Low-shear viscosity

The reactive extrusion of polypropylene-natural rubber blends in the presence of a peroxide (1,3-bis(/-butyl per-oxy benzene) and a coagent (trimethylol propane triacrylate) was reported by Yoon et al. [64]. The effect of the concentration of the peroxide and the coagent was evaiuated in terms of thermal, morphological, melt, and mechanical properties. The low shear viscosity of the blends increased with the increase in peroxide content initially, and beyond 0.02 phr the viscosity decreased with peroxide content (Fig. 9). The melt viscosity increased with coagent concentration at a fixed peroxide content. The morphology of the samples indicated a decrease in domain size of the dispersed NR phase with a lower content of the peroxide, while at a higher content the domain size increases. The reduction in domain size... 

All sliding friction forces are dramatically affected by surface contamination. If the surface is covered with a material that prevents the adhesive forces from acting, the coefficient is reduced. If the material is a liquid which has low shear viscosity the condition exists of lubricated sliding where the characteristics of the liquid control the friction rather than the surface friction characteristics of the materials. It is possible by the addition of surface materials that have high adhesion to increase the coefficient of friction. 

For practical purposes, it is convenient to define the relaxation time in terms of macroscopic quantities which can be readily determined. Within the validity limit of Hookean connectors (Eq. 13), the low-shear viscosity of a polymer solution is given by the relation ... 

This is an extended exponential. It operates within the remit of linear viscoelastic theory. So for example for a simple exponential we can show that the integral under the relaxation function gives the low shear viscosity ... 

Figure 5.17 The low shear viscosity as a function of concentration for a latex particle with an electrolyte concentration of 10 4M and radius of 38 nm. This is compared with the modified Eyring23 model and the hydrodynamic contribution to the flow...

This relationship between the relaxation modes and the low shear viscosity is an important one. It indicates that the longest Rouse relaxation time, i.e. the p = 1 mode ... 

This model, whilst not entirely satisfactory, can give a reasonable prediction of the elasticity in the plateau zone. The approach does not readily lend itself to a prediction of the dynamic behaviour. There have been numerous attempts to predict the low shear viscosity using entanglement models. For example Graessley obtained... 

The plateau modulus is determined by the region in which these two relaxation modes cross. The plateau modulus, the low shear viscosity and the tube disengagement time are given in Section 6.4.3 as... 

Figure 5.30 The low shear viscosity versus chain overlap for polyacrylamide (PAM) and acrylamide dodecyl methacrylate copolymers (DMA-AM). The figures refer to the mole percentage of hydrophobic chains...

If we compare the shear stress against shear rate it can be practically difficult to distinguish between plastic and pseudoplastic behaviour. However when the same data is represented on a log-log plot clear differences emerge. The low shear viscosity begins to reduce the stress... 

If we extrapolate this slope toward low rates, where the tangent equates with the low shear viscosity and assume the Peclet number here is unity we eventually obtain a value of b = 2.55. This defines the Peclet number as unity, at a stress somewhere just after the curvature of the viscosity curve deviates from the low shear limit. This seems quite an appropriate reference system. By setting the Peclet number to the appropriate value of b we can determine the variation in packing fraction with stress between the high and low shear limits to the viscosity ... 

We would expect a difference between the average time and that which determines the onset of shear thinning since the low shear viscosity tends to be dominated by the longest mode of relaxation. 

Highly fluid cement slurries with good water retention characteristics are used to grout the space between the formation and the metal pipe in the construction of oil wells. The grout must be highly fluid to prevent excessive friction during placement, must not lose water to the formation, and must provide ample low-shear viscosity to prevent creating free water and... 

Low shear viscosity measurements for both heated and unheated oils should be similar. 

The MacMichael viscometer is probably the most straightforward rotational viscometer. The outer cup rotates and the inner cylinder is suspended from a torsion wire. The drag on the inner cylinder is measured as degree of twist on the wire. Wires of different stiffness are available, and the maximum viscosity is ca 106 mPa-s. The shear rate range is limited, ca 2—12 s-1, but with modification, higher shear rates can be attained. The instrument is best suited for slow, time-dependent effects and low shear viscosities. 

Wyman and co-workers (120) studied the viscosity of narrow MWD linear and 4-armed star polystyrenes as a function of shear rate. At low shear rates, the star polymers (of MW 204000 and 430000) had low-shear viscosities much lower than linear ones of the same MW it may be remarked that the branch length... 

Asphalt is a semi-solid variety of bitumen having a (low shear) viscosity of about... 

Figure 3.21 shows the influence of extensional viscosity on the flow behavior of an aqueous PEO solution. The high extensional viscosity in comparison with the relatively low shear viscosity can cause the upper container to empty when pouring, even when the liquid surface is below the glass rim. This is visible in Fig. 3.21 by the liquid level markings. In the case of the viscous silicone oil however, the liquid thread breaks as the pouring container is tipped back (not shown here). 

The viscosity in the low shear regime depends mainly on the effective volume fraction of the particles in the suspension. There are many expressions given in the literature which relate the low shear viscosity of a suspension rjo to the viscosity of the suspending fluid ris. Two formulas which are independent of parameters specific... 

In the first formula only hydrodynamic contributions are considered, while in the second formula interparticle interactions are taken into account. These formulas are expected to hold at least approximately. The decrease of the low shear viscosity of ceramic suspensions with increasing mean particle size at fixed solids concentration is reported in Ref. 1. 

FIGURE 12S Schematic of the low shear viscosity of TiOj as a function of pH. Near the zero point of charge (ZPC) the rheology is non-Newtonian for dilute suspensions, conforming to the Cross equation, which suggests that aggregation is responsible for this increase in viscosity. Away from the ZPC, the rheology is Newtonian for dilute suspensions. 

Biroad Size Distributioiis Suspensions of broad size distributions of ceramic particles show in general that the low shear viscosity, 7jo> and the high shear viscosity, 7j , diverge according to... 

A plot of the stress-strain relationship for an ion-exchange ka-olinite also follows the Crossian rheology with very high low shear viscosities. In fact, the data show a yield stress at the lowest shear rate measured of y 1 sec and a high shear viscosity, which are both a function of the volume fraction of the clay, as shown in Figure... 

FIGURE 12 As aggregation proceeds, the low shear viscosity increases drastically as the percolation limit is reached at the gel time, tg. 

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