are used to determine the impeller constant, c, and non-Newtonian calibration fluids are used to calculate the shear rate constant, k. These constants are then used to aid in the determination of rheologic properties of a selected non-Newtonian fluid, such as wet grains. 

Some rotational viscometers employ a rotating disc, bar, paddle or pin at a constant speed (or series of constant speeds). It is extremely difficult to obtain tme shear stress, and the shear rate usually varies from point to point in the rotating member. In particular, the velocity field of a rotating disc geometry can be considerably distorted in viscoelastic fluids. Nevertheless, because they are simple to operate and give results easily, and their cost is low, they are widely used in the food industry. While they may be useful for quality control purposes, especially Newtonian foods, the reliability of their values should be verified by comparison with data obtained with well defined geometries (capillary/tube, concentric cylinder, and cone-plate). 

Cone and Plate Viscometer, A cone and plate viscometer is shown in Figure 6. The test fluid is placed in the gap between the cone and the plate. The cone angle can be from 0.3 to 10 . The cone is made to rotate. In instruments such as a rheogoniometer, the flat bottom plate is provided with pressure-sensing devices for the measurement of normal stresses for viscoelastic fluids (quantities if/i and 02 of Appendix 1). For small cone angles (e.g., 1 ), the shear rate within the gap is very uniform. However, for the larger angles (e.g., 5 ), the shear rate within the gap is not very uniform, and it is not suitable for non-Newtonian fluids. Because of the small gap, this... 

The viscosity is typically measured by a viscometer. The SI unit of viscosity is the pascal second (Pa s). However, the widely used unit is poise (P) or centipoise (cP) (1 cP = 1 mPa s). The routine laboratory testing of viscosity is typically done using Brookfield viscometers and reported in cP. For non-Newtonian fluids such as those discussed above, the viscosity is dependent on the spindle size and type (number) and speed of rotation (rotation per minute or r/min) of the viscometer. 

In the rotating sphere viscometer, a solid sphere of radius R is suspended from a wire and rotates slowly at constant angular velocity about the long axis of the wire in an incompressible Newtonian fluid. The fluid is quiescent far from the sphere. 

The wide-gap rotational viscometer determination of the flow curve for a non-Newtonian fluid... 

Procedmes for extracting valid shear stress versus shear rate data from measurements involving wide gap coaxial cylinder systems (the Brookfield viscometer being an extreme example of wide gap devices) are therefore of considerable interest in making quantitative measurements of the flow properties of non-Newtonian process products. Most of these data-treatment procedures necessarily involve some assumption regarding the functional form of the flow curve of the material. One example is that made in the derivation of data from the Brookfield-type instrument, which assumes that the speed of rotation of the cylinder or spindle is proportional to the shear rate experienced by the fluid. This assumption implies that the flow curve is adequately described by a simple power-law (which for many shear-thinning non-Newtonian fluids may be acceptable), but this assiunption is widely taken to exclude all fluids which display an apparent yield stress and/or non-power law type behaviour. 

By changing the size of the spindles, the rotational viscometer can measure the viscosity of any fluid substance. Additionally, due to the fact that the apparatus has the ability to fluctuate shear rate, the identification of a Newtonian (a fluid having a viscosity that is independent of the shear rate) or non-Newtonian fluid is also possible. Additionally, in the case... 

Determination of Flow Properties of Non-Newtonian Fluids Using Rotational Viscometer... 

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. 

S. Flow Properties of a Non-Newtonian Fluid from Rotational Viscometer Data. Following are data obtained on a fluid using a Brookfield rotational viscometer. 

The rheological parameters of non-Newtonian fluids can be estimated by using any type of coaxial viscometer. In these instruments a bob or spindle rotates within a test fluid contained into a cup. The torque necessary to overcome the viscous resistance is measured while the degree to which the spring... 

Numerous methods for measuring fluid viscosity exist, for example, capillary tube flow methods (Ostwald viscometer), Zahn cup method, falling sphere methods, vibrational methods, and rotational methods. Rotational viscometers measure the torque required to turn an object immersed or in contact with a fluid this torque is related to the fluid s viscosity. A well-known example of this type of system is the Couette viscometer. However, it should be noted that as some CMP slurries may be non-Newtonian fluids, the viscosity may be a function of the rotation rate (shear rate). An example of this is the dilatant behavior (increasing viscosity unda increasing shear) of precipitated slurries that have symmetrical particles [33]. Furthermore, the CMP polisher can be thought of as a large rotational plate viscometer where shear rates can exceed 10 s and possibly affect changes to the apparoit viscosity. The reader can refer to the comprehensive review of viscosity measurement techniques in the book by Viswanath et aL [34]. 

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