Flow Curves of Polymers

A lower Newtonian region exists at low shear rates or stresses, and this leads to the definition of zero-shear viscosity (// ), i.e., value of / as y - 0. 

The shear-thinning region is observed over several decades of intermediate shear rates. 

At veiy high shear rates, an upper Newtonian region is attained and the viscosity is defined as 7.  

Many equations have been proposed to quantitatively represent the flow ciuves of polymer melts and solutions. Among them, the power law equation discussed in 

In practical application, to represent the polymer flow curves in a relatively narrow shear rate range (e g., one or two decades of shear rate), the power law equation has sufficient accuracy. To represent the polymer flow curves in a wider shear rate range (e.g., three or four decades), the Carreau equation can be used. In addition to these two equations, other models also have been developed. The interested reader is referred to the works by Tanner (2000), Dealy and Larson (2006), and Brazel and Rosen (2012). 

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Due to their buffering action and low reactivity with the rock matrix, many researchers have suggested using buffered alkalis in alkali-polymer slugs. The effect of sodium carbonate on the flow curves of polymer solutions having 1,000 ppm polymer was examined by Nasr-EI-Din et al. [41]. Figure 15 shows the influence of sodium carbonate concentration on the low-shear relative viscosity measured one... 

The Statoii polymer has a lower pyruvate content than that of Flocon 4800. It is of interest to examine the effect of sodium chloride on the flow curves of this polymer. Figure 25 illustrates the flow curves of polymer solutions having 2,000 ppm Statoii polymer and sodium chloride concentrations of 0, 4, and 10 wt%. Similar to the trends observed with Flocon 4800, the effect of sodium chloride was observed at low shear rates only. However, the apparent viscosity at low shear rates for polymer solutions containing 4 and 10 wt% sodium chloride was higher than that at 0 wt% sodium chloride. This result is due to the lower ionic character (lower pyruvate content) of the Statoii polymer. 

Figure 24. Effect of sodium chloride concentration on the flow curves of polymer solutions having 2,000 ppm Flocon 4800.

Many researchers have reported a significant viscosity enhancement when sodium chloride was added to xanthan solutions having polymer concentrations > 4,000 ppm [19,24,28,80]. This effect was explained in terms of the association of polymer chains having collapsed side chains. To investigate this point further, the flow curves of polymer solutions containing 10,000 ppm polymer and various sodium chloride concentrations were measured. Figure 26 shows that the apparent viscosity of Flocon... 

Figure 29 depicts the effect of sodium hydroxide concentration (up to 10 wt%) on the flow curves of polymer solutions having 3,000 ppm Flocon 4800 at 20°C. The effect of sodium hydroxide on the polymer flow curve depended on the shear... 

Figure 34 displays the effect of Triton X-100 on the flow curves of polymer solutions having 2,000 ppm Statoil polymer. The influence of up to 10 wt% Triton X-100 on the flow curves of Statoil polymer was not significant. These results suggest that Triton X-100 (a nonionic species) does not interact physically or chemically with the polymer chain in deionized water. 

The flow curves of polymer will change because of hydrophobic association. Figure 43 shows the flow curves of 0.75 mol% N octylacrylamide/acrylamide copolymer. At polymer concentrations greater than 3,000 ppm the apparent viscosity is constant at low shear rate, then increases with shear rate (shear thickening) up to a maximum, and finally decreases with increasing shear rate (shear thinning). This unique and complex behavior is due to shifting the relative amount of inter and intramolecular association with shear rate [89]. One possible explanation for... 

It is known that polymer chains are fully relaxed and exhibit characteristic homopolymerlike terminal flow behavior, resulting in that the flow curves of polymers being expressed by the power law G oc a/ and G" oc a> [93-95]. Krisnamoorti and Giannelis [96] reported that the slopes of G (a) and G"(a) for polymer/layered silicate nanocomposites were much smaller than 2 and 1, respectively, which are the values expected for linear homodispersed polymer melts. They suggested that large deviations in the presence of a small quantity of layered silicate were caused by the formation of a network structure in the molten state. The slopes of the terminal zone of G and G for the PEN/CNT nanocomposites are presented in Table 7. This result indicated the non-terminal behavior with the power-law dependence for G and G of the PEN/CNT nanocomposites the flow eurves of the PEN/CNT nanocomposites can be expressed by a power law of G [Pg.64]

NobUe, M. R., Cocchini, F., Lawler, J. V. On the stabUity of molecular weight distributions as computed from the flow curves of polymer melts. J. Rheol. (1996) 40, pp. 363 382... 

As discussed above, polymer melts and solutions can be treated as shear-thinning fluids. However, this is trae only over a certain shear rate range. Figure 8.10 shows the typical logarithmic flow curves of polymer melts and solutions over a very wide range of shearing. Three different regions can be found in the flow curves ... 

As discussed above, the flow curves of polymer fluids can be obtained by Equations 8.18 and 8.38 (or 8.39), and the viscosities of the fluids can be calculated by Equation 8.41. While deriving these equations, one of the assumptions is that the flow pattern is constant along the pipe. However, in a real capillary flow, the polymer fluid exhibits different flow patterns in the entrance and exit regions of the pipe. For example, the pressure drops at the die entrance and exit regions are different from AP/Z. Therefore, corrections, e.g., Bagley correction, are needed to address the entrance and exit effects. Another assumption is that there is no slip at the wall. However, in a real flow, polymer fluid may slip at the wall and this reduces the shear rate near the wall. The Mooney analysis can be used to address the effect of the wall slip. In addition, the velocity profile shown in Figure 8.13 is a parabolic flow. However, the tme flow in the die orifice is not necessarily a simple parabolic flow, and hence Weissenberg-Rabinowitsch correction often is used to correct the shear rate at the wall for the non-parabohc velocity profile. 

In a number of works (e.g. [339-341]) the authors sought to superimpose graphically the flow curves of filled melts and polymer solutions with different filler concentrations however, it was only possible to do so at high shear stresses (rates). More often than not it was impossible to obtain a generalized viscosity characteristic at low shear rates, the obvious reason being the structurization of the system. 

Fig. 7. A pattern for displacing flow curves of filled polymers with the growth in temperature. The arrow indicates the direction of temperature growth...

The interaction effect between a dispersion medium and a filler on the net-formation in a filled polymer melt is mostly visuallized in the fact that the finishing treatment of the surface of solid particles results in a significant change of the position of the flow curve of the filled polymer on the whole, and yield stress as well [5, 8-10]. 

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

[Pg.86]

The flow properties of polymers provide a basis for predicting processing characteristics and are usually determined by measurements which relate a shear stress to some shear rate. Any polymer is characterized by its flow curves. Even interactions between compounding ingredients and the polymer can be detected in this way. 

Analysis of flow curves of these polymers has shown that for a nematic polymer XII in a LC state steady flow is observed in a broad temperature interval up to the glass transition temperature. A smectic polymer XI flows only in a very narrow temperature interval (118-121 °C) close to the Tcl. The difference in rheological behaviour of these polymers is most nearly disclosed when considering temperature dependences of their melt viscosities at various shear rates (Fig. 20). 

Viscosity measurements on emulsions were carried out with three types of viscometers. Figure 2 shows the flow curves of emulsions with different volume ratios of the two solutions, as measured with a Ferranti-Shirley cone-plate viscometer. The ratio between the viscosities of the two pure polymer solutions is about 3 at low shear rates but only 2 at the highest shear rates. 

The flow curves of the two polymers are very similar except for the different consistency degree and the time at which the thermal degradation starts (Figure 7). 

Fig. 12.24 Flow curves of LLDPE resins E and C, indicating the onset of sharkskin and gross melt fracture for each resin. T — 170°C, capillary D = 1 mm, L/D = 16, with entrance angle 2a = 180°. [Reprinted by permission from E. G. Muliawan, S. G. Hatzikiriakos, and M. Sentmanat, Melt Fracture of Linear Polyethylene, hit. Polym. Process., 20, 60 (2005).]...

In the vast literature on melt flow instabilities in capillary extrusion, the most misleading information is the report that the material of construction of the capillary die has no effect on the flow curve of linear polyethylene, or, in particular, on the instability region [32, 68] - see a quotation by Tordella cited in Sect. 3. Experiments using screw-threaded dies have further led people to believe that the slip (at the flow discontinuity transition) with linear polyethylene therefore appears not to result from adhesive breakdown at the polymer-die in-... 

Fig. 11-30. Apparent flow curves of differeni polymers with the same MFI (at the intersection point).

A more serious deficiency resides in reliance on MFI to characterize different polymers. No single rheological property can be expected to provide a complete prediction of the properties of a complex material like a thermoplastic polymer. Figure 11-27 shows log — log flow curves for polymers having the same melt index, at the intersection of the curves, but very differeni viscosities at higher shear stress where the materials are extruded or molded. This is the main reason why MFI is repeatedly condemned by purer practitioners of our profession. The parameter is locked into industrial practice, however, and is unlikely to be displaced. 

B 3. — Power law flow curves of dimethylsiloxane polymers. J. Appl. Phys. 30,... 

FIG. 5.18 Flow curves of various natural polymers. (Reproduced with permission from CP Kelco ApS, Copyright 2004, CP Kelco, San Diego, CA.)... 

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