Shear rate-dependent solution

Shear-Rate-Dependent Solution Viscosities of Polymers Crosslinked by Micelles. 

For polymer melts or solutions, Graessley [40-42] has shown that for a random coil molecule with a Gaussian segment distribution and a uniform number of segments per unit volume, a shear rate dependent viscosity arises. This effect is attributed to shear-induced entanglement scission. 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

Fig. 28a, b. Shear rate dependence of the primary and secondary normal stress diffemeces (oN1, alN2) a Magda et al. s experimental results [148] for a liquid crsytal solution of PBLG with M, = 23.5 x 10 (N = 0.54) at 25 °C b Larson s theoretical results [154]... 

Fig. 8.11. Dimensionless shear rate / 0 locating the onset of shear rate dependence for viscosity in narrow distribution polystyrene systems. Symbols are O for solutions at 30° C in n-butyl benzene (155), 9 f°r solutions at 25° C in arochlor (177), and 4 for undiluted polymers at 159° and 183° C (324). Values for the intrinsic viscosity (cM=0) lie in the range /i0 = 1-2, varying somewhat with solvent-polymer interaction and molecular weight...

Fig. 8.13. Dimensionless shear rate /30 locating the onset of shear rate dependence in the viscosity in narrow distribution systems of linear polymers vs cM/qM. Symbols for data on additional polymers are A for undiluted 1,4 polybutadiene (322), for undiluted poly(dimethyl siloxane) (323), and O for solutions of polyvinyl acetate in diethyl phthalate (195). The dotted lines indicate the ranges of for the intrinsic viscosity...

Graessley, W.W., Hazleton,R.L., Lindeman,L.R, The shear-rate dependence of viscosity in concentrated solutions of narrow-distribution polystyrene. Trans. Soc. Rheol. 11,267-285 (1967). 

Solution We do not have good data on 2. but we know that it is an order of magnitude smaller than 1, therefore, we shall assume the former to be negligible compared to the latter. The shear rate ranges from zero at the center to a maximum value at R, y R) = QR/H — 314.2s-1. Figure 3.26 shows experimental data on T] for LDPE. At 200°C we can calculate the following shear rate dependence... 

Kalashnikov VN (1994) Shear-rate dependent viscosity of dilute polymer solutions. J Rheol... 

Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., and Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydr. Polym. 1 5-21. 

The ratio Sq, which is defined to be equal to 1 /i /rj1, is equal to the elastic shear compliance /° for shear rates approaching zero. Both Th and 77 are shear rate dependent, but it is previously not clear whether it increases or decreases with increasing shear rate. In Fig. 16.20 both 77/r]0 and Sq //( are plotted vs. qi0 on double logarithmic scales for solutions and melts of poly (a-methyl styrene) as well (Sakai et al., 1972). First, it appears that the... 

Figure 3.15 The frequency-dependent in-phase and out-of-phase components of the dynamic viscosity, rj and rj in small-amplitude oscillatory shear, along with the shear-rate dependence of the first normal stress coefficient hi (y) for a 0.05 wt% solution of polystyrene of molecular weight 2.25 X 10 in a solvent of oligomeric styrene. The lines through the data show the predictions of the Zimm theory for r and 2r)"f(o and the Zimm theory for hi(y) modified to account for finite extensibility, as discussed in Section 3.6.2.2.I. The dashed lines are the contributions of the individual Zimm relaxation modes to 2rj"((o) /

As discussed in Section 12.3.3, unusual time- and shear-rate-dependencies have been reported for some wormy micellar solutions at dilute concentrations—for example, 1-5 mTAB/NaSal. At higher concentrations, 7-250 mM, of a similar surfactant, tetrade-cyltrimethyammonium bromide in NaSal, the extensional viscosity increases with in-creasing extension rate until a maximum is reached, and extension thinning then follows Thomme and Warr 1994). Prud homme and Warr interpret the maximum as the critical... 

Figure 13.28 Schematic plot showing the influence of concentration on the shear rate dependence of the viscosity of polymer solutions.

The average molecular weight, polydispersity, temperature, hydrostatic pressure, and shear rate dependences of polymer melt viscosity will be discussed in Chapter 13, resulting in a set of correlations which can be used to obtain a rough estimate of melt viscosity as a function of all of these variables. A new correlation will be presented for the molar viscosity-temperature function. The dependences of the zero-shear viscosity of concentrated polymer solutions on the average molecular weight and on the temperature will also be discussed. Finally, a new model that was developed to predict the shear viscosities of dispersions of particles in both polymeric fluids and ordinary molecular fluids will be presented. 

An example is shown in Figure 6.6, lower curve. At very low shear rate, the solution shows Newtonian behavior (no dependence of r] on shear rate), and this is also the case at very high shear rate, but in the intermediate range a marked strain rate thinning is observed. The viscosity is thus an apparent one (/ ,), depending on shear rate (or shear stress). It is common practice to give the (extrapolated) intrinsic viscosity at zero shear rate, hence the symbol [ri]0 in Eq. (6.6). The dependence of t] on shear rate may have two causes. 

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