Low-shear relative viscosity

FIGURE 12.19 Effect of a mixture of particles of different sizes on low shear relative viscosity, tjo/tJs = d for multimodal systems. Data for <)> in multimodal... 

Figure 9 displays the effect of NaCl concentration on the low-shear relative viscosity at polymer concentrations of 500, 1,000 and 2,000 ppm, respectively. At all polymer concentrations, the low-shear relative viscosity sharply decreased with increasing NaCl concentration up to 1 wt%. The rate of change of the low-shear... 

Figure 9. Effect of sodium chloride on the low-shear relative viscosity at various polymer concentrations.

Figures 9 and 10 show that both the low-shear relative viscosity and the power-law index approached limiting values with increasing NaCl concentration. These results indicate that there is a lower limit for the hydrodynamic radius for the polymer chain beyond which all the charges on the polymer chain are completely shielded with the cations. Increasing NaCl concentration further will not change the polymer chain configuration and, as a result, the relative viscosity of the polymer solution remains constant. Figures 9 and 10 also show that the limiting values for the relative viscosity and the power-law index are functions of polymer concentration.

Figures 11 and 12 display the influence of cation type and concentration on the low-shear relative viscosity and the power-law index at a polymer concentration of 1,000 ppm and a temperature of 20°C.

To examine the effect of alkalis on the viscosity of HPAM, the viscosity of polymer solutions was measured as a function of shear rate at various alkali concentrations. Viscosity measurements were repeated on the same solutions after two weeks (336 h) and four weeks (696 h) from initial mixing. Figure 13 depicts the variation of the low-shear relative viscosity with sodium hydroxide concentration at polymer concentration = 1,000 ppm and a temperature of 20°C. After approximately one hour from initial mixing, the low-shear relative viscosity decreased with sodium hydroxide concentration to a limiting value. This result is similar to the trend previously observed with sodium chloride and is due to the shielding effect of the sodium ion. The influence of sodium hydroxide on the low-shear viscosity measured two weeks (336 h) from initial mixing was more dramatic where higher viscosities were obtained at low alkali concentrations. Low-shear viscosity measurements after four weeks (696 h) were very similar to those obtained after two weeks. 

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... 

Figure 14. Variation of the low-shear relative viscosity with sodium hydroxide concentration at various sodium chloride concentrations.

Figure 28 displays the low-shear relative viscosity as a function of salt (sodium or calcium chloride) concentration. The low-shear relative viscosity dropped from... 

Figure 28. Effect of cation type on the low-shear relative viscosity of Flocon 4800 solutions having 2,000 ppm polymer.

The effect of sodium hydroxide concentration on xanthan flow curves also was examined at various polymer concentrations from 500 to 3,000 ppm. Figure 30 shows the low-shear relative viscosity as a function of sodium hydroxide concentration. Increasing sodium hydroxide concentration up to 10 wt% caused a dramatic drop in the low-shear relative viscosity (up to 90%). Most of this drop occurred during the addition of the first I wt% sodium hydroxide. Increasing sodium hydroxide further caused only a gradual decrease in the low-shear relative viscosity. This gradual drop was very noticeable at a polymer concentration of 3,000 ppm. 

Pannell (38) has studied a range of polystyrenes with comb-like branching, but with relatively long branches. He has correlated the low-shear melt viscosities with calculated values of , finding i/o°c(so)4 8, whereas the exponent for linear polymers is about 3.4. Fujimoto s results can be correlated in a similar way, but with a rather higher exponent, 5.1, though rather better correlations would be obtained if separate lines were used for each branching frequency. 

Figure 11. Relative low shear limit viscosity variation with volume fraction.

Figure 13 shows a typical plot of the steady shear relative viscosity versus the Peclet number for polystyrene spheres of various sizes suspended in various fluids. The success of the Peclet number scaling is well observed. One can also observe that the viscosity is higher when the shear rate is small, and at both high and low shear limits, the viscosity curve shows a plateau, corresponding to the high and low shear limit Newtonian behavior. The explanation for this behavior has been, in part, discussed earlier for the random packing limit of the particles. 

Cell models akin to those discussed in Section 8.5 have also been applied to the determination of the properties of concentrated suspensions (Happel Brenner 1983, van de Ven 1989). Although it is another method which has been used to obtaining approximate expressions for the high shear relative viscosity, we choose not to expand upon it here, instead referring the reader to the references cited. One of the difficulties is that the determination of the boundary conditions at the cell surface is somewhat arbitrary. Furthermore, expressions obtained by this approach indicate that the cell model is inappropriate for highly concentrated suspensions and is most satisfactory only at low to moderate concentrations. 

A most conspicuous and, as it turns out, a technologically most important property of the ordered phase is its relatively low viscosity. This characteristic is illustrated in Figure 4, which displays the low-shear rate viscosity against concentration of PPTA solutions in 100% sulfuric acid (13). Clearly, a sharp drop in viscosity is observed at the onset of the formation of the anisotropic phase. It is essential to point out that this maximum in the viscosity is sensitive to the applied shear rate, and, in fact, fully disappears at high shear rates. This observation can be construed as to indicate that at high shear rates the critical concentration for the onset of the formation of the anisotropic phase shifts to increasingly lower values (see also Figure 6). 

For a given polymer molecule, its motion may be divided into relatively fast motions of the segments which are smaller than Me and relatively slower motions of the whole chain, which is larger than Me. This interpretation may be expanded to include polymers having MW distribution. Considering the whole polymer there must be a relationship between the longest relaxation time (terminal relaxation time) and its MW. An example is the relationship between low shear Newtonian viscosity, rjg, and MW. With commercial gum rubbers, rjg is observed only with low MW polymer or a polymer whose MW distribution lacks the high MW tail. Nevertheless, rjg will be considered for a moment. 

Depending on the concentration, the solvent, and the shear rate of measurement, concentrated polymer solutions may give wide ranges of viscosity and appear to be Newtonian or non-Newtonian. This is illustrated in Eigure 10, where solutions of a styrene—butadiene—styrene block copolymer are Newtonian and viscous at low shear rates, but become shear thinning at high shear rates, dropping to relatively low viscosities beyond 10 (42). The... 

These two instmments form a relatively inexpensive package that allows the characterization of a large number of materials over a wide range of viscosities and shear rates. Brookfield has also developed a digital Stormer-type viscometer (ASTM D562), Model KU-1, which is an improvement over the old manual Stormer. This low shear (- 50 ) viscometer is commonly used to test house paints. 

This combination of long riser and relatively shallow hole probably favours a polymer with a high pseudoplastic index - high viscosity at the low shear rate in the slow-moving fluid in the riser - and rapid, clean breaking at the well bottom temperature. 

Figure H1.1.4 A complete flow curve for a time-independent non-Newtonian fluid. r 0 and i , are the viscosities associated with the first and second Newtonian plateaus, respectively. Regions (1) and (2) correspond to viscosities relative to low shear rates induced by sedimentation and leveling, respectively. Regions (3) and (4) correspond to viscosities relative to the medium shear rates induced by pouring and pumping, respectively. Regions (5) and (6) correspond to viscosities relative to high shear rates by rubbing and spraying, respectively.

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