Viscosity, shear

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

In most rotational viscometers the rate of shear varies with the distance from a wall or the axis of rotation. However, in a cone—plate viscometer the rate of shear across the conical gap is essentially constant because the linear velocity and the gap between the cone and the plate both increase with increasing distance from the axis. No tedious correction calculations are required for non-Newtonian fluids. The relevant equations for viscosity, shear stress, and shear rate at small angles a of Newtonian fluids are equations 29, 30, and 31, respectively, where M is the torque, R the radius of the cone, v the linear velocity, and rthe distance from the axis. 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

Figure 8.5. Apparent viscosity-shear rate curves for dilatant fluid, a Newtonian fluid and pseudoplastic fluid which have the same apparent viscosity at zero shear rate...

Figure 3.27. Plot of apparent viscosity-shear rate relation using logarithmic axes...

Dynamic viscosity Kinematic viscosity Density Surface tension Shear stress Vapor quality Contact angle Shear viscosity Shear rate... 

FIGURE 5.16 Viscosity-shear stress relationships for various compositions of nylon-6-acrylate rubber (ACM) blends at 240°C. 

The probability that a chain will break at its midpoint increases with increasing viscosity, shear rate, and the square of the molecular weight of the chain under consideration. 

Fig. 4.7.9 MRI apparent viscosity-shear rate data in comparison with a conventional rotational viscometer shear viscosity-shear rate data. (Permission granted to reprint Figure 4 on page 517 in Ref. [49].)...

So far the results have been shown in which the metal alkoxide solutions are reacted in the open system. It has been shown that the metal alkoxide solutions reacted in the closed container never show the spinnability even when the starting solutions are characterized by the low acid content and low water content (4). It has been also shown from the measurements of viscosity behavior that the solution remains Newtonian in the open system, while the solution exhibits structural viscosity (shear-thinning) in the closed system. 

Figure 3 Viscosity - shear rate curves at three different temperatures...

A similar variety of samples was tested for thermal stability by capillary rheometry and TGA. Figure 6.3 shows the viscosity-shear rate dependence for PCTFE homopolymers and one copolymer (Alcon 3000). All materials, save one, showed virtually identical viscosity relationships despite large changes in inherent viscosity. Only the polymers from runs initiated by fluorochemical peroxides (FCP) showed a dependence of molecular weight (as measured by inherent viscosity) upon melt viscosity. 

Viscometer Price Viscosity Shear rate capability, Temperature M anufacturer... 

Fig. 13. Viscosity/shear stress relationship for EPDM compounds at 100 °C at various carbon black filler levels [50]...

A model has been developed to describe the penetration of polydimethylsi-loxane (PDMS) into silica agglomerates [120]. The kinetics of this process depend on agglomerate size and porosity, together with fluid viscosity. Shearing experiments demonstrated that rupture and erosion break-up mechanisms occurred, and that agglomerates which were penetrated by polymer were less readily dispersed than dry clusters. This was attributed to the formation of a network between sihca aggregates and penetrated PDMS, which could deform prior to rupture, thereby inhibiting dispersion. 

Fig. 8.10. Viscosity-shear rate master curve for concentrated polystyrene-n-butyl benzene solutions. The data were obtained for molecular weights ranging from 160000 to 2400000 concentrations from 0.255 to 0.55 gm/ml, and temperatures from 30° C to 60° C (155)...

Judged by the superposability of viscosity-shear rate data on the same master curve for a variety of polymers [polystyrene (155) (Fig. 8.10), poly(a-methyl... 

Experimental viscosity-shear rate curves at high concentrations turns out to be rather similar to an expression for non-Newtonian viscosity derived from the Eyring s activated complex theory for the transport properties of liquids (341) ... 

See Table 3.2). One additional remark should be made with respect to Fig. 3.2. In this figure parameter p is calculated with the aid of the experimental viscosity-shear rate relation. As a consequence, the deviation from the quadratic relationship is less pronounced than in Fig. 3.1. 

Viscometer type Lowest viscosity Highest viscosity Shear rate range (s 1)... 

As we have seen in Section 6.6.1 such confined liquids may behave quite differently from the bulk lubricant. Near the surfaces, the formation of layered structures can lead to an oscillatory density profile (see Fig. 6.12). When these layered structures start to overlap, the confined liquid may undergo a phase transition to a crystalline or glassy state, as observed in surface force apparatus experiments [471,497-500], This is correlated with a strong increase in viscosity. Shearing of such solidified films, may lead to stick-slip motions. When a critical shear strength is exceeded, the film liquefies. The system relaxes by relative movement of the surfaces and the lubricant solidifies again. 

Since the apparent viscosity of a non-Newtonian fluid holds only for the shear rate (as weii as temperature) at which it is determined, the Brookfield viscometer provides a known rate of shear by means of a spindle of specified configuration that rotates at a known constant speed in the fluid. The torque imposed by fluid friction can be converted to absolute viscosity units (centipoises) by a multiplication factor. See viscosity, shear stress. The viscosities of certain petroleum waxes and wax-polymer blends in the molten state can also be determined by the Brookfield test method ASTM D 2669. 

Material or process stream Approximate viscosity Shear rate Temperature... 

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