Sheared fluids, behavior

Fig. 10. Fluid behavior in simple shear flow where A is Bingham B, pseudoplastic C, Newtonian and D, dilatant.

Slurry Viscosity. Viscosities of magnesium hydroxide slurries are determined by the Brookfield Viscometer in which viscosity is measured using various combinations of spindles and spindle speeds, or other common methods of viscometry. Viscosity decreases with increasing rate of shear. Fluids, such as magnesium hydroxide slurry, that exhibit this type of rheological behavior are termed pseudoplastic. The viscosities obtained can be correlated with product or process parameters. Details of viscosity deterrnination for slurries are well covered in the Hterature (85,86). 

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... 

Other schemes have been proposed in which data are fit to a lower, even order polynomial [19] or to specific rheological models and the parameters in those models calculated [29]. This second approach can be justified in those cases when the range of behavior expected for the shear viscosity is limited. For example, if it is clear that power-law fluid behavior is expected over the shear rate range of interest, then it would be possible to calculate the power-law parameters directly from the velocity profile and pressure drop measurement using the theoretical velocity profile... 

Utilization of a microfabricated rf coil and gradient set for viscosity measurements has recently been demonstrated [49]. Shown in Figure 4.7.9 is the apparent viscosity of aqueous CMC (carboxymethyl cellulose, sodium salt) solutions with different concentrations and polymer molecular weights as a function of shear rate. These viscosity measurements were made using a microfabricated rf coil and a tube with id = 1.02 mm. The shear stress gradient, established with the flow rate of 1.99 0.03 pL s-1 was sufficient to observe shear thinning behavior of the fluids. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

The second approach used in first-principles tribological simulations focuses on the behavior of the sheared fluid. That is, the walls are not considered and the system is treated as bulk fluid, as discussed. These simulations are typically performed using ab initio molecular dynamics (AIMD) with DFT and plane-wave basis sets. A general tribological AIMD simulation would be run as follows. A system representing the fluid would be placed in a simulation cell repeated periodically in all three directions. Shear or load is applied to the system using schemes such as that of Parrinello and Rahman, which was discussed above. In this approach, one defines a (potentially time-dependent) reference stress tensor aref and alters the nuclear and cell dynamics, such that the internal stress tensor crsys is equal to aref. When crsys = aref, the internal and external forces on the cell vectors balance, and the system is subject to the desired shear or load. 

Undoubtedly other factors may promote pseudoplastic behavior. For example, a decrease in size of swollen, solvated, or even entangled molecules or particles may occur under the influence of shearing stresses, to give the same changes in fluid behavior as in particle alignment. 

Power law model fluid with temperature dependent viscosity m0 = e( a(-T Tm The rate of melting is strongly dependent on the shear thinning behavior and the temperature dependent viscosity of the polymer melt. However, we can simplify the problem significantly by assuming that the viscous dissipation is low enough that the temperature profile used to compute the viscosity is linear, i.e.,... 

Another important ramification of shear-thinning behavior in capillary or tube flow, relevant to polymer processing, relates to the shape of the velocity profiles. Newtonian and shear-thinning fluids are very different, and these differences have profound effects on the processing of polymer melts. The former is parabolic, whereas the latter is flatter and pluglike. The reason for such differences emerges directly from the equation of motion. The only nonvanishing component for steady, incompressible, fully developed, isothermal capillary flow, from Table 2.2, is... 

Complementing these hydrodynamic issues has been an ongoing effort to examine the rheological properties of blood as well as other body fluids. Blood exhibits shear thinning behavior and appears to have a yield stress owing to the formation of macroscopic structures that incorporate protein-aided bridging of red cells. 

Thus, the fluid appears to be more viscous at the lower speed. Another view of the fluid properties is that as agitator speed increases, the shear rate increases and the viscosity decreases. This fluid behavior is called shear thinning and is typical of many polymers. 

Resolution of the velocity data and removal of data points near the center of the tube which are distorted by noise aid robustness of the curve fit the polynomial curve fit introduced a systematic error when plug-like flow existed at radial positions smaller than 4 mm in a tube of 22 mm diameter. The curve fit method correctly fit the velocity data of Newtonian and shear-thinning behaviors but was unable to produce accurate results for shear-thickening fluids (Arola et ah, 1999). 

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