Representative viscosity

As mentioned earlier, space or Held dependent material properties can also be represented with radial functions. This is the case with rate of deformation- or velocity-dependent viscosity. Here, we present two alternatives to represent viscosity and viscosity gradients. The first and simpler form, also referred to a the direct method, simply applies the RFM to the viscosity itself as... 

Information about the behavior of shear thinning melts in twin screws can be derived from Eq. 7.13, in addition to the approximation of the measured values. The concept of representative viscosity based on Frederickson [3] is used for this purpose. The representative viscosity is the viscosity that provides the same pressure generation as a Newtonian fluid under the specified conditions. If we combine Eqs. 7.13 and 7.2, we obtain for the representative viscosity ... 

The representative viscosity represents a point on the flow curve Eq. 7.11. It occurs when the representative shear rate is imposed on the shear thinning fluid. If we compare Eqs. 7.11 and 7.14, we can see that the representative shear speed is proportional to the rotational speed and proportional to (1-A). 

One advantage of the concept of representative viscosity is that the measured flow curve is entirely sufficient to determine the pressure and energy behaviors. It is not necessary to determine the flow exponent m and the time constant . As can be seen in Fig. 7.12, the representative viscosity is determined with reference to the representative shear rate from the flow curve using Eq. 7.15. This then replaces the constant Newtonian viscosity in Eq. 7.2. 

Figure 7.12 Determination of the representative viscosity from the flow curve...

As with the pressure behavior, a representative viscosity can also be specified for the energy behavior. The representative viscosity is the viscosity that gives the same energy absorption as a Newtonian fluid at the same operating point (A = idem). The formulae are derived as for the procedure for the pressure generation behavior. Only the result is shown here ... 

Figure 7.13 Ratio between the representative viscosities for energy and pressure...

Values in parentheses represent viscosity maxima after 1200 seconds. 

In promotional, advertising, and even technical literature there are anomalies in the data representing viscosities of grout solutions. Since grout viscosity is one of the more important factors in regulating the movement of grout injected into a porous formation, it is desirable to define the terms clearly. 

To arrive at a representative viscosity for the mixing process, Tebel and Zehner [539] used the proportionality between the circulation number N s and the mixing effect in a loop reactor driven by a propulsion jet (where qi is the total liquid circulating and qi is the throughput of the propulsion jet). Its circulation characteristic N (Reeff) was due to the purposeful flow direction and momentum... 

This expression relates the film thickness h (Eq. [18a]) as a function of the chemical potential u and the mean velocity, and is valid only when the liquid viscosity is constant throughout the film. Experimental and theoretical evidence shows a presence of a thin layer with modified viscosity close to the solid surface. Liquid viscosity is elevated relative to bulk liquid due to short- and long-range interfacial forces (Low, 1976,1979 Derjaguin et ah, 1987 McBride Baveye, 1995). Expressions derived by Low (1979) for viscosity profiles of water altered by interfacial forces were recently modified by Or and Wraith (1999) to represent viscosity r in terms of distance from the solid surface ... 

If we assume that the modulus is essentially temperature-independent, we can ascribe the temperature dependence of t to the temperature dependence of the viscosity. Assuming a typical room temperature value of G of -10 N m", the value of x at a viscosity of 10 Pa s is 10 seconds. Relaxation of approximately 95% of the initial stress occurs by a time of 3x, or 30 seconds. It follows that relaxation at temperatures in the glass transformation range would be expected to occur over times ranging from hours to seconds, as the viscosity decreases with increasing temperature. Since most experimental measurements of Tg involve heating specimens at rates of 3 to 20 K min (0.05 to 0.33 K s ) we expect that these measurements will indicate relaxation processes occurring on similar timescales, and that Tg values will represent viscosities of 10 to 10 Pa s. 

Van der Wyk has advanced a theory of viscosity of binary mixtures based on Andrado s theory of the viscosity of pure liquids referred to above. He tried to find an explanation first for the processes in normal binary mixtures. The formulas current for these mixtures, which represent viscosity as dependent on the concentration of the constituents, arc, however, without exception, empirical laws. Attempts have certainly been made to give theoretical support to the laws but they usually turn out to be not quite successful. 

Table 5 and Table 6 give some representative viscosity data for PAMAA and D-g-AM respectively in 1.5% NaCl solution after allowing for viscosity stability. The last column in the table displays the ratio of the intrinsic viscosity in deionized water, [ti]H20, and in 1.5% NaCl solution, [ri]NaCl. The ratio for PAMAA is a function of copolymer composition and structure and shows a maximum at about 50 mole % acrylamide we observe here an almost 50-fold decrease in [t]] for a 1.5% NaCl solution, whereas [r ] for homo-PAM is relatively insensitive to salt effects. The intrinsic viscosity for D-g-AM in salt solution shows no significant change from the intrinsic viscosity in water. The ratio [r ]H20/[r ]NaCl is comparable to that of dextran. 

Figure 7.4 Viscosity versus shear rate for a typical resin, as obtained from the particle model of Kindt and Briels [158] and van der Noort et al. [162], The solid line represents experimental data while the crosses are simulation results including all forces in the stress tensor. The squares represent viscosities...

In a bubbling bed cold flow assessment performed by Lindborg [97], the two-fluid model employed was closed by a semi-empirical elasticity modulus parameterization for the particle phase collisional pressure and a constant representative viscosity... 

A representative viscosity of 0.9 mPas for the 25% bovine serum frequently used in simulator studies has been suggested by Dowson (2002). It is important to distinguish between the effective viscosity of the joint fluid bafiiing implants in vivo and that of the fluids used in simulator tests. The later is important in the analysis of experimental data on wear, friction and lubrication undo carefully controlled conditions, while the fr mer determines the tribological performance of implants in the body. The viscosity of synovial fluid from arthroplasty patients is probably somewhat higher than that of most of the lubricants adopted in simulator tests, as pointed out by Mazzucco et al (2002), and therefi)re a representative value of between 1.5 and 5 mPas appears to be reasonable fi>r in-vivo evaluations. 

The Mooney index is often called Mooney viscosity hut there is no rationale that the index represents viscosity. It is an expression of some aspect of viscoelasticity in that there may be some relationship to the processability. The method uses an instrument with a particular design, which provides a simple operation and a quick result. Compared to the dilute solution method, the sample size required is much larger so that it is more representative of the commercial lot. The Mooney index has been used worldwide as a specification for gum rubbers. 

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