Apparent viscosity Extension shear

Appendix B explains how polymer melt flow curves can be derived, and defines apparent (shear) viscosity. It is difficult to correlate the apparent viscosity with a single molecular weight average, because it depends on the width of the molecular weight distribution. However, in the limit of very low shear strain rates 7, when the entanglements between polymer chains produce negligible molecular extension, the apparent viscosity approaches a limiting value... 

Many mathematical expressions of varying complexity and form have been proposed in the literature to model shear-thinning characteristics some of these are straightforward attempts at cmve fitting, giving empirical relationships for the shear stress (or apparent viscosity)-shear rate curves for example, while others have some theoretical basis in statistical mechanics - as an extension of the application of the kinetic theory to the liquid state or the theory of rate processes, etc. Only a selection of the more widely used viscosity models is given here more complete descriptions of such models are available in many books [Bird et al., 1987 Carreau et al., 1997] and in a review paper [Bird, 1976],... 

In conclusion, it should be emphasised that most of the cmrently available information on heat transfer to non-Newtonian fluids in stirred vessels relates to specific geometrical arrangements. Few experimental data are available for the independent verification of the individual correlations presented here which, therefore, must be regarded somewhat tentative. Reference should also be made to the extensive compilations [Edwards and Wilkinson, 1972 Poggermann et al., 1980 Dream, 1999] of other correlations available in the literature. Although the methods used for the estimation of the apparent viscosity vary from one correlation to another, especially in terms of the value of ks, this appears to exert only a moderate influence on the value of h, at least for shear-thinning fluids. For instance, for n = 0.3 (typical of suspensions and polymer solutions), a two-fold variation in the value of ks will give rise to a 40% reduction in viscosity, and the effects on the heat transfer coefficient will be further diminished because Nu [Pg.371]

One method is based on the measurement of viscosity. 1° 105 Fig. 5.7610 shows an example measurement with a Brookfield viscometer, In this procedure, the gel solution is mixed in a thermally Jacketed beaker and then the viscometer is turned on with a specified spindle at a set shear rate. Apparent viscosity is measured as a function of time and typically yields a curve like that shown in Fig. 5,76. There is no apparent increase in viscosity for a period of time, and then a period of rapid increase occurs. Gel time may be arbitrarily defined as the time at which viscosity starts to increase, the tirne at which the extensions of the two approximately straight lines intersect, or the time at which the apparent viscosity reaches a specified value. This method has been found to give reproducible results for gel times of up to 10 days or more, l ... 

Figure 7.7.7 shows data collected in suction (uniaxial extension) and expulsion (biaxial or compression) plotted as apparent viscosity versus apparent extension rate. The liquid was Newtonian a glycerin-water mixture with shear viscosity of 1.6 poise. The dashed line gives Stjo, the value we would expect for pulling of the sample in air. We see that the values are closer to Ar)o because of the departure of the flow from ideal extensional flow. The solid lines represent calculations by Schunk et ai. (1990), who have carried out a fairly complete analysis of this flow, solving the Na-vier-Stokes equations via the finite element method. 

Normal mode relaxation is usually studied by the frequency dependence of the shear viscosity. An extensive literature exists on this topic (l6) and a number of features have been successfully identified which can be used to characterize such motion. For a flexible polymer the shape of the relaxation curve and its position will primarily be determined by the strength of the interaction of the polymer with the solvent, the length of the chain and its flexibility as defined by the intramolecular interaction constants. Theoretical analysis has been developed for the flexible coil with virtually no interaction with the solvent, with interaction of the solvent and the chain and also for the partially rigid polymer. Numerous examples of polymer-solvent combinations which possess the desired characteristics can be found in the literature (17 - ll). In general the theory predicts the initial shape of the low frequency viscoelastic behaviour of the polymer quite well but fails to describe the limiting high frequency properties. This apparent... 

The statement in connection with equations 56 and 57 that simple extension gives the same information as simple shear is limited not only to materials with n very near i but also to small deformations. With large deformations and/or large rates of deformation, the two types of strain show very different behavior. For example, in steady-state flow, the apparent shear viscosity (ratio of stress to rate of strain) commonly decreases with increasing rate of strain, whereas the apparent elonga-tional viscosity may remain constant or increase. Some examples will be shown in Chapters 13 and 17. 

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