Newtonian fluids rheological measurements

The measurements are carried out at preselected shear rates. The resulting curves are plotted in form of flow-curves t (D) or viscosity-curves ti (D) and give information about the viscosity of a substance at certain shear rates and their rheological character dividing the substances in Newtonian and Non-Newtonian fluids. 

Many materials are conveyed within a process facility by means of pumping and flow in a circular pipe. From a conceptual standpoint, such a flow offers an excellent opportunity for rheological measurement. In pipe flow, the velocity profile for a fluid that shows shear thinning behavior deviates dramatically from that found for a Newtonian fluid, which is characterized by a single shear viscosity. This is easily illustrated for a power-law fluid, which is a simple model for shear thinning [1]. The relationship between the shear stress, a, and the shear rate, y, of such a fluid is characterized by two parameters, a power-law exponent, n, and a constant, m, through... 

Anklam et al. [91] have attempted to measure the extensional rheological properties of w/o emulsions and HIPEs, using a nozzle-type viscometer. However, the results showed a dependence on the nozzle size used, and long relaxation times. Experiments on other non-Newtonian fluids indicated that it was not possible to obtain reliable results with this kind of instrument. 

This last value compares very well to that given by Blauch and Anson [12]. An extension of this application was proposed by Deslouis and Tribollet to the diffusivity measurement in non-Newtonian fluids [63, 64]. They considered a power-law fluid characterized by a rheological law ... 

There are a number of types of rheological measurement, some are appropriate for Newtonian fluids only, while others may be used for Newtonian or non-Newtonian fluids. Some of the principal types are listed in Table 6.4. Some very useful descriptions of experimental techniques have been given by Whorlow [355] and others [215,352,353,356,357]. The principal methods are discussed in the next several sections. 

Index Entries Com stover rheological measurement shear stress shear rate non-Newtonian fluids Power Law parameters. 

To avoid the apparent complications with absolute rheologic measurement techniques, a number of investigators (4,5). have used relative measurement systems to make rheologic measurements. The major difference between the relative and absolute measurement techniques is that the fluid mechanics in the relative systems are complex. The constitutive equations needed to find the fundamental rheologic variables cannot be readily solved. Relative measurement systems require the use of Newtonian and non-Newtonian calibrations fluids with known properties to relate torque and rotational speed to the shear rate and shear stress (6). 

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. 

However, they may not indicate the true bulk viscosity of a suspension that forms a thin layer of the continuous phase (e.g., serum of tomato juice) around the immersed probe or when the probe is covered by a higher viscosity gel due to fouling. Vibrational viscometers are suitable for measuring viscosities of Newtonian fluids, but not the shear-dependent rheological behavior of a non-Newtonian fluid (e.g., to calculate values of the power law parameters). 

Sometimes, this expectation is not met. At high flow rates, there can be hydrodynamic instabilities that lead to secondary flows which ruin the rheological measurement. Such instabilities occur in Newtonian fluids, due, for example, to inertial effects, such as those in Poiseuille flow at Reynolds numbers exceeding 2000 (Drazin and Reid 1981). For some complex fluids, even at low Reynolds number there are instabilities that are driven by elastic effects (Larson 1992). 

Coupled controlled velocity, magnetic resonance imaging (MRI)/rheology measurements of thixotropic and yielding colloidal suspensions further demonstrate the importance of paired measurements [63], Shear rate profiles obtained in laminar tube flow for both Newtonian and non-Newtonian fluids from MRI... 

This standard covers measurement of the rheological properties of polymers with both stable and unstable melt viscosity parameters at various temperatures and shear rates. The test procedure lists typical test temperature conditions for polyethylene 190°C, for polypropylene 230°C, for poly(vinyl chloride) 170-205°C, however, this indicates that the most useful data are generally obtained at temperatures consistent with processing experience. The test method also prescribes using the Rabinowitsch shear rate correction (see above) and indicates that the basic rheology equations (17.10), (17.15) and (17.16) yield true shear rate and true viscosity for Newtonian fluids only for non-Newtonian fluids only the apparent shear rate and viscosity are obtained. 

N. A. Park, Measurement of Rheological Properties of Non-Newtonian Fluids With the Falling Needle Viscometer, Ph.D. thesis, Mech. Eng. Dept., State Univ. of New York at Stony Brook, 1984. 

In practical applications, flow of the material through an orifice is perhaps the most frequently encountered rheological phenomenon. It is then natural to be used for the viscosity measurement of suspensions (53-55). However, the flow through an orifice is not precise in terms of shear measurement because the shear rate is not well defined under such circumstances. To meet this objection, the orifice is in most cases extended to a tube. This leads to the capillary flow type of viscometers, the simplest, and for Newtonian fluids, the most accurate type, comprising the familiar Ostwald und Ubbelohde viscometers. The fully developed axial velocity in the laminar regime is given by... 

Even the measurement of the steady-state characteristics of shear-dependent fluids is more complex than the determination of viscosities for Newtonian fluids. In simple geometries, such as capillary tubes, the shear stress and shear rate vary over the cross-section and consequently, at a given operating condition, the apparent viscosity will vary with location. Rheological measurements are therefore usually made with instraments in which the sample to be sheared is subjected to the same rate of shear throughout its whole mass. This condition is achieved in concentric cylinder geometry (Fi re 3.37) where the fluid is sheared in the annular space between a fixed and a rotating cylinder if the gap is small compared with the dimneters of the cylinders, the shear rate is approximately... 

---