Dependence of viscosity on shear rate

Of the viscometric functions, the viscosity is by far the easiest to measure and is thus the most often reported. As in the case of Newtonian fluids, the viscosity of a polymer depends on temperature and pressure, but for polymeric fluids it also depends on shear rate, and this dependency is quite sensitive to molecular structure. In particular, the curve of viscosity versus shear rate can be used to infer the molecular weight distribution of a linear polymer as is explained in Chapter 8. And in certain cases it can also tell us something about the level of long-chain branching. This curve is also of central importance in plastics processing, where it is directly related to the energy required to extrude a melt. 

Double logarithmic plot of viscosity as a function of shear rate for an LDPE. From top to bottom, the temperatures are 115,130,150,170 190,210 and 240 °C. These data were obtained using a specially modified rotational rheometer that made it possible to reach exceptionally low shear rates. From Meissner [63]. 

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Modify the dependence of viscosity on shear rate, producing low viscosity at high rates, and vice versa. 

The viscosity of a thermosetting resin undergoing a curing reaction is a function of time, temperature, and degree of cure. In case a resin presents a non-Newtonian behavior, a dependence of viscosity on shear rate needs to be accounted for as well [111]. 

Figure 8. Dependence of viscosity on shear rate at various pH s for 85 15 MMA-MAA batch latex (SPB-2-(3))...

Although attempts to measure and interpret nonlinear behavior are potentially useful, there are few reports in the literature on the measurement of the nonlinear viscoelastic properties of foods. This has been due to a lack of both suitable instrumentation and suitably developed theory nonlinear behavior, the predominant form of which is the exhibition of normal stresses, and a dependence of viscosity on shear rate, is much more complex than linear behavior (Gunasekaran and Ak, 2002). 

FIGURE 12.16 Shear thickening found by Hoffman [47] for 1.25 pm diameter polyvinyl chloride (PVC) latex particles in di-2-ethylhexyl phtiialate with the discontinuous dependence of viscosity on shear rate. Redrawn fi m Hofhnan [49]. 

Several models have been proposed to describe the dependence of viscosity on shear rate. One of the most used in engineering applications is the two-parameter Ostwald-De Waele model given by (45)... 

Flowability of plastics is largely determined by the dependence of viscosity on shear rate. Viscosity of water, for example, does not change with shear rate. When water moves through a capillary, fast or slow, its viscosity is same. In a forced oscillation rheometer, parallel plates immersed in water can move fast or slow, but the viscosity of water remains still the same. Therefore, a plot of viscosity against shear rate looks as a flat straight line, parallel to the horizontal axis (Fig. 17.1). 

If one needs to investigate the dependence of r] on shear rate, y, one must have access to a rheometer, an instrument that can characterize the dependence of viscosity on shear rate, thus enabling an extrapolation to the Newtonian limit. Typically, such measurements are conducted in Couette (concentric cylinder) or cone and plate geometry. In the Newtonian limit, for Couette geometry, when the inner cylinder is rotated, and provided that the gap between the inner and outer cylinder is small (i.e., RilRo < 0.99, where Ri and Ro are the radii of the inner and outer cylinders), the shear stress on the wall of the outer (resting) cylinder is... 

Capillary and slit-die rheometers are used to determine the dependency of viscosity on shear rate. Since most molten polymers exhibit non-Newtonian behavior, it is important to be able to characterize this behavior. Measurements are made using a piston-driven cylinder that drives the molten polymer through a die of precise dimensions. The pressure drop across the die is measured, as is the flow rate through the die. Temperature is precisely controlled throughout the measurement. This test yields precise viscosity measurements as a function of temperature and shear rate. However, measurements tend to have artifacts in them, which need to be corrected in order to obtain true viscosity using Bagley and Rabinowitsch corrections. Capillary rheometers are also used to determine the effects of slip, a phenomenon in which the velocity of the melt at the capillary wall is nonzero. Slip has important implications for highly filled materials. 

A property related to viscosity is the thixotropic index, a measure ofthe dependence of viscosity on shear-rate. The thixotropic index (TI) is the ratio of viscosities measured at speeds that have a ratio of 1 10 rpm, for example, at 2 rpm and 20 rpm. For non-Newtonian materials used in automated dispensing, shear thinning is apparent Ifom TI values of 2-6. In general, capillary-flow underfills have thixotropic indices of 1, or close to 1. 

For a small-scale laboratory type extruder L/D = 24/1 with barrel and die orifice radius 0.3 cm and 0.075 cm, respectively, the equation becomes t=272-S from which it is inferred that x can vary from t=136 sec Hor a slow operation speed of 30 rpm, to t=408 sec for a high screw speed of 90 rpm, with a profound effect on viscosity within the recommended processing temperatures [25]. Most polymers in the molten state exhibit pseudo-plastic behaviom, that is, viscosity decreases at higher shear rates. Ihe dependence of viscosity on shear rate can be expressed by a power equation [52] ... 

Figure 4.11 Dependence of viscosity on shear rate at different temperatures for the biological solution of sodium salt of hyaluronan at two biopolymer concentrations (2.7 and Wmg/ml)...

The effects of shear rate on the rheological behavior of feedstocks were extensively studied. Dependence of viscosity on shear rate can be expressed by the power law equation. 

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