Non-Newtonian characteristics

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

A Newtonian liquid of viscosity 0.1 N s/m2 is flowing through a pipe of 25 mm diameter and 20 m in lenglh, and the pressure drop is 105 N/m2. As a result of a process change a small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-Newtonian characteristics its rheology is described adequately by the power-law model and the flow index is 0.33. The apparent viscosity of the modified fluid is equal to ihc viscosity of the original liquid at a shear rate of 1000 s L... 

As indicated earlier, non-Newtonian characteristics have a much stronger influence on flow in the streamline flow region where viscous effects dominate than in turbulent flow where inertial forces are of prime importance. Furthermore, there is substantial evidence to the effect that for shear-thinning fluids, the standard friction chart tends to over-predict pressure drop if the Metzner and Reed Reynolds number Re R is used. Furthermore, laminar flow can persist for slightly higher Reynolds numbers than for Newtonian fluids. Overall, therefore, there is a factor of safety involved in treating the fluid as Newtonian when flow is expected to be turbulent. 

When a liquid exhibits non-Newtonian characteristics, the above procedures for Newtonian fluids are valid provided that the liquid flow is turbulent. 

Fine suspensions are reasonably homogeneous and segregation of solid and liquid phases does not occur to any significant extent during flow. The settling velocities of the particles are low in comparison with the liquid velocity and the turbulent eddies within the fluid are responsible for the suspension of the particles. In practice, turbulent flow will always be used, except when the liquid has a very high viscosity or exhibits non-Newtonian characteristics. The particles may be individually dispersed in the liquid or they may be present as floes. 

Though most of the industrial fluids show non-Newtonian characteristics, the drop formation studies in them have not been reported. The results will very strongly depend on whether the non-Newtonian fluid forms the dispersed or continuous phase. 

Extensive comparisons of predictions and experimental results for drag on spheres suggest that the influence of non-Newtonian characteristics progressively diminishes as the value of the Reynolds number increases, with inertial effects then becoming dominant, and the standard curve for Newtonian fluids may be used with little error. Experimentally determined values of the drag coefficient for power-law fluids (1 < Re n < 1000 0.4 < n < 1) are within 30 per cent of those given by the standard drag curve 37 38. ... 

Nonsettling slurries are formed with fine particles or plastics or fibers. Although their essentially homogeneous nature would appear to make their flow behavior simpler than that of settling slurries, they often possess non-Newtonian characteristics which complicate their flow patterns. In Newtonian flow, the shear stress is proportional to the shear strain,... 

The relationship between shear stress and shear rate is also an indication of the degree of Newtonian behavior that a fluid exhibits. The linearity of the relationship is a direct indication of Newtonian behavior. The 5% corn stover suspension exhibited Newtonian behavior the remaining corn stover suspensions exhibited non-Newtonian behavior. At the other concentrations (>5%), the degree of linearity decreased with increasing mass concentration. Figure 4 illustrates the non-Newtonian characteristics of the remaining corn stover suspensions. 

Thermoplastics have non-Newtonian melt flow characteristics it means that their viscosity will change dependent on their velocity or the amount of shear that occurs in the melt (Chapter 1). This non-Newtonian characteristic is a key in thin wall molding. As in any molding setup one cannot just simply ram the melt into the cavity. It s flow characteristic, gate size as well as position, and venting have to be balanced in order to obtain the desired structural part and meet tight tolerance requirements. 

The addition of fillers to blow molded materials does not require special equipment but frequently the process parameters must be adjusted to compensate for the changes in the rheological properties of the melt. Larger additions of fillers tend especially to introduce non-Newtonian characteristics which require careful consideration. Also, timing of processes requires adjustment to deal with the higher nucleation rate caused by the presence of filler. 

Selby, T.W. (1958) The non-Newtonian characteristics of lubricating oils. Trans. ASLE I 68-81. 

Owing primarily to the organic character of the cell and the rich content in water, the suspension, once concentrated, tends to exhibit the non-Newtonian behavior. Transportation, heat transfer and mass transfer (i.e. drying and so on), all of which are the subjects adjunct to the separation, abound with problems still remaining to be dissolved in regard to the non-Newtonian characteristics. 

The significance of the non-Newtonian characteristics of the resist solution is illustrated in Figure 3. It is apparent that the assumption of Newtonian behavior leads to a weaker dependence of film thickness on spin speed than is observed experimentally, and one which is independent of polymer concentration in the initial resist. The non-Newtonian model not only gives quantitative predictions of the film thickness, but also generates the correct dependence on spinner speed. The dependence on spinner speed is stronger for the higher concentration solutions. This is attributable to the more prominant non-Newtonian behavior of the resist at higher concentrations. 

The rheological data are given in Table 1. The second column of the table is the evaporation state of the oil in mass pereentage lost. The third column is the assessment of the stability of the emulsion based on both visual appearance and rheological properties. The power law constants, k and n, are given next. These are parameters from the Ostwald— de Waele equation which describes the Newtonian (or non-Newtonian) characteristics of the material. The viscosity of the emulsion is next and in column 7, the complex modulus which is the vector sum of the viscosity and elasticity. Column 8 lists the elasticity modulus and column 9, the viscosity modulus. In column 10, the isolated, low-shear viscosity is given. This is the viscosity of emulsion at very low shear rate. In column 9, the tan 5, the ratio of the viscosity to the elasticity component, is given. Finally, the water content of the emulsion is presented. 

This classification scheme is arbitrary in that most real materials often exhibit a combination of two or even all three types of non-Newtonian features. Generally, it is, however, possible to identify the dominant non-Newtonian characteristic and to take this as the basis for the subsequent process calculations. Also, as mentioned earlier, it is convenient to define an apparent viscosity of these materials as the ratio of shear stress to shear rate, though the latter ratio is a fimction of the shear stress or shear rate and/or of time. Each type of non-Newtonian fluid behaviour will now be dealt with in some detail. 

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