Viscosity, effective

Same definitions as 5-26-M. ILff = effective viscosity from power law model, Pa-s. <3 = surface tension liquid, N/m. 

At extremely high shear rates, however, the degree of orientation reaches a maximum so that a further decrease in effective viscosity cannot occur—the polymer in this range again becomes Newtonian. 

Measurements of the effective viscosity as a function of composition may be fitted to equation 80 or presented in graphic form as in Figure 16. The correction factor, R, also may be determined by accounting for the volume fraction, ti , of particles through the Andress formula ... 

A proper representation of the effective viscosity is often problematic. Based on the Prandtl mixing length model for turbulence, Bloor and Ingham-suggest that the variation in p, should be of the form... 

The inelastic wave shows rise times that vary quite substantially. Recognizing that the rise time is a direct indication of the balance between the viscous response of the sample and the driving force, Grady [81G01] has analyzed and compared the effective viscosity of a range of materials. These viscosities are manifestations of the dynamic deformation controlled by the shock-induced defects, heterogeneities, and their motions. 

For non-Newtonian drilling fluids, the concept of an effective viscosity can be used to replace the dynamic viscosity in Equation 4-89. 

For a Bingham plastic fluid flow in a circular pipe and annular space, the effective viscosities are given as [61]. 

The alternative large scale recovery method to precipitation is ultrafiltration. For concentration of viscous exopolysaccharides, ultrafiltration is only effective for pseudoplastic polymers (shearing reduces effective viscosity see section 7.7). Thus, pseudoplastic xanthan gum can be concentrated to a viscosity of around 30,000 centipoise by ultrafiltration, whereas other polysaccharides which are less pseudoplastic, are concentrated only to a fraction of this viscosity and have proportionally lower flux rates. Xanthan gum is routinely concentrated 5 to 10-fold by ultrafiltration. 

Many microbial polysaccharides show pseudoplastic flow, also known as shear thinning. When solutions of these polysaccharides are sheared, the molecules align in the shear field and the effective viscosity is reduced. This reduction of viscosity is not a consequence of degradation (unless the shear rate exceeds 105 s 1) since the viscosity recovers immediately when die shear rate is decreased. This combination of viscous and elastic behaviour, known as viscoelasticity, distinguishes microbial viscosifiers from solutions of other thickeners. Examples of microbial viscosifiers are ... 

For scaly fillers the increase of relative viscosity with filler concentration is not as pronounced as in case of fibrous fillers [177,178]. Owing to filler orientation, the flow curves for systems with different concentrations of a fibrous and a scaly filler may merge together at high shear rates [181]. In composites with a dispersed filler the decrease of the effective viscosity of the melt with increasing strain rate is much weaker. 

Relative elongation at rupture, % Effective viscosity logarithm 641 656 703... 

The effective viscosity of a non-Newtonian fluid can be expressed by the relationship ... 

A roughness-viscosity model was proposed to interpret the experimental data. An effective viscosity /tef was introduced for this purpose as the sum of physical and imaginary = Mm(f) viscosities. The momentum equation is... 

The effective viscosity of a suspension of particles in a fluid medium is greater than that of the pure fluid, owing to the energy dissipation within the electrical double layers. 

SFA has made a great contribution to the investigations of thin him rheology [41], The measurements on SFA conhrm that there is a signihcant enhancement of the effective viscosity in molecularly thin liquid hlms, and the viscosity grows constantly as the him thickness diminishes. 

It is also observed in SFA experiments that the effective viscosity declines in a power law, as the shear rate increases. The observations of the dynamic shear response of conhned liquid imply that the relaxation process in thin hlms is much slower and the time for the conhned molecules to relax can increase by several orders. 

Figure 4 shows the director profile at various ydv idy values. Figure 5 shows the corresponding effective viscosity values. Only one set of Leslie coefficients are presented, so no general conclusions can be drawn from the data on the rela-... 

The angular momentum conservation equation couples the viscous and the elastic effects. The angular profiles of the director and the effective viscosity data are computed for one set of material parameters based on published data in literature. The velocity profiles are also attained from the same dataset. The results show that the alignment of molecules has a strong influence on the lubrication properties. 

For a given film thickness, we can get the effective viscosity from Eq (17), then the ratio can be obtained from Eq (18). The relation between the ratios versus the film thickness is plotted in Fig. 18. Interestingly, this figure is very close to the experimental results (see, for example. Fig. 7 in Chapter 5). In the thick film regime, the ratio approaches unity. In the thin film regime, however, it increases with the diminishing film thickness. Therefore, microrotation and... 

The effective viscosity is also affected by the microrotation of the rigid particles. If the gap is much larger than the molecular dimensions, the boundary walls will have little influence on the microrotation motion. This means that if the gap between the solid walls is sufficiently large, the micropolarity can be reasonably taken out of consideration without losing precision. The microrotation in thin film lubrication will result in viscosity-enhancements and consequently higher film thicknesses, which contribute to a better performance of lubrication. 

Fig. 18—Effective viscosity versus minimum film thickness.

The effective viscosity predicted with micropolar theory is in very close agreement with that found by experimental results in a previous work. This does not adequately assure that it is the only possible way to explain the traits of thin him lubrication, but it shows the roles the microstructure and microrotation of the particles will play in the lubrication process in the very thin him EHL situation. 

---